## 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. |

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### 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 - 2001 |

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 assume Bayesian bias bootstrap Cauchy model compute confidence density covariance coverage probability data in Example dataset deﬁned degrees of freedom derive deviance effects model EM algorithm empirical likelihood estimating equation exact Exercise exponential family exponential model Figure ﬁrst ﬁxed formula frequentist given iid sample inference iterative Let x1 likelihood function likelihood interval likelihood principle likelihood ratio likelihood-based log-likelihood marginal likelihood matrix method mixed model nonparametric normal model normal with mean nuisance parameter observed data outcome P-value parameter of interest plot Poisson model Poisson regression predictor problem proﬁle profile likelihood quadratic approximation random effects random effects model regression model result sample mean score function score statistic Section shows smoothing specification standard error sufficient statistic Suppose x1 term theorem transformation true uncertainty unknown parameter variable variance vector zero