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seemed to have in the past towards the logit transformation have now been withdrawn but the use of logits is not described in this book.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...

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...

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...

The most frequent measure of phylogenetic uncertainty for splits is bootstrap support. Although large bootstrap support intuitively suggests that a split in a tree is well supported, it has not been clear how large bootstrap support needs to be to conclude that there is significant evidence that a hypothesized split is present. Indeed, recent work has shown that bootstrap support is not first-o...

In this paper we investigate the large-sample behavior of the maximum likelihood estimate (MLE) of the unknown parameter θ for processes following the model dξt = θf(t)ξt dt+ dBt where f : R → R is a continuous function with period, say P > 0, and which is observed through continuous time interval [0, T ] as T → ∞. Here the periodic function f(·) is assumed known. We establish the consistency o...

This tutorial describes a parameter estimation technique that is little-known in social sciences, namely maximum a posteriori estimation. This technique can be used in conjunction with prior knowledge to improve maximum likelihood estimation of the best-fitting parameters of a data set. The estimates are based on the mode of the posterior distribution of a Bayesian analysis. The relationship be...

This paper concerns the estimation of the parameters that describe a stable distribution. Stable distributions are characterised by four parameters which can be estimated using a number of methods and although approximate maximum likelihood estimation (MLE) techniques do exist, they are computationally intensive. There are a number of techniques that are much faster thanMLE and these are the fo...