Название: Statistics for Making Decisions Автор: Nicholas T. Longford Издательство: Chapman and Hall/CRC Press Год: 2021 Страниц: 309 Язык: английский Формат: pdf (true) Размер: 13.9 MB
Making decisions is a ubiquitous mental activity in our private and professional or public lives. It entails choosing one course of action from an available shortlist of options. Statistics for Making Decisions places decision making at the centre of statistical inference, proposing its theory as a new paradigm for statistical practice. The analysis in this paradigm is earnest about prior information and the consequences of the various kinds of errors that may be committed. Its conclusion is a course of action tailored to the perspective of the specific client or sponsor of the analysis. The author’s intention is a wholesale replacement of hypothesis testing, indicting it with the argument that it has no means of incorporating the consequences of errors which self-evidently matter to the client.
The volume appeals to the analyst who deals with the simplest statistical problems of comparing two samples (which one has a greater mean or variance), or deciding whether a parameter is positive or negative. It combines highlighting the deficiencies of hypothesis testing with promoting a principled solution based on the idea of a currency for error, of which we want to spend as little as possible. This is implemented by selecting the option for which the expected loss is smallest (the Bayes rule).
The price to pay is the need for a more detailed description of the options, and eliciting and quantifying the consequences (ramifications) of the errors. This is what our clients do informally and often inexpertly after receiving outputs of the analysis in an established format, such as the verdict of a hypothesis test or an estimate and its standard error. As a scientific discipline and profession, statistics has a potential to do this much better and deliver to the client a more complete and more relevant product.
A foundation course in calculus and linear algebra, with some experience of differentiation and integration, as well as matrix operations associated with ordinary least squares, are essential prerequisites. The text makes frequent references to computing in R and some exercises require computing and graphics, which could in principle be accomplished in other software, but I have thought about them in R only. Computing is also invaluable for exploring and confirming the properties and conclusions derived analytically. I have a suite of functions and their applications that implement all the computing and graphics described and reproduced in the text, and would be happy to share it with the reader, but I believe that greater benefit will be derived by the reader developing a personal (and personalised) library. The book is not for a beginner in statistics. The student or reader has to be familiar with ordinary regression, the most common distributions in statistics, maximum likelihood estimation and analysis of variance, hypothesis testing and the frequentist and Bayesian paradigms, although it is necessary to be conversant only in one of them.