cshalizi + to_teach:statcomp + simulation   7

[1909.11827] Convergence diagnostics for Markov chain Monte Carlo
"Markov chain Monte Carlo (MCMC) is one of the most useful approaches to scientific computing because of its flexible construction, ease of use and generality. Indeed, MCMC is indispensable for performing Bayesian analysis. In spite of its widespread use, two critical questions that MCMC practitioners need to address are where to start and when to stop the simulation. Although a great amount of research has gone into establishing convergence criteria and stopping rules with sound theoretical foundation, in practice, MCMC users often decide convergence by applying empirical diagnostic tools. This review article discusses the most widely used MCMC convergence diagnostic tools. Some recently proposed stopping rules with firm theoretical footing are also presented. The convergence diagnostics and stopping rules are illustrated using three detailed examples."
to:NB  monte_carlo  statistics  computational_statistics  simulation  to_teach:statcomp 
12 days ago by cshalizi
[1909.03813] INTEREST: INteractive Tool for Exploring REsults from Simulation sTudies
"Simulation studies allow us to explore the properties of statistical methods. They provide a powerful tool with a multiplicity of aims; among others: evaluating and comparing new or existing statistical methods, assessing violations of modelling assumptions, helping with the understanding of statistical concepts, and supporting the design of clinical trials. The increased availability of powerful computational tools and usable software has contributed to the rise of simulation studies in the current literature. However, simulation studies involve increasingly complex designs, making it difficult to provide all relevant results clearly. Dissemination of results plays a focal role in simulation studies: it can drive applied analysts to use methods that have been shown to perform well in their settings, guide researchers to develop new methods in a promising direction, and provide insights into less established methods. It is crucial that we can digest relevant results of simulation studies. Therefore, we developed INTEREST: an INteractive Tool for Exploring REsults from Simulation sTudies. The tool has been developed using the Shiny framework in R and is available as a web app or as a standalone package. It requires uploading a tidy format dataset with the results of a simulation study in R, Stata, SAS, SPSS, or comma-separated format. A variety of performance measures are estimated automatically along with Monte Carlo standard errors; results and performance summaries are displayed both in tabular and graphical fashion, with a wide variety of available plots. Consequently, the reader can focus on simulation parameters and estimands of most interest. In conclusion, INTEREST can facilitate the investigation of results from simulation studies and supplement the reporting of results, allowing researchers to share detailed results from their simulations and readers to explore them freely."
to:NB  simulation  R  to_teach:statcomp 
25 days ago by cshalizi
[1106.4929] Simulating rare events in dynamical processes
"Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that are responsible for intermittency in a turbulent liquid, the active regions that allow a supercooled liquid to flow... Simulating them in an efficient, accelerated way, is in fact quite simple.
"In this paper we review a computational technique to study such rare events in both stochastic and Hamiltonian systems. The method is based on the evolution of a family of copies of the system which are replicated or killed in such a way as to favor the realization of the atypical trajectories. We illustrate this with various examples."
to:NB  stochastic_processes  simulation  large_deviations  to_teach:data_over_space_and_time  to_teach:statcomp  re:fitness_sampling  re:do-institutions-evolve 
10 weeks ago by cshalizi
Burn-In is Unnecessary
Hmmm. Shouldn't one be able to address this as, given that the initial state X_0 comes from a distribution \pi which is not the invariant distribution \rho of the Markov operator, for what b does the empirical distribution of X_{b:n} come closest, on average and in some reasonable metric, to \rho? The answer presumably depends on how far \pi is from \rho and how rapidly T mixes.
monte_carlo  to_teach:statcomp  ergodic_theory  markov_models  geyer.charles_j.  have_read  simulation  computational_statistics 
april 2013 by cshalizi

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