Biological and medical data have been growing exponentially over the past several years [1, 2]. In particular, proteomics has seen automation dramatically change the rate at which data are generated [3]. Analysis that systemically incorporates prior information is becoming essential to making inferences about the myriad, complex data [4-6]. A Bayesian approach can help capture such information ...

Regulators such as the U.S. Food and Drug Administration have elaborate, multi-year processes for approving new drugs as safe and effective. Nonetheless, in recent years, several approved drugs have been withdrawn from the market because of serious and sometimes fatal side effects. We describe statistical methods for post-approval data analysis that attempt to detect drug safety problems as qui...

. Most of this book emphasizes frequentist methods, especially for nonparametric problems. However, there are Bayesian approaches to many nonparametric problems. In this chapter we present some of the most commonly used nonparametric Bayesian methods. These methods place priors on infinite dimensional spaces. The priors are based on certain stochastic processes called Dirichlet processes and Ga...

The emergent field of probabilistic numerics has thus far lacked rigorous statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain Bayesian inverse problems, albeit problems that are non-standard. This allows us to establish general conditions under which Bayesian probabilistic numerical methods are well-defined, ...

Bayesian methods allow for a simple and intuitive representation of the function spaces used by kernel methods. This chapter describes the basic principles of Gaussian Processes, their implementation and their connection to other kernel-based Bayesian estimation methods, such as the Relevance Vector Machine.

Bayesian methods have proven themselves to be successful across a wide range of scientific problems and have many well-documented advantages over competing methods. However, these methods run into difficulties for two major and prevalent classes of problems: handling data sets with outliers and dealing with model misspecification. We outline the drawbacks of previous solutions to both of these ...

We note the main points of history, as a framework on which to hang many background remarks concerning the nature and motivation of Bayesian/Maximum Entropy methods. Experience has shown that these are needed in order to understand recent work and problems. A more complete account of the history, with many more details and references, is given in Jaynes (1978). The following discussion is essen...

This paper is a study of the application of Bayesian Exponentