11802
How Robust Are Probabilistic Models of Higher-Level Cognition?
"An increasingly popular theory holds that the mind should be viewed as a near-optimal or rational engine of probabilistic inference, in domains as diverse as word learning, pragmatics, naive physics, and predictions of the future. We argue that this view, often identified with Bayesian models of inference, is markedly less promising than widely believed, and is undermined by post hoc practices that merit wholesale reevaluation. We also show that the common equation between probabilistic and rational or optimal is not justified."
to:NB  have_read  psychology  cognitive_science  bayesianism  marcus.gary_f. 
7 hours ago
What can individual differences tell us about the specialization of function?
"Can the study of individual differences inform debates about modularity and the specialization of function? In this article, we consider the implications of a highly replicated, robust finding known as positive manifold: Individual differences in different cognitive domains tend to be positively inter- correlated. Prima facie, this fact, which has generally been interpreted as reflecting the influence of a domain-general cognitive factor, might be seen as posing a serious challenge to a strong view of modularity. Drawing on a mixture of meta-analysis and computer simulation, we show that positive manifold derives instead largely from between-task neural overlap, suggesting a potential way of reconciling individual differences with some form of modularity."

--- Journal version: http://dx.doi.org/10.1080/02643294.2011.609813
--- The model simulated from is, I think, just another version of Thompson's ability sampling model.
to:NB  have_read  iq  factor_analysis  marcus.gary_f.  neuropsychology  re:g_paper 
7 hours ago
Data Science at the Command Line - O'Reilly Media
"This hands-on guide demonstrates how the flexibility of the command line can help you become a more efficient and productive data scientist. You’ll learn how to combine small, yet powerful, command-line tools to quickly obtain, scrub, explore, and model your data."
books:noted  unix  to_teach:statcomp 
14 hours ago
Over at Project Syndicate: Making Do with More (Brad DeLong's Grasping Reality...)
Brad channeling Keynes, and indeed _The German Ideology_. But notice: he's talking about how prosperity is moving us into areas where we know markets generically fail badly, and are very artificial creatures of state power at best...
economics  market_failures_in_everything  delong.brad 
yesterday
Overdispersion Diagnostics for Generalized Linear Models on JSTOR
"Generalized linear models (GLM's) are simple, convenient models for count data, but they assume that the variance is a specified function of the mean. Although overdispersed GLM's allow more flexible mean-variance relationships, they are often not as simple to interpret nor as easy to fit as standard GLM's. This article introduces a convexity plot, or C plot for short, that detects overdispersion and relative variance curves and relative variance tests that help to understand the nature of the overdispersion. Convexity plots sometimes detect overdispersion better than score tests, and relative variance curves and tests sometimes distinguish the source of the overdispersion better than score tests."
to:NB  have_read  statistics  regression  model_checking  kith_and_kin  roeder.kathryn  to_teach:undergrad-ADA 
2 days ago
Delay Differential Embedding of Time Series
"Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time compared with frequency-based methods such as the DFT and cross-spectral analysis."
to:NB  time_series  dynamical_systems  geometry_from_a_time_series 
3 days ago
Why I Just Asked My Students To Put Their Laptops Away… — Medium
I think Clay actually misses a trick here. A computer is a really useful note-taking device, and writing notes helps you remember (even if you don't consult the notes). What is really needed, for instructional purposes, is a switch we can throw which jams all wifi signals. (I actually tried to get the computing lab to block Internet access during my class hour, but they said it was technically infeasible.)
teaching  pedagogy  education  attention  networked_life  shirky.clay 
4 days ago
Chernozhukov , Chetverikov , Kato : Gaussian approximation of suprema of empirical processes
"This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm. We prove an abstract approximation theorem applicable to a wide variety of statistical problems, such as construction of uniform confidence bands for functions. Notably, the bound in the main approximation theorem is nonasymptotic and the theorem allows for functions that index the empirical process to be unbounded and have entropy divergent with the sample size. The proof of the approximation theorem builds on a new coupling inequality for maxima of sums of random vectors, the proof of which depends on an effective use of Stein’s method for normal approximation, and some new empirical process techniques. We study applications of this approximation theorem to local and series empirical processes arising in nonparametric estimation via kernel and series methods, where the classes of functions change with the sample size and are non-Donsker. Importantly, our new technique is able to prove the Gaussian approximation for the supremum type statistics under weak regularity conditions, especially concerning the bandwidth and the number of series functions, in those examples."
to:NB  empirical_processes  to_read 
5 days ago
Evans , Richardson : Markovian acyclic directed mixed graphs for discrete data
"Acyclic directed mixed graphs (ADMGs) are graphs that contain directed (→) and bidirected (↔) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the conditional independence structure induced by a DAG model containing hidden variables on its observed margin. The Markovian model associated with an ADMG is simply the set of distributions obeying the global Markov property, given via a simple path criterion (m-separation). We first present a factorization criterion characterizing the Markovian model that generalizes the well-known recursive factorization for DAGs. For the case of finite discrete random variables, we also provide a parameterization of the model in terms of simple conditional probabilities, and characterize its variation dependence. We show that the induced models are smooth. Consequently, Markovian ADMG models for discrete variables are curved exponential families of distributions."
to:NB  graphical_models  probability  richardson.thomas  exponential_families 
5 days ago
Feng , He : Statistical inference based on robust low-rank data matrix approximation
"The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634–1654] developed tests on dimensionality of the mean structure of a data matrix based on the singular value decomposition. However, the first singular values and vectors can be driven by a small number of outlying measurements. In this paper, we consider a robust alternative that moderates the effect of outliers in low-rank approximations. Under the assumption of random row effects, we provide the asymptotic representations of the robust low-rank approximation. These representations may be used in testing the adequacy of a low-rank approximation. We use oligonucleotide gene microarray data to demonstrate how robust singular value decomposition compares with the its traditional counterparts. Examples show that the robust methods often lead to a more meaningful assessment of the dimensionality of gene intensity data matrices."
to:NB  dimension_reduction  low-rank_approximation  statistics  re:g_paper 
5 days ago
What Do Data on Millions of U.S. Workers Reveal about Life-Cycle Earnings Risk?
"We study the evolution of individual labor earnings over the life cycle, using a large panel data set of earnings histories drawn from U.S. administrative records. Using fully nonparametric methods, our analysis reaches two broad conclusions. First, earnings shocks display substantial deviations from lognormality—the standard assumption in the literature on incomplete markets. In particular, earnings shocks display strong negative skewness and extremely high kurtosis—as high as 30 compared with 3 for a Gaussian distribution. The high kurtosis implies that, in a given year, most individuals experience very small earnings shocks, and a small but non-negligible number experience very large shocks. Second, these statistical properties vary significantly both over the life cycle and with the earnings level of individuals. We also estimate impulse response functions of earnings shocks and find important asymmetries: Positive shocks to high-income individuals are quite transitory, whereas negative shocks are very persistent; the opposite is true for low-income individuals. Finally, we use these rich sets of moments to estimate econometric processes with increasing generality to capture these salient features of earnings dynamics."

