APTS Statistical Inference, Lecture notes

Computer Intensive Statistics 1. Introduction

The principle aim of these notes is to provide context and motivation for the APTS Computer Intensive Statistics Module and to make the module as self-contained as is feasible. Statistics is a broad discipline and the APTS cohort naturally has a diverse range of backgrounds. If you have attended the earlier APTS modules this year, especially Statistical Computing and Statistical Inference, then...

Lecture Notes on Statistical Inference

STAT 566 Fall 2013 Statistical Inference Lecture Notes

2 Lecture 2: Evaluation of Statistical Procedures I 2 2.1 How to compare δ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Comparing risk function I: Bayes risk . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Bayes theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.4 Bayes risk revisited . . . . . . . . . . . . . . . . . . . . . . . . . ...

APTS – Statistical Modelling – Preliminary Material

Linear and generalised linear models: A student who has covered Chapters 8 and 10.110.4 of Statistical Models by A. C. Davison (Cambridge University Press, 2003) will be more than adequately prepared for the APTS module. For students without access to this book, the main theory is repeated below. The inference methodology described is largely based on classical statistical theory. Although prio...

Statistical Models are Algebraic Varieties

My goal in this chapter of lecture notes is to introduce the basic notions of a statistical model and an algebraic variety and show how they are related to one another. The title “Statistical Models are Algebraic Varieties” could be considered as a mantra of algebraic statistics. It is the ubiquity of the polynomial structures that arise when describing statistical models that makes some statis...