Introduction to statistical modelling and inference / Murray Aitkin, University of Melbourne, Australia.
| Author/creator | Aitkin, Murray A. |
| Format | Electronic |
| Edition | First edition. |
| Publication Info | Boca Raton : CRC Press, Taylor & Francis Group, 2023. |
| Description | 1 online resource |
| Supplemental Content | Full text available from Taylor & Francis eBooks |
| Subjects |
| Contents | What is (or are) big data? -- Data and research studies -- The Statlab data base -- Sample surveys : should we believe what we read? -- Probability -- Statistical inference I : discrete distributions -- Comparison of binomials : the randomised clinical trial -- Data visualisation -- Statistical inference II : the continuous exponential, Gaussian and uniform distributions -- Statistical inference III : two-parameter continuous distributions -- Model assessment -- The multinomial distribution -- Model comparison and model averaging -- Gaussian linear regression models -- Incomplete data and their analysis with the EM and DA algorithms -- Generalised linear models (GLMs) -- Extensions of GLMs. |
| Abstract | "The complexity of large-scale data sets ("Big Data") has stimulated the development of advanced computational methods for analyzing them. 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 analyzed. 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 of 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. The development of the model-based theory is accelerated by recent developments in Bayesian analysis"-- Provided by publisher. |
| General note | "A Chapman & Hall book." |
| Bibliography note | Includes bibliographical references and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Source of description | Description based on print version record and CIP data provided by publisher. |
| Issued in other form | Print version: Aitkin, Murray A. Introduction to statistical modelling and inference First edition. Boca Raton : CRC Press, Taylor & Francis Group, 2023 9781032105710 |
| Genre/form | Electronic books. |
| LCCN | 2022011483 |
| ISBN | 9781003216025 (ebook) |
| ISBN | (hardback) |
| ISBN | (paperback) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |