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A wide range of case studies is provided, using the normal, binomial, Poisson, multinomial, gamma, exponential and Weibull distributions. A feature of the book is a detailed discussion of survival analysis. Statisticians working in a wide range of fields, including biomedical and social sciences, will find this book an invaluable desktop companion to aid their statistical modelling. 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There are two different kinds of methods to aid this. The  model-based method uses probability models and likelihood and Bayesian theory, while the model-free  method does not require a probability model, likelihood or Bayesian theory. These two approaches  are based on different philosophical principles of probability theory, espoused by the famous  statisticians Ronald Fisher and Jerzy Neyman. 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. Features • Probability 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.  This book is aimed at students in a wide range of disciplines including Data Science. The book is  based on the model-based theory, used widely by scientists in many fields, and compares it, in less  detail, with the model-free theory, popular in computer science, machine learning and official  survey analysis. 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