Probability Basics

I’ve written up some intuitive, summary descriptions of several probability distributions and statistical techniques that I use frequently in my research.  I hope these serve as a useful reference for other students.

Probability Distributions

Bayesian Autoregressive Time Series Models

This post is intended to introduce an unfamiliar reader to some basic techniques in Bayesian modeling of autoregressive time series.  We’ll cover the basics of autoregressive models, use the Matrix Normal Inverse Wishart (MNIW) as a conjugate prior for efficient inference, and give some examples of using this model for a point moving in a …

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Change of Random Variables

I always forget the rules for transforming random variables, so I’ve made this page to show two simple examples, both involving the humble Gaussian. Generic Theory In general, we know random variable with density , for . Suppose we have a quantity of interest . We know that the function is invertible, so each maps …

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Inverse Wishart Distribution

The inverse Wishart distribution represents positive definite matrices.  This can be extremely useful in Bayesian analysis, as the inverse Wishart can serve as a prior for any covariance matrix .

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Normal Inverse Wishart Distribution

Summary The normal inverse Wishart provides a joint distribution over a vector and covariance matrix .

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