Aitkin Murray. Introduction to Statistical Modelling and Inference

Chapman & Hall, 2022. — 390 p. — ISBN 9781032105710.The complexity of large-scale data sets (“Big Data”) has stimulated the development of advanced computational methods for analysing them. Introduction to Statistical Modelling and Inference covers simple experimental and survey designs, and probability models up to and including generalised linear (regression) models and some extensions of these, including finite mixtures. A wide range of examples from different application fields are also discussed and analysed. No special software is used, beyond that needed for maximum likelihood analysis of generalised linear models. Students are expected to have a basic mathematical background in algebra, coordinate geometry and calculus.FeaturesProbability models are developed from the shape of the sample empirical cumulative distribution function (cdf) or a transformation of it.
Bounds for the value of the population cumulative distribution function are obtained from the Beta distribution at each point of the empirical cdf.
Bayes’s theorem is developed from the properties of the screening test for a rare condition.
The multinomial distribution provides an always-true model for any randomly sampled data.
The model-free bootstrap method for finding the precision of a sample estimate has a model-based parallel – the Bayesian bootstrap – based on the always-true multinomial distribution.
The Bayesian posterior distributions of model parameters can be obtained from the maximum
likelihood analysis of the model.