--- Last tag conditional on what exactly is in the "data appendix" at https://fguvenendotcom.files.wordpress.com/2014/04/moments_for_publication.xls
to:NB  to_read  economics  inequality  heavy_tails  to_teach:undergrad-ADA  statistics  great_risk_shift 
9 days ago
Make - GNU Project - Free Software Foundation
My book needs a make file. Which means I need to figure out how to really write one, with the source files spread across a gazillion sub-directories...
programming  re:ADAfaEPoV 
10 days ago
Philip Kitcher: The Lure of the Peak | The New Republic
I must say this (politely) makes Parfit's book sound exquisitely boring and pointless.
book_reviews  ethics  philosophy_of_science  kitcher.philip 
10 days ago
Why does financial sector growth crowd out real economic growth?
"In this paper we examine the negative relationship between the rate of growth of the financial sector and the rate of growth of total factor productivity. We begin by showing that by disproportionately benefiting high collateral/low productivity projects, an exogenous increase in finance reduces total factor productivity growth. Then, in a model with skilled workers and endogenous financial sector growth, we establish the possibility of multiple equilibria. In the equilibrium where skilled labour works in finance, the financial sector grows more quickly at the expense of the real economy. We go on to show that consistent with this theory, financial growth disproportionately harms financially dependent and R&D-intensive industries."
to:NB  to_read  economics  financialization  productivity  via:jbdelong 
10 days ago
My email is a monster - The Oatmeal
Why I have not written an adequate reply to your gracious note. (And yet I much prefer e-mail to just about every other online or printed medium; I have Issues.)
email  networked_life  moral_psychology  cartoons  funny:because_its_true 
10 days ago
On the Interpretation of Instrumental Variables in the Presence of Specification Errors
"The method of instrumental variables (IV) and the generalized method of moments (GMM), and their applications to the estimation of errors-in-variables and simultaneous equations models in econometrics, require data on a sufficient number of instrumental variables that are both exogenous and relevant. We argue that, in general, such instruments (weak or strong) cannot exist."

--- I think they are too quick to dismiss non-parametric IV; if what one wants is consistent estimates of the partial derivatives at a given point, you _can_ get that by (e.g.) splines or locally linear regression. Need to think through this in terms of Pearl's graphical definition of IVs.
to:NB  have_read  instrumental_variables  misspecification  regression  linear_regression  causal_inference  statistics  econometrics  via:jbdelong  to_teach:undergrad-ADA  re:ADAfaEPoV 
10 days ago
The Promises and Pitfalls of Genoeconomics
"This article reviews existing research at the intersection of genetics and economics, presents some new findings that illustrate the state of genoeconomics research, and surveys the prospects of this emerging field. Twin studies suggest that economic outcomes and preferences, once corrected for measurement error, appear to be about as heritable as many medical conditions and personality traits. Consistent with this pattern, we present new evidence on the heritability of permanent income and wealth. Turning to genetic association studies, we survey the main ways that the direct measurement of genetic variation across individuals is likely to contribute to economics, and we outline the challenges that have slowed progress in making these contributions. The most urgent problem facing researchers in this field is that most existing efforts to find associations between genetic variation and economic behavior are based on samples that are too small to ensure adequate statistical power. This has led to many false positives in the literature. We suggest a number of possible strategies to improve and remedy this problem: (a) pooling data sets, (b) using statistical techniques that exploit the greater information content of many genes considered jointly, and (c) focusing on economically relevant traits that are most proximate to known biological mechanisms."

--- Not bad, of its kind, but notice that when they get impossible-according-to-the-model results (like negative environmental variance components, or non-identical twins being more similar on some traits than identical twins), the response is always an ad-hoc modification or data exclusion, rather than re-thinking the model. Also, I really think they need to give more attention to population structure than they do, because we _know_ PCA doesn't control it away (http://dx.doi.org/10.1016/j.ajhg.2011.05.025). Full points for honesty, however, in their examples of sheer failure to replicate.
to:NB  have_read  genomics  human_genetics  economics  statistics 
11 days ago
Characterizing Autopoiesis in the Game of Life
"Maturana and Varela's concept of autopoiesis defines the essential organization of living systems and serves as a foundation for their biology of cognition and the enactive approach to cognitive science. As an initial step toward a more formal analysis of autopoiesis, this article investigates its application to the compact, recurrent spatiotemporal patterns that arise in Conway's Game-of-Life cellular automaton. In particular, we demonstrate how such entities can be formulated as self-constructing networks of interdependent processes that maintain their own boundaries. We then characterize the specific organizations of several such entities, suggest a way to simplify the descriptions of these organizations, and briefly consider the transformation of such organizations over time."
to:NB  self-organization  cellular_automata  emergence  artificial_life  beer.randall 
12 days ago
Korostelev : A minimaxity criterion in nonparametric regression based on large-deviations probabilities
"A large-deviations criterion is proposed for optimality of nonparametric regression estimators. The criterion is one of minimaxity of the large-deviations probabilities. We study the case where the underlying class of regression functions is either Lipschitz or Hölder, and when the loss function involves estimation at a point or in supremum norm. Exact minimax asymptotics are found in the Gaussian case."
to:NB  large_deviations  regression  nonparametrics  statistics  have_read 
12 days ago
Fu : Large Sample Point Estimation: A Large Deviation Theory Approach
"In this paper the exponential rates of decrease and bounds on tail probabilities for consistent estimators are studied using large deviation methods. The asymptotic expansions of Bahadur bounds and exponential rates in the case of the maximum likelihood estimator are obtained. Based on these results we have obtained a result parallel to the Fisher-Rao-Efron result concerning second-order efficiency (see Efron, 1975). Our results also substantiate the geometric observation given by Efron (1975) that if the statistical curvature of the underlying distribution is small, then the maximum likelihood estimator is nearly optimal.'
to:NB  large_deviations  statistics  estimation  have_read 
12 days ago
Symmetry and Collective Fluctuations in Evolutionary Games - Books - IOPscience
"In this monograph we bring together a conceptual treatment of evolutionary dynamics and a path-ensemble approach to non-equilibrium stochastic processes. Our framework is evolutionary game theory, in which the map from individual types and their interactions to the fitness that determines their evolutionary success is modeled as a game played among agents in the population. Our approach, however, is not anchored either in analogy to play or in motivations to interpret particular interactions as games. Rather, we argue that games are a flexible and reasonably generic framework to capture, classify and analyze the processes in development and some forms of inter-agent interaction that lie behind arbitrary frequency-dependent fitness models."
to:NB  books:noted  evolutionary_game_theory  stochastic_processes  large_deviations  smith.eric  kith_and_kin  re:do-institutions-evolve 
13 days ago
Finance vs. Wal-Mart: Why are Financial Services so Expensive?
"Despite its fast computers and credit derivatives, the current financial system does not seem better at transferring funds from savers to borrowers than the financial system of 1910."

