Introduction to WINBUGS for Ecologists – Marc Kery

Introduction to WINBUGS for Ecologists – Marc Kery

I borrowed this book from Monash University library. I won't read it all, as I'm not ready to teach myself Winbugs  yet. I do hope the introductory chapters will explain the concepts of  Bayesian statistics. The book by Berry has been good, but the focus of that book (or at least my reading of it) has been on the mechanic of Bayesian statistics, and I'd still like to understand a bit more about what makes Bayesian statistics different from "traditional statistics"

Introductory quotation

To make sense of an observation, everybody needs a model… whether he or she knows it or not.

It is difficult to imagine another method that so effectively fosters clear thinking about a system than the use of a model written in the language of algebra.

Foreword

-          Models must be completely specified by the user.

-          All inference is based on underlying models

-          Necessity of specifying models, and thus of thinking clearly about underlying sampling and processes.

-          Ecological data sets are generated by at least two classes of processes: ecological and  sampling. The ecological process generates the true patterns that our studies are designed to investigate, and conditional on this truth, the sampling process generates the data that we actually obtain.

-          Hierarchical models

-          Statistical models as abstract representations of the various processes that give rise to a data set.

Preface

-          All data sets are simulated ("assembled") before analysis ("disassembly")

-          Typical readership: advanced undergraduate, graduate students

Introduction

-          Bayesian: statistical inference based on the posterior distribution, which expresses all that is known about the parameters of a statistical model, given the data and existing knowledge.

-          Classical inference is based on large samples, in the long run. However, for finite sample sizes, ie, your data set …

-          By basing inference on both what we knew before (the prior) and what we see now (the data at hand), and using solely the laws of probability for that combination, Bayesian statistics provides a formal mechanism for introducing external knowledge into an analysis.

-          In Bayesian statistics, a probability statement is made about a parameter, wheras in the classical approach, it is about a data set

Introduction to the Bayesian Analysis of a Statistical Model

-          Stochastic systems – systems that are not fully predictable but include random processes that add a degree of chance- and therefore uncertainty – in their outcome.

-          Both Bayesian and classical statistics view data as the observed realizations of stochastic systems that contain one or several random processes

-          However, in classical statistics, the quantities used to describe these random processes (parameters) are fixed and unknown constants.

-          Whereas in Bayesian statistics,, parameters are themselves viewed as unobserved realizations of random processes.

-          In classical statistics, because parameters are fixed, and only the data are random.

-          Posterior distribution is proportional to (likelihood * prior distribution)

-          Likelihood : information about unknown parameter contained in the observed data