In All Likelihood: Statistical Modelling and Inference Using LikelihoodBased on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood. |
Contents
1 Introduction | 1 |
2 Elements of likelihood inference | 21 |
3 More properties of likelihood | 53 |
4 Basic models and simple applications | 73 |
5 Frequentist properties | 117 |
regression models | 149 |
7 Evidence and the likelihood principle | 193 |
8 Score function and Fisher information | 213 |
12 EM Algorithm | 341 |
13 Robustness of likelihood specification | 365 |
14 Estimating equations and quasilikelihood | 385 |
15 Empirical likelihood | 409 |
16 Likelihood of random parameters | 425 |
17 Random and mixed effects models | 435 |
18 Nonparametric smoothing | 473 |
| 503 | |
Other editions - View all
In All Likelihood: Statistical Modelling and Inference Using Likelihood Yudi Pawitan Limited preview - 2013 |
In All Likelihood: Statistical Modelling and Inference Using Likelihood Yudi Pawitan Limited preview - 2001 |
In All Likelihood: Statistical Modelling and Inference Using Likelihood Yudi Pawitan Limited preview - 2013 |
Common terms and phrases
algorithm analysis apply approach approximation assume binomial called compute conditional confidence constant dataset defined density dependence derive described discussed distribution effects empirical equation error estimate evidence exact example Exercise expected experiment exponential family Figure Fisher information fixed formula given iid sample independent indicates inference interest interpret interval known likelihood function linear log-likelihood matrix mean measure method normal Note nuisance observed obtain outcome P-value parameter plot Poisson possible practice principle probability problem procedure profile likelihood quadratic quantity random regression regular repeated result sample mean score shown shows simple smoothing solution specific standard statistic sufficient Suppose term theorem theory transformation true uncertainty unknown usually variable variance vector zero