"[Our strategy needs] to address the motivation, opportunity and capability of those actors. We have found three sets of activities that, in our experience, are most likely to lead to that sustainable change. 1) Sector programmes – coordinating organisations to tackle a social or economic problem with data and an open approach. 2) Practical advocacy – working as a critical friend with businesses and government, and creating products they can use to support change.
3) Peer networks – bringing together peers in similar situations to learn together."

Stein's example (or phenomenon or paradox), in decision theory and estimation theory, is the phenomenon that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters separately. It is named after Charles Stein of Stanford University, who discovered the phenomenon in 1955.[1]

An intuitive explanation is that optimizing for the mean-squared error of a combined estimator is not the same as optimizing for the errors of separate estimators of the individual parameters. In practical terms, if the combined error is in fact of interest, then a combined estimator should be used, even if the underlying parameters are independent; this occurs in channel estimation in telecommunications, for instance (different factors affect overall channel performance). On the other hand, if one is instead interested in estimating an individual parameter, then using a combined estimator does not help and is in fact worse.

...

Many simple, practical estimators achieve better performance than the ordinary estimator. The best-known example is the James–Stein estimator, which works by starting at X and moving towards a particular point (such as the origin) by an amount inversely proportional to the distance of X from that point.

LD Score regression distinguishes confounding from polygenicity in genome-wide association studies: https://sci-hub.bz/10.1038/ng.3211
- Po-Ru Loh, Nick Patterson, et al.

https://www.biorxiv.org/content/biorxiv/early/2014/02/21/002931.full.pdf

Both polygenicity (i.e. many small genetic effects) and confounding biases, such as cryptic relatedness and population stratification, can yield inflated distributions of test statistics in genome-wide association studies (GWAS). However, current methods cannot distinguish between inflation from bias and true signal from polygenicity. We have developed an approach that quantifies the contributions of each by examining the relationship between test statistics and linkage disequilibrium (LD). We term this approach LD Score regression. LD Score regression provides an upper bound on the contribution of confounding bias to the observed inflation in test statistics and can be used to estimate a more powerful correction factor than genomic control. We find strong evidence that polygenicity accounts for the majority of test statistic inflation in many GWAS of large sample size.

Supplementary Note: https://images.nature.com/original/nature-assets/ng/journal/v47/n3/extref/ng.3211-S1.pdf

An atlas of genetic correlations across human diseases
and traits: https://sci-hub.bz/10.1038/ng.3406

https://www.biorxiv.org/content/early/2015/01/27/014498.full.pdf

Supplementary Note: https://images.nature.com/original/nature-assets/ng/journal/v47/n11/extref/ng.3406-S1.pdf

https://github.com/bulik/ldsc
ldsc is a command line tool for estimating heritability and genetic correlation from GWAS summary statistics. ldsc also computes LD Scores.

- Pickrell, Pritchard
treemix

- Patterson, Reich et al., 2012
Population mixture is an important process in biology. We present a suite of methods for learning about population mixtures, implemented in a software package called ADMIXTOOLS, that support formal tests for whether mixture occurred and make it possible to infer proportions and dates of mixture. We also describe the development of a new single nucleotide polymorphism (SNP) array consisting of 629,433 sites with clearly documented ascertainment that was specifically designed for population genetic analyses and that we genotyped in 934 individuals from 53 diverse populations. To illustrate the methods, we give a number of examples that provide new insights about the history of human admixture. The most striking finding is a clear signal of admixture into northern Europe, with one ancestral population related to present-day Basques and Sardinians and the other related to present-day populations of northeast Asia and the Americas. This likely reflects a history of admixture between Neolithic migrants and the indigenous Mesolithic population of Europe, consistent with recent analyses of ancient bones from Sweden and the sequencing of the genome of the Tyrolean “Iceman.”

https://betadecay.wordpress.com/2009/10/02/the-physics-of-scaling-laws-and-dimensional-analysis/
http://galileo.phys.virginia.edu/classes/304/scaling.pdf

Galileo’s Discovery of Scaling Laws: https://www.mtholyoke.edu/~mpeterso/classes/galileo/scaling8.pdf
Days 1 and 2 of Two New Sciences

An example of such an insight is “the surface of a small solid is comparatively greater than that of a large one” because the surface goes like the square of a linear dimension, but the volume goes like the cube.5 Thus as one scales down macroscopic objects, forces on their surfaces like viscous drag become relatively more important, and bulk forces like weight become relatively less important. Galileo uses this idea on the First Day in the context of resistance in free fall, as an explanation for why similar objects of different size do not fall exactly together, but the smaller one lags behind.

pf:
- for triangle w/ one side = a diameter, draw isosceles triangle and use supplementary angle identities
- otherwise draw second triangle w/ side = a diameter, and use above result twice

- rationals perfectly approximated by themselves, badly approximated (eps~1/q) by other rationals
- irrationals well-approximated (eps~1/q^2) by rationals: https://en.wikipedia.org/wiki/Dirichlet%27s_approximation_theorem

In probability theory and intertemporal portfolio choice, the Kelly criterion, Kelly strategy, Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any essentially different strategy in the long run (that is, over a span of time in which the observed fraction of bets that are successful equals the probability that any given bet will be successful). It was described by J. L. Kelly, Jr, a researcher at Bell Labs, in 1956.[1] The practical use of the formula has been demonstrated.[2][3][4]

The Kelly Criterion is to bet a predetermined fraction of assets and can be counterintuitive. In one study,[5][6] each participant was given $25 and asked to bet on a coin that would land heads 60% of the time. Participants had 30 minutes to play, so could place about 300 bets, and the prizes were capped at $250. Behavior was far from optimal. "Remarkably, 28% of the participants went bust, and the average payout was just $91. Only 21% of the participants reached the maximum. 18 of the 61 participants bet everything on one toss, while two-thirds gambled on tails at some stage in the experiment." Using the Kelly criterion and based on the odds in the experiment, the right approach would be to bet 20% of the pot on each throw (see first example in Statement below). If losing, the size of the bet gets cut; if winning, the stake increases.

also has supporting hyperplane theorems

Supporting Hyperplane Theorem
Separating Hyperplane Theorems