Murray Aitkin – författare

The complexity of large-scale data sets (“Big Data”) has stimulated the development of advanced computational methods for analysing 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 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. The development of the model-based theory is accelerated by recent developmentsin Bayesian analysis.

The complexity of large-scale data sets (“Big Data”) has stimulated the development of advanced computational methods for analysing 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 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. The development of the model-based theory is accelerated by recent developmentsin Bayesian analysis.

The purpose of this book is to evaluate a new approach to the analysis and reporting of the large-scale surveys for the National Assessment of Educational Progress carried out for the National Center for Education Statistics. The need for a new approach was driven by the demands for secondary analysis of the survey data by researchers who needed analyses more detailed than those published by NCES, and the need to  accelerate the processing and publication of results from the surveys.

This new approach is based on a full multilevel statistical and psychometric model for students’ responses to the test items, taking into account the design of the survey, the backgrounds of the students, and the classes, schools and communities in which the students were located. The authors detail a fully integrated single model that incorporates both the survey design and the psychometric model by extending the traditional form of the psychometric model to accommodate the design structure while allowing for student, teacher, and school covariates.