--- I really wish papers like this would give more details about their calculations, and not use graphs which are so freaking painful to the eye.

--- ETA: Also, he never does get around to answering the question in his subtitle!
to:NB  finance  financialization  economics  whats_gone_wrong_with_america  via:jbdelong  have_read 
14 days ago
Federal Reserve Bank San Francisco | The Recent Rise and Fall of Rapid Productivity Growth |
"Information technology fueled a surge in U.S. productivity growth in the late 1990s and early 2000s. However, this rapid pace proved to be temporary, as productivity growth slowed before the Great Recession. Furthermore, looking through the effects of the economic downturn on productivity, the reduced pace of productivity gains has continued and suggests that average future output growth will likely be relatively slow."

--- But mightn't these also be sectors where measuring value-added is particularly difficult? (Especially when a lot of the valuable product is supposed to be given away.)
to:NB  have_read  economics  productivity  innovation  via:jbdelong 
14 days ago
Wickham, C.: Sleepwalking into a New World: The Emergence of Italian City Communes in the Twelfth Century. (eBook and Hardcover)
"Amid the disintegration of the Kingdom of Italy in the eleventh and twelfth centuries, a new form of collective government—the commune—arose in the cities of northern and central Italy. Sleepwalking into a New World takes a bold new look at how these autonomous city-states came about, and fundamentally alters our understanding of one of the most important political and cultural innovations of the medieval world.
"Chris Wickham provides richly textured portraits of three cities—Milan, Pisa, and Rome—and sets them against a vibrant backcloth of other towns. He argues that, in all but a few cases, the elites of these cities and towns developed one of the first nonmonarchical forms of government in medieval Europe, unaware that they were creating something altogether new. Wickham makes clear that the Italian city commune was by no means a democracy in the modern sense, but that it was so novel that outsiders did not know what to make of it. He describes how, as the old order unraveled, the communes emerged, governed by consular elites “chosen by the people,” and subject to neither emperor nor king. They regularly fought each other, yet they grew organized and confident enough to ally together to defeat Frederick Barbarossa, the German emperor, at the Battle of Legnano in 1176."
to:NB  italy  medieval_european_history  political_science  cities 
14 days ago
Chernozhukov , Chetverikov , Kato : Anti-concentration and honest, adaptive confidence bands
"Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the classical Smirnov–Bickel–Rosenblatt (SBR) condition; see, for example, Giné and Nickl [Probab. Theory Related Fields 143 (2009) 569–596]. This condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process (equivalently, for the supremum of a Gaussian process with the same covariance function as that of the studentized empirical process). The principal contribution of this paper is to remove the need for this classical condition. We show that a considerably weaker sufficient condition is derived from an anti-concentration property of the supremum of the approximating Gaussian process, and we derive an inequality leading to such a property for separable Gaussian processes. We refer to the new condition as a generalized SBR condition. Our new result shows that the supremum does not concentrate too fast around any value.
"We then apply this result to derive a Gaussian multiplier bootstrap procedure for constructing honest confidence bands for nonparametric density estimators (this result can be applied in other nonparametric problems as well). An essential advantage of our approach is that it applies generically even in those cases where the limit distribution of the supremum of the studentized empirical process does not exist (or is unknown). This is of particular importance in problems where resolution levels or other tuning parameters have been chosen in a data-driven fashion, which is needed for adaptive constructions of the confidence bands. Finally, of independent interest is our introduction of a new, practical version of Lepski’s method, which computes the optimal, nonconservative resolution levels via a Gaussian multiplier bootstrap method."

--- Ungated version: http://arxiv.org/abs/1303.7152
in_NB  confidence_sets  bootstrap  density_estimation  nonparametrics  statistics  regression  to_read  re:ADAfaEPoV 
14 days ago
Silverman : Spline Smoothing: The Equivalent Variable Kernel Method
"The spline smoothing approach to nonparametric regression and curve estimation is considered. It is shown that, in a certain sense, spline smoothing corresponds approximately to smoothing by a kernel method with bandwidth depending on the local density of design points. Some exact calculations demonstrate that the approximation is extremely close in practice. Consideration of kernel smoothing methods demonstrates that the way in which the effective local bandwidth behaves in spline smoothing has desirable properties. Finally, the main result of the paper is applied to the related topic of penalized maximum likelihood probability density estimates; a heuristic discussion shows that these estimates should adapt well in the tails of the distribution."
to:NB  have_read  splines  kernel_estimators  nonparametrics  regression  density_estimation  statistics  silverman.b.w. 
14 days ago
Levine, A.: American Insecurity: Why Our Economic Fears Lead to Political Inaction. (eBook and Hardcover)
"Americans today face no shortage of threats to their financial well-being, such as job and retirement insecurity, health care costs, and spiraling college tuition. While one might expect that these concerns would motivate people to become more politically engaged on the issues, this often doesn’t happen, and the resulting inaction carries consequences for political debates and public policy. Moving beyond previously studied barriers to political organization, American Insecurity sheds light on the public’s inaction over economic insecurities by showing that the rhetoric surrounding these issues is actually self-undermining. By their nature, the very arguments intended to mobilize individuals—asking them to devote money or time to politics—remind citizens of their economic fears and personal constraints, leading to undermobilization and nonparticipation.
"Adam Seth Levine explains why the set of people who become politically active on financial insecurity issues is therefore quite narrow. When money is needed, only those who care about the issues but are not personally affected become involved. When time is needed, participation is limited to those not personally affected or those who are personally affected but outside of the labor force with time to spare. The latter explains why it is relatively easy to mobilize retirees on topics that reflect personal financial concerns, such as Social Security and Medicare. In general, however, when political representation requires a large group to make their case, economic insecurity threats are uniquely disadvantaged."

