Preface

This text presents a brief summary of the theoretical content of the course ``Computational statistics I’’, taught at the University of Helsinki. Despite the name, the course covers basics of both statistical computation and computational statistics, with a heavy focus on Bayesian methods.

The book contains programming examples. There are mainly written in Python 3, unless otherwise mentioned. The reason for using Python instead of e.g. R is that R does not support one of the corner stones of modern numerical computation: automatic differentiation, that will be heavily used during the course.

Some general debugging tips for computational statistics

Always set the random seed at the beginning and save the value
Test any random samplers you have implemented by sampling from a known distribution
When implementing a probability density function, always test numerically that it sums/integrates to 1
When implementing procedures for statistical inference from data, simulate data from a known model, apply the inference to that data and check if you obtain the original parameters back