Jordan Bryan

Power and the moving block bootstrap

Suppose that, following the design of the previous well contamination study, a new group of researchers wants to conduct a survey to characterize the effect that distance to the nearest safe drinking water source has on well switching behavior. For the next study, we would like to estimate the number of residents that need to be polled in order ... Read more

Structural dependence in binary regression

Drinking water contamination affects many communities in the developing world. When safe water sources become available to these communities, various factors may determine whether residents modify their drinking habits. We analyze data gathered from \(3020\) residents in a developing country with Frequentist and Bayesian methods in order to unde... Read more

Incompleteness and the Underground

We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.1 Though not a writer himself, David Hilbert had a flair for the literary. And, at the moment in history when he spoke these words, he had every right to indulge it. When he delivered his ... Read more

Conjugate prior bootcamp

This post follows the table at the end of the Conjugate prior Wikipedia page to derive posterior distributions for parameters of a range of likelihood functions. Many resources for learning the mechanics of posterior inference under conjugate priors already exist, so there’s nothing particularly new to be seen here. However, maybe others learnin... Read more

Pairwise independence does not imply countable mutual independence

Define a sequence of random variables indexed by \(n\) as follows: Divide the unit interval into sub-intervals of size \(1/3^n\) Let the random variable be equal to \(1\) if \(\omega\) falls within the “middle” third of each subinterval, and let it be equal to \(0\) otherwise More formally, let \[X_n := \mathbf{1}_{B_n}\... Read more