--- If only we could conceive of institutions that would organize ordinary people for political action around economic concerns! (I.e., I wonder what his results would've looked like back when we had a labor movement.)
to:NB  books:noted  inequality  great_risk_shift  political_science  us_politics  whats_gone_wrong_with_america 
15 days ago
Le Grand, J. and New, B.: Government Paternalism: Nanny State or Helpful Friend?. (eBook and Hardcover)
"Should governments save people from themselves? Do governments have the right to influence citizens’ behavior related to smoking tobacco, eating too much, not saving enough, drinking alcohol, or taking marijuana—or does this create a nanny state, leading to infantilization, demotivation, and breaches in individual autonomy? Looking at examples from both sides of the Atlantic and around the world, Government Paternalism examines the justifications for, and the prevalence of, government involvement and considers when intervention might or might not be acceptable. Building on developments in philosophy, behavioral economics, and psychology, Julian Le Grand and Bill New explore the roles, boundaries, and responsibilities of the government and its citizens.
"Le Grand and New investigate specific policy areas, including smoking, saving for pensions, and assisted suicide. They discuss legal restrictions on risky behavior, taxation of harmful activities, and subsidies for beneficial activities. And they pay particular attention to “nudge” or libertarian paternalist proposals that try to change the context in which individuals make decisions so that they make the right ones. Le Grand and New argue that individuals often display “reasoning failure”: an inability to achieve the ends that they set themselves. Such instances are ideal for paternalistic interventions—for though such interventions might impinge on autonomy, the impact can be outweighed by an improvement in well-being."

--- Unfairly, the affiliations and the endorsements make me more skeptical.
to:NB  books:noted  political_philosophy  re:anti-nudge 
15 days ago
[1502.02398] Towards a Learning Theory of Causation
"We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(Si,li)}ni=1, where each Si is a sample drawn from the probability distribution of Xi×Yi, and li is a binary label indicating whether "Xi→Yi" or "Xi←Yi". Given these data, we build a causal inference rule in two steps. First, we featurize each Si using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables."

--- Finally, I am sympathetic to complaints about ML-ish methods giving us no understanding even when they work predictively.
to:NB  to_read  causal_inference  hilbert_space  statistics  via:vaguery 
15 days ago
Uniform random generation of large acyclic digraphs - Springer
"Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs."
to:NB  graphical_models  monte_carlo  graph_sampling 
17 days ago
On parallel implementation of sequential Monte Carlo methods: the island particle model - Springer
"The approximation of the Feynman-Kac semigroups by systems of interacting particles is a very active research field, with applications in many different areas. In this paper, we study the parallelization of such approximations. The total population of particles is divided into sub-populations, referred to as islands. The particles within each island follow the usual selection/mutation dynamics. We show that the evolution of each island is also driven by a Feynman-Kac semigroup, whose transition and potential can be explicitly related to ones of the original problem. Therefore, the same genetic type approximation of the Feynman-Kac semi-group may be used at the island level; each island might undergo selection/mutation algorithm. We investigate the impact of the population size within each island and the number of islands, and study different type of interactions. We find conditions under which introducing interactions between islands is beneficial. The theoretical results are supported by some Monte Carlo experiments."
to:NB  particle_filters  monte_carlo  computational_statistics  stochastic_processes  interacting_particle_systems  re:amplification_sampling 
17 days ago
Critique of The History Manifesto | Deborah Cohen
If the claims made (with quotations) about what's said in the book are accurate, and so are Figures 1--3, then it's really incredibly damning.
book_reviews  evisceration  historiography  have_read 
21 days ago
Benjamin, A. and Chartrand, G., Zhang, P.: The Fascinating World of Graph Theory (eBook and Hardcover).
"The fascinating world of graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. For example, what is the shortest route for a traveling salesman seeking to visit a number of cities in one trip? What is the least number of colors needed to fill in any map so that neighboring regions are always colored differently? Requiring readers to have a math background only up to high school algebra, this book explores the questions and puzzles that have been studied, and often solved, through graph theory. In doing so, the book looks at graph theory’s development and the vibrant individuals responsible for the field’s growth.
"Introducing graph theory’s fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, the Minimum Spanning Tree Problem, the Königsberg Bridge Problem, the Chinese Postman Problem, a Knight’s Tour, and the Road Coloring Problem. They present every type of graph imaginable, such as bipartite graphs, Eulerian graphs, the Petersen graph, and trees. Each chapter contains math exercises and problems for readers to savor."

--- For a freshman seminar?
to:NB  books:noted  mathematics  graph_theory 
22 days ago
Harris, M.: Mathematics without Apologies: Portrait of a Problematic Vocation. (eBook and Hardcover)
"What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources.
"Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party?
"Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond."

--- From looking at the online teaser material, I'll say that its heart is in the right place, but the authorial voice makes me recoil.
books:noted  mathematics  popular_science 
22 days ago
AEAweb: JEP (29,1) p. 67 - Putting Distribution Back at the Center of Economics: Reflections on Capital in the Twenty-First Century
"When a lengthy book is widely discussed in academic circles and the popular media, it is probably inevitable that the arguments of the book will be simplified in the telling and retelling. In the case of my book Capital in the Twenty-First Century (2014), a common simplification of the main theme is that because the rate of return on capital r exceeds the growth rate of the economy g, the inequality of wealth is destined to increase indefinitely over time. In my view, the magnitude of the gap between r and g is indeed one of the important forces that can explain historical magnitudes and variations in wealth inequality. However, I do not view r > g as the only or even the primary tool for considering changes in income and wealth in the 20th century, or for forecasting the path of income and wealth inequality in the 21st century. In this essay, I will take up several themes from my book that have perhaps become attenuated or garbled in the ongoing discussions of the book, and will seek to re-explain and re-frame these themes. First, I stress the key role played in my book by the interaction between beliefs systems, institutions, and the dynamics of inequality. Second, I briefly describe my multidimensional approach to the history of capital and inequality. Third, I review the relationship and differing causes between wealth inequality and income inequality. Fourth, I turn to the specific role of r > g in the dynamics of wealth inequality: specifically, a larger r - g gap will amplify the steady-state inequality of a wealth distribution that arises out of a given mixture of shocks. Fifth, I consider some of the scenarios that affect how r - g might evolve in the 21st century, including rising international tax competition, a growth slowdown, and differential access by the wealthy to higher returns on capital. Finally, I seek to clarify what is distinctive in my historical and political economy approach to institutions and inequality dynamics, and the complementarity with other approaches."

