In all likelihood : statistical modelling and inference using likelihood / Yudi Pawitan.

Format:

Book

Author/Creator:

Pawitan, Yudi, author.

Series:

Oxford statistical science series ; 40.

Oxford statistical science series ; 40

Language:

English

Subjects (All):

Mathematical statistics.

Probabilities.

probability.

Physical Description:

1 online resource : illustrations.

Edition:

Second edition.

Other Title:

Statistical modelling and inference using likelihood

Place of Publication:

Oxford ; New York, NY : Oxford University Press, 2026.

Summary:

This volume explores the central role of likelihood in a wide spectrum of statistical problems, ranging from simple comparisons - such as evaluating accident rates between two groups - to sophisticated analyses involving generalized linear models and semiparametric methods. Rather than treating likelihood merely as a tool for point estimation, the book highlights its broader value as a foundational framework for constructing, understanding and computational implementation of statistical models. It emphasizes how likelihood perspectives inform model development, assessment, and inference in a cohesive and intuitive way. While grounded in essential mathematical theory, the book adopts an informal and accessible approach, using heuristic reasoning and illustrative, realistic examples to convey key ideas.

Contents:

Cover

Series page

Title page

Copyright page

Preface to the Second Edition

Preface to the First Edition

Contents

List of abbreviations and notations

1 Introduction

1.1 Prototype of statistical problems

Aspirin data example

1.2 Statistical problems and their models

Inductive process

Empirical or mechanistic models

1.3 Uncertainty and the inevitable controversies

Pedagogic aspect

1.4 The emergence of statistics

Bayesians and frequentists

Inverse probability: the Bayesians

Repeated sampling principle: the frequentists

Bayesians vs. frequentists

1.5 Fisher and the third way

Legacies

1.6 Exercises

2 Elements of likelihood inference

2.1 Classical definition

Discrete models

Continuous models

Mathematical convention

2.2 Examples

2.3 Combining likelihoods

2.4 Likelihood ratio

2.5 Maximum and curvature of the likelihood function

2.6 Likelihood-based intervals

Pure likelihood inference

Probability-based inference

When can we use a pure likelihood interval?

Likelihood ratio test

2.7 Standard error and Wald statistic

2.8 Invariance principle

2.9 Implications of the invariance principle

Invariance property of the MLE

Improving the quadratic approximation

Likelihood-based CI is better than Wald CI

2.10 Exercises

3 More properties of the likelihood

3.1 Sufficiency

3.2 Minimal sufficiency

Monotone likelihood ratio property

3.3 Multiparameter models

3.4 Profile likelihood

Curvature of profile likelihood

3.5 Calibration in multiparameter case

Likelihood-based confidence region

AIC-based calibration

3.6 Exercises

4 Basic models and simple applications

4.1 Binomial or Bernoulli models

Negative binomial model

4.2 Binomial model: underor overdispersion

4.3 Comparing two proportions

A series of 2×2 tables

4.4 Poisson model

4.5 Poisson with overdispersion

4.6 Traffic deaths example

4.7 Aspirin data example

Delta method

4.8 Continuous data

Normal models

The case n = 1

Two-sample case

Nonnormal models

4.9 Exponential family

Exponential dispersion model

Approximate likelihood⋆

Minimal sufficiency and the exponential family⋆

4.10 Box-Cox transformation family

4.11 Location-scale family

4.12 Exercises

5 Frequentist properties

5.1 Bias of point estimates

Producing an unbiased estimate is never automatic

Not all parameters have an unbiased estimator

The unbiasedness requirement can produce terrible estimates

5.2 Estimating and reducing bias

Taylor series method for functions of the mean

Jackknife and cross-validation methods

Bootstrap method

5.3 Variability of point estimates

Estimating variance

5.4 Likelihood and P-value

5.5 CI and coverage probability

5.6 Confidence density, CI, and the bootstrap

Bootstrap density as confidence density

Notes:

Previous edition: 2001.

Includes bibliographical references and index.

Description based on online resource; title from digital title page (Oxford Academic, viewed on July 6, 2026).

Other Format:

Print version: Pawitan, Yudi. In all likelihood.

ISBN:

9780198950950

0198950950

9780198950943

0198950942

OCLC:

1565403539

Publisher Number:

CIPO000335238

Access Restriction:

Restricted for use by site license