Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demo...

This paper considers settings where populations of units may experience recurrent events, termed failures for convenience, and where the units are subject to varying levels of usage. We provide joint models for the recurrent events and usage processes, which facilitate analysis of their relationship as well as prediction of failures. Data on usage are often incomplete and we show how to impleme...

seemed to have in the past towards the logit transformation have now been withdrawn but the use of logits is not described in this book. The later chapters of the book provide both a framework of theory based on maximum likelihood estimation and a discussion of more specialized practical problems such as the study of the joint action of drugs. These later sections are not easy to read but are w...

Network meta-analysis is used to simultaneously compare multiple treatments in a single analysis. However, network meta-analyses may exhibit inconsistency, where direct and different forms of indirect evidence are not in agreement with each other, even after allowing for between-study heterogeneity. Models for network meta-analysis with random inconsistency effects have the dual aim of allowing...

This chapter is a brief introduction to two important statistical methods— maximum likelihood estimation and hypothesis testing. We shall show how to use these methods to test the biological sequence models developed in previous chapters against experimental data. We shall also show how hypothesis testing ideas inspire scoring methods for sequence alignment. denote the outcome of an experiment ...

We study the problem of multiple hypothesis testing for correlated clustered data. As the existing multiple comparison procedures based on maximum likelihood estimation could be computationally intensive, we propose to construct multiple comparison procedures based on composite likelihood method. The new test statistics account for the correlation structure within the clusters and are computati...

This chapter is a brief introduction to two important statistical methods— maximum likelihood estimation and hypothesis testing. We shall show how to use these methods to test the biological sequence models developed in previous chapters against experimental data. We shall also show how hypothesis testing ideas inspire scoring methods for sequence alignment. denote the outcome of an experiment ...

Estimators of the conditional expectation, i.e., prediction, function involve a global bias-variance trade off. In some cases, an estimator that yields unbiased estimates of the conditional expectation for a particular partitioning of the data may be desirable. Such estimators are calibrated with respect to the partitioning. We identify the conditional expectation given a particular partitionin...

We propose a class of transformation models for multivariate failure times. The class of transformation models generalize the usual gamma frailty model and yields a marginally linear transformation model for each failure time. Nonparametric maximum likelihood estimation is used for inference. The maximum likelihood estimators for the regression coefficients are shown to be consistent and asympt...