--- A reply to critics, including being very polite to the utterly bizarre critique of Acemoglou and Robinson.
piketty.thomas  economics  inequality  have_read 
22 days ago
Corbeill, A.: Sexing the World: Grammatical Gender and Biological Sex in Ancient Rome. (eBook and Hardcover)
"From the moment a child in ancient Rome began to speak Latin, the surrounding world became populated with objects possessing grammatical gender—masculine eyes (oculi), feminine trees (arbores), neuter bodies (corpora). Sexing the World surveys the many ways in which grammatical gender enabled Latin speakers to organize aspects of their society into sexual categories, and how this identification of grammatical gender with biological sex affected Roman perceptions of Latin poetry, divine power, and the human hermaphrodite.
"Beginning with the ancient grammarians, Anthony Corbeill examines how these scholars used the gender of nouns to identify the sex of the object being signified, regardless of whether that object was animate or inanimate. This informed the Roman poets who, for a time, changed at whim the grammatical gender for words as seemingly lifeless as “dust” (pulvis) or “tree bark” (cortex). Corbeill then applies the idea of fluid grammatical gender to the basic tenets of Roman religion and state politics. He looks at how the ancients tended to construct Rome’s earliest divinities as related male and female pairs, a tendency that waned in later periods. An analogous change characterized the dual-sexed hermaphrodite, whose sacred and political significance declined as the republican government became an autocracy. Throughout, Corbeill shows that the fluid boundaries of sex and gender became increasingly fixed into opposing and exclusive categories."
to:NB  books:noted  linguistics  ancient_history  latin  history_of_ideas  sex_vs_gender 
22 days ago
The Limits of Matter: Chemistry, Mining, and Enlightenment, Fors
"During the seventeenth and eighteenth centuries, Europeans raised a number of questions about the nature of reality and found their answers to be different from those that had satisfied their forebears. They discounted tales of witches, trolls, magic, and miraculous transformations and instead began looking elsewhere to explain the world around them. In The Limits of Matter, Hjalmar Fors investigates how conceptions of matter changed during the Enlightenment and pins this important change in European culture to the formation of the modern discipline of chemistry."
to:NB  books:noted  chemistry  history_of_science  enlightenment  early_modern_european_history 
23 days ago
Loving Literature: A Cultural History, Lynch
"Of the many charges laid against contemporary literary scholars, one of the most common—and perhaps the most wounding—is that they simply don't love books. And while the most obvious response is that, no, actually the profession of literary studies does acknowledge and address personal attachments to literature, that answer risks obscuring a more fundamental question: Why should they?
"That question led Deidre Shauna Lynch into the historical and cultural investigation of Loving Literature. How did it come to be that professional literary scholars are expected not just to study, but to love literature, and to inculcate that love in generations of students?"
to:NB  books:noted  academia  literary_criticism  literary_history  criticism_of_criticism_of_criticism  history_of_ideas  history_of_tastes 
23 days ago
What Eudoxus and Aristotle Thought
_Not_ the Ptolemaic system, because all the spheres have the same center. Still pretty funky by the time you get to some of the planets.
history_of_science  astronomy 
25 days ago
[1501.00960] Characterizing the Google Books corpus: Strong limits to inferences of socio-cultural and linguistic evolution
"It is tempting to treat frequency trends from Google Books data sets as indicators for the true popularity of various words and phrases. Doing so allows us to draw novel conclusions about the evolution of public perception of a given topic, such as time and gender. However, sampling published works by availability and ease of digitization leads to several important effects. One of these is the surprising ability of a single prolific author to noticeably insert new phrases into a language. A greater effect arises from scientific texts, which have become increasingly prolific in the last several decades and are heavily sampled in the corpus. The result is a surge of phrases typical to academic articles but less common in general, such as references to time in the form of citations. Here, we highlight these dynamics by examining and comparing major contributions to the statistical divergence of English data sets between decades in the period 1800--2000. We find that only the English Fiction data set from the second version of the corpus is not heavily affected by professional texts, in clear contrast to the first version of the fiction data set and both unfiltered English data sets. Our findings emphasize the need to fully characterize the dynamics of the Google Books corpus before using these data sets to draw broad conclusions about cultural and linguistic evolution."
to:NB  selection_bias  linguistics  history_of_ideas 
26 days ago
[1501.01571] An Introduction to Matrix Concentration Inequalities
"In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix concentration inequalities, research has advanced to the point where we can conquer many (formerly) challenging problems with a page or two of arithmetic. The aim of this monograph is to describe the most successful methods from this area along with some interesting examples that these techniques can illuminate."
in_NB  probability  random_matrices  concentration_of_measure  deviation_inequalities 
26 days ago
[1501.06794] Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations
"We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations which can be applied to points drawn from the respective distributions. We refer to our approach as {\em kernel probabilistic programming}. We illustrate it on synthetic data, and show how it can be used for nonparametric structural equation models, with an application to causal inference."
to:NB  kernel_methods  hilbert_space  computational_statistics  causal_inference  statistics 
26 days ago
[1501.02663] Extremes on river networks
"Max-stable processes are the natural extension of the classical extreme-value distributions to the functional setting, and they are increasingly widely used to estimate probabilities of complex extreme events. In this paper we broaden them from the usual setting in which dependence varies according to functions of Euclidean distance to the situation in which extreme river discharges at two locations on a river network may be dependent because the locations are flow-connected or because of common meteorological events. In the former case dependence depends on river distance, and in the second it depends on the hydrological distance between the locations, either of which may be very different from their Euclidean distance. Inference for the model parameters is performed using a multivariate threshold likelihood, which is shown by simulation to work well. The ideas are illustrated with data from the upper Danube basin."
to:NB  spatio-temporal_statistics  extreme_values  statistics  rivers 
26 days ago
[1404.1578] Models as Approximations: How Random Predictors and Model Violations Invalidate Classical Inference in Regression
"We review and interpret the early insights of Halbert White who over thirty years ago inaugurated a form of statistical inference for regression models that is asymptotically correct even under "model misspecification," that is, under the assumption that models are approximations rather than generative truths. This form of inference, which is pervasive in econometrics, relies on the "sandwich estimator" of standard error. Whereas linear models theory in statistics assumes models to be true and predictors to be fixed, White's theory permits models to be approximate and predictors to be random. Careful reading of his work shows that the deepest consequences for statistical inference arise from a synergy --- a "conspiracy" --- of nonlinearity and randomness of the predictors which invalidates the ancillarity argument that justifies conditioning on the predictors when they are random. Unlike the standard error of linear models theory, the sandwich estimator provides asymptotically correct inference in the presence of both nonlinearity and heteroskedasticity. An asymptotic comparison of the two types of standard error shows that discrepancies between them can be of arbitrary magnitude. If there exist discrepancies, standard errors from linear models theory are usually too liberal even though occasionally they can be too conservative as well. A valid alternative to the sandwich estimator is provided by the "pairs bootstrap"; in fact, the sandwich estimator can be shown to be a limiting case of the pairs bootstrap. We conclude by giving meaning to regression slopes when the linear model is an approximation rather than a truth. --- In this review we limit ourselves to linear least squares regression, but many qualitative insights hold for most forms of regression."

-- Very close to what I teach in my class, though I haven't really talked about sandwich variances.
to:NB  have_read  statistics  regression  linear_regression  bootstrap  misspecification  estimation  approximation 
26 days ago
The Sharing Economy Isn’t About Sharing at All - HBR
Well, yes, obviously. (I have used Zipcar regularly for years, but it would never have occurred to me that it was some form of _sharing_; it's a car _rental_ company which is a lot more convenient for me than the older ones.) Something like Uber or Airbnb makes its money by being the centralized intermediary between consumers and asset owners/service workers. (The goal would be to become the only effective marketplace for that sort of good or service --- would that be the monagorist? --- and so collect rents.) I guess I'd supposed/hoped that people actually in the industry realized this, and the "sharing" rhetoric was conscious camouflage, but this article makes it sound like they believe their own press.
corporations  networked_life  marketing  market_making  economics  have_read  via:wh 
27 days ago
The cultural evolution of mind reading
"It is not just a manner of speaking: “Mind reading,” or working out what others are thinking and feeling, is markedly similar to print reading. Both of these distinctly human skills recover meaning from signs, depend on dedicated cortical areas, are subject to genetically heritable disorders, show cultural variation around a universal core, and regulate how people behave. But when it comes to development, the evidence is conflicting. Some studies show that, like learning to read print, learning to read minds is a long, hard process that depends on tuition. Others indicate that even very young, nonliterate infants are already capable of mind reading. Here, we propose a resolution to this conflict. We suggest that infants are equipped with neurocognitive mechanisms that yield accurate expectations about behavior (“automatic” or “implicit” mind reading), whereas “explicit” mind reading, like literacy, is a culturally inherited skill; it is passed from one generation to the next by verbal instruction."

--- ETA after reading: interesting and not crazy, though not completely convincing; I'd need to think carefully, and look at their references, to decide how much of this is about mind-reading, the activity, vs. talking about mind-reading. (It's also interesting to imagine the psychological theories we might have if literacy were a cultural universal, which it could well be in a century or two.)
to:NB  have_read  cognitive_science  cognitive_development  cultural_transmission_of_cognitive_tools  theory_of_mind 
28 days ago
[1411.6179] Spatiotemporal Detection of Unusual Human Population Behavior Using Mobile Phone Data
"With the aim to contribute to humanitarian response to disasters and violent events, scientists have proposed the development of analytical tools that could identify emergency events in real-time, using mobile phone data. The assumption is that dramatic and discrete changes in behavior, measured with mobile phone data, will indicate extreme events. In this study, we propose an efficient system for spatiotemporal detection of behavioral anomalies from mobile phone data and compare sites with behavioral anomalies to an extensive database of emergency and non-emergency events in Rwanda. Our methodology successfully captures anomalous behavioral patterns associated with a broad range of events, from religious and official holidays to earthquakes, floods, violence against civilians and protests. Our results suggest that human behavioral responses to extreme events are complex and multi-dimensional, including extreme increases and decreases in both calling and movement behaviors. We also find significant temporal and spatial variance in responses to extreme events. Our behavioral anomaly detection system and extensive discussion of results are a significant contribution to the long-term project of creating an effective real-time event detection system with mobile phone data and we discuss the implications of our findings for future research to this end. "
to:NB  spatio-temporal_statistics  re:social_networks_as_sensor_networks  data_mining  statistics  dobra.adrian  eagle.nathan  anomaly_detection 
28 days ago
Discovery: Fish Live beneath Antarctica - Scientific American
All that's missing is commentary from Drs. Lake and Danforth, and maybe the adjective "Stygian".
antarctica  biology  cthulhiana 
28 days ago
[1411.2664] Preserving Statistical Validity in Adaptive Data Analysis
"A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses.
"In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples.
"We show that, surprisingly, there is a way to estimate an \emph{exponential} in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question."
to:NB  to_read  statistics  learning_theory  via:arthegall  concentration_of_measure  stability_of_learning 
28 days ago
Sociolinguistic Typology: Social Determinants of Linguistic Complexity
"Peter Trudgill looks at why human societies at different times and places produce different kinds of language. He considers how far social factors influence language structure and compares languages and dialects spoken across the globe, from Vietnam to Nigeria, Polynesia to Scandinavia, and from Canada to Amazonia.
"Modesty prevents Pennsylvanian Dutch Mennonites using the verb wotte ('want'); stratified society lies behind complicated Japanese honorifics; and a mountainous homeland suggests why speakers of Tibetan-Burmese Lahu have words for up there and down there. But culture and environment don't explain why Amazonian Jarawara needs three past tenses, nor why Nigerian Igbo can make do with eight adjectives, nor why most languages spoken in high altitudes do not exhibit an array of spatial demonstratives. Nor do they account for some languages changing faster than others or why some get more complex while others get simpler. The author looks at these and many other puzzles, exploring the social, linguistic, and other factors that might explain them and in the context of a huge range of languages and societies."
to:NB  books:noted  cultural_evolution  linguistics  complexity 
28 days ago
The C&O Canal Companion
"A comprehensive guide to one of America's unique national parks, The C&O Canal Companion takes readers on a mile-by-mile, lock-by-lock tour of the 184-mile Potomac River waterway and towpath that stretches from Washington, D.C., to Cumberland, Maryland, and the Allegheny Mountains. Making extensive use of records at the National Archives and the C&O Canal Park Headquarters, Mike High demonstrates how events and places along the canal relate to the history of the nation, from Civil War battles and river crossings to the frontier forts guarding the route to the West. Using attractive photographs and drawings, he introduces park visitors to the hidden history along the canal and provides practical advice on cycling, paddling, and hiking—all the information needed to fully enjoy the park's varied delights.
"Thoroughly overhauled and expanded, the second edition of this popular, fact-packed book features updated maps and photographs, as well as the latest information on lodgings and other facilities for hikers, bikers, and campers on weekend excursions or extended outdoor vacations. It also delves deeper into the history of the upland region, relaying new narratives about Native American settlements, the European explorers and traders who were among the first settlers, and the lives of slaves and free blacks who lived along or escaped slavery via the canal.
"Visitors to the C&O Canal who are interested in exploring natural wonders while tracing the routes of pioneers and engineers—not to mention the path of George Washington, who explored the Potomac route to the West as a young man and later laid out the first canals to make the river navigable—will find this guide indispensable."
books:noted  maryland  appalachia  travel  american_history  re:GAP_trail_trip 
28 days ago
Abandoned Footnotes: The Saudi Monarchy as a Family Firm
"Indeed, in some respects the Saudi system has more in common with systems of single party rule than with medieval European kingship. The Al Saud are an odd party, to be sure; only women can join voluntarily (by marrying into the family) but without gaining any formal power (though they may have influence through their sons). But, with its internal dispute resolution mechanisms, its intelligence networks, its “service” requirements, the family basically mimics the institutions of an effective (if small) party on the Leninist model. And thus the incentives that keep it in power are not dissimilar from the incentives that kept the PRI in Mexico or the Chinese Communist Party in power: they are basically reasons for insiders to stick together and not seek outsider support, and thus to prefer corporate control of the state to going alone."
saudi_arabia  political_science  have_read 
29 days ago
Pop Sonnets
Ogged: "That Website Than Which No Greater Can Be Conceived".
funny  poetry  popular_culture  affectionate_parody  via:unfogged 
29 days ago
Of Course You Hear What I Hear — Christmas Music Season Is Totally Data-Driven | FiveThirtyEight
Observations: (i) The domination of our popular culture by the childhoods of baby boomers --- my students' grandparents! --- is truly a force to behold. (ii) And of course that helps shape what all subsequent generations hear as "Christmas music". (iii) I am unreasonably charmed by the idea of using something like pagerank (or is it Kleinberg's HITS?) to identify Christmas-ness. (iv) Wait, _that's_ what happened to the author of _The War Against Silence_?
data_mining  music  christmas  popular_culture  towards_an_algorithmic_criticism  to_teach:data-mining  path_dependence  pagerank  to:blog  have_read 
4 weeks ago
Numenera
Because what the Dying Earth/Viriconium/Urth etc. needed was a role-playing game. (Actually, it looks pretty good.)
role-playing_games  via:??? 
4 weeks ago
r - knitr - How to align code and plot side by side - Stack Overflow
Could this be modified to put figure on top, then code, then caption?
R  kntir  re:ADAfaEPoV 
4 weeks ago
A practical introduction to functional programming at Mary Rose Cook
Uses python, but these ideas are exactly the ones I try to teach in that part of my R course, only better expressed.
programming  functional_programming  have_read  via:tealtan  to_teach:statcomp 
4 weeks ago
How To Tell If You Are In A High Fantasy Novel
Funny, but really this is a criticism of extruded epic fantasy product, rather than high fantasy proper; it's about mistaking Poughkeepsie for Elfland.
funny:geeky  funny:malicious  literary_criticism  fantasy 
4 weeks ago
Dehling , Durieu , Tusche : Approximating class approach for empirical processes of dependent sequences indexed by functions
"We study weak convergence of empirical processes of dependent data (Xi)i≥0, indexed by classes of functions. Our results are especially suitable for data arising from dynamical systems and Markov chains, where the central limit theorem for partial sums of observables is commonly derived via the spectral gap technique. We are specifically interested in situations where the index class  is different from the class of functions f for which we have good properties of the observables (f(Xi))i≥0. We introduce a new bracketing number to measure the size of the index class  which fits this setting. Our results apply to the empirical process of data (Xi)i≥0 satisfying a multiple mixing condition. This includes dynamical systems and Markov chains, if the Perron–Frobenius operator or the Markov operator has a spectral gap, but also extends beyond this class, for example, to ergodic torus automorphisms."
to:NB  empirical_processes  approximation  stochastic_processes  markov_models  dynamical_systems  ergodic_theory  mixing 
4 weeks ago
Lederer , van de Geer : New concentration inequalities for suprema of empirical processes
"While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive concentration inequalities assuming only low moments for an envelope of the empirical process. These concentration inequalities are beneficial even when the envelope is much larger than the single functions under consideration."
to:NB  empirical_processes  concentration_of_measure  deviation_inequalities  van_de_geer.sara  stochastic_processes  to_read 
4 weeks ago
Crisan , Míguez : Particle-kernel estimation of the filter density in state-space models
"Sequential Monte Carlo (SMC) methods, also known as particle filters, are simulation-based recursive algorithms for the approximation of the a posteriori probability measures generated by state-space dynamical models. At any given time t, a SMC method produces a set of samples over the state space of the system of interest (often termed “particles”) that is used to build a discrete and random approximation of the posterior probability distribution of the state variables, conditional on a sequence of available observations. One potential application of the methodology is the estimation of the densities associated to the sequence of a posteriori distributions. While practitioners have rather freely applied such density approximations in the past, the issue has received less attention from a theoretical perspective. In this paper, we address the problem of constructing kernel-based estimates of the posterior probability density function and its derivatives, and obtain asymptotic convergence results for the estimation errors. In particular, we find convergence rates for the approximation errors that hold uniformly on the state space and guarantee that the error vanishes almost surely as the number of particles in the filter grows. Based on this uniform convergence result, we first show how to build continuous measures that converge almost surely (with known rate) toward the posterior measure and then address a few applications. The latter include maximum a posteriori estimation of the system state using the approximate derivatives of the posterior density and the approximation of functionals of it, for example, Shannon’s entropy."
to:NB  particle_filters  kernel_estimators  density_estimation  filtering  state_estimation  state-space_models  statistics  computational_statistics 
4 weeks ago
Trashorras , Wintenberger : Large deviations for bootstrapped empirical measures
"We investigate the Large Deviations (LD) properties of bootstrapped empirical measures with exchangeable weights. Our main results show in great generality how the resulting rate functions combine the LD properties of both the sample weights and the observations. As an application, we obtain new LD results and discuss both conditional and unconditional LD-efficiency for many classical choices of entries such as Efron’s, leave-p-out, i.i.d. weighted, k-blocks bootstraps, etc."
to:NB  bootstrap  empirical_processes  large_deviations  stochastic_processes  statistics  re:almost_none 
4 weeks ago
Fischer : On the form of the large deviation rate function for the empirical measures of weakly interacting systems
"A basic result of large deviations theory is Sanov’s theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by relative entropy with respect to the common distribution. Large deviation principles for the empirical measures are also known to hold for broad classes of weakly interacting systems. When the interaction through the empirical measure corresponds to an absolutely continuous change of measure, the rate function can be expressed as relative entropy of a distribution with respect to the law of the McKean–Vlasov limit with measure-variable frozen at that distribution. We discuss situations, beyond that of tilted distributions, in which a large deviation principle holds with rate function in relative entropy form."
to:NB  interacting_particle_systems  large_deviations  information_theory  stochastic_processes  to_read  re:almost_none 
4 weeks ago
Blanchard , Delattre , Roquain : Testing over a continuum of null hypotheses with False Discovery Rate control
"We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding p-value) is known for each individual hypothesis. We extend to this setting the notion of false discovery rate (FDR) as a measure of type I error. Our main result studies specific procedures based on the observation of the p-value process. Control of the FDR at a nominal level is ensured either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting. Its interest is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables."
to:NB  multiple_testing  hypothesis_testing  statistics 
4 weeks ago
Lions , Nisio : A uniqueness result for the semigroup associated with the Hamilton-Jacobi-Belman operator
b/c the Feng and Kurtz book on large deviations for stochastic processes (e.g., evolutionary models) seems to presume the reader knows what a "Nisio semigroup" is, and I don't.

ETA: I should have known better than to expect reading pure mathematicians would be clarifying.
stochastic_processes  stochastic_differential_equations  control_theory  algebra  have_read 
5 weeks ago
[1312.7851] Effective Degrees of Freedom: A Flawed Metaphor
"To most applied statisticians, a fitting procedure's degrees of freedom is synonymous with its model complexity, or its capacity for overfitting to data. In particular, it is often used to parameterize the bias-variance tradeoff in model selection. We argue that, contrary to folk intuition, model complexity and degrees of freedom are not synonymous and may correspond very poorly. We exhibit and theoretically explore various examples of fitting procedures for which degrees of freedom is not monotonic in the model complexity parameter, and can exceed the total dimension of the response space. Even in very simple settings, the degrees of freedom can exceed the dimension of the ambient space by an arbitrarily large amount. We show the degrees of freedom for any non-convex projection method can be unbounded."

--- I have never really liked "degrees of freedom"...

--- ETA after reading: to be clear, no one is arguing about "effective degrees of freedom", in the sense of Efron (1986), telling us about over-fitting. The demonstrations here are that the geometric metaphor behind "degrees of freedom", while holding for linear models (without model selection), becomes very misleading in other contexts. Now, since I prefer to think of model selection in terms of capacity to over-fit, rather than the number of adjustable knobs...
to:NB  model_selection  regression  statistics  hastie.trevor  to_teach:undergrad-ADA  have_read  convexity 
5 weeks ago
Fully Exponential Laplace Approximations to Expectations and Variances of Nonpositive Functions (Tierny, Kass and Kadane, 1989)
The un-numbered equation defining $A_K$, between (2.3) and (2.4), is wrong --- the O(1/n) terms are off by various powers of $\sigma^2$. However, both (2.3) and (2.4) are right...
in_NB  have_read  laplace_approximation  statistics  approximation  kith_and_kin  kass.robert 
5 weeks ago
[1410.1184] Graphical LASSO Based Model Selection for Time Series
"We propose a novel graphical model selection (GMS) scheme for high-dimensional stationary time series or discrete time process. The method is based on a natural generalization of the graphical LASSO (gLASSO), introduced originally for GMS based on i.i.d. samples, and estimates the conditional independence graph (CIG) of a time series from a finite length observation. The gLASSO for time series is defined as the solution of an l1-regularized maximum (approximate) likelihood problem. We solve this optimization problem using the alternating direction method of multipliers (ADMM). Our approach is nonparametric as we do not assume a finite dimensional (e.g., an autoregressive) parametric model for the observed process. Instead, we require the process to be sufficiently smooth in the spectral domain. For Gaussian processes, we characterize the performance of our method theoretically by deriving an upper bound on the probability that our algorithm fails to correctly identify the CIG. Numerical experiments demonstrate the ability of our method to recover the correct CIG from a limited amount of samples."
to:NB  graphical_models  time_series  model_selection  statistics 
5 weeks ago
[1411.6512] Graphical Modeling of Spatial Health Data
"The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying graph is unknown and needs to be inferred from the data. The second research domain dominates the applications in spatial epidemiology. In this context GGMs are typically referred to as Gaussian Markov random fields (GMRFs). Here the underlying graph is assumed to be known: the vertices correspond to geographical areas, while the edges are associated with areas that are considered to be neighbors of each other (e.g., if they share a border). We introduce multi-way Gaussian graphical models that unify the statistical approaches to inference for spatiotemporal epidemiology with the literature on general GGMs. The novelty of the proposed work consists of the addition of the G-Wishart distribution to the substantial collection of statistical tools used to model multivariate areal data. As opposed to fixed graphs that describe geography, there is an inherent uncertainty related to graph determination across the other dimensions of the data. Our new class of methods for spatial epidemiology allow the simultaneous use of GGMs to represent known spatial dependencies and to determine unknown dependencies in the other dimensions of the data."
to:NB  spatial_statistics  spatio-temporal_statistics  graphical_models  statistics  dobra.adrian 
5 weeks ago
Beyond Models: Forecasting Complex Network Processes Directly from Data
"Complex network phenomena – such as information cascades in online social networks – are hard to fully observe, model, and forecast. In forecasting, a recent trend has been to forgo the use of parsimonious models in favor of models with in- creasingly large degrees of freedom that are trained to learn the behavior of a process from historical data. Extrapolat- ing this trend into the future, eventually we would like to renounce models all together. But is it possible to forecast the evolution of a complex stochastic process directly from the data without a model? In this work we show that the answer is yes. We present SED, an algorithm that forecasts process statistics based on relationships of statistical equiv- alence using two general axioms and historical data. To the best of our knowledge, SED is the first method that can perform axiomatic, model-free forecasts of complex stochas- tic processes. Our simulations using simple and complex evolving processes and tests performed on a large real-world dataset show promising results."

--- The last tag applies with extreme vehemence.
to:NB  network_data_analysis  information_cascades  time_series  bootstrap  statistics  prediction  to_be_shot_after_a_fair_trial 
5 weeks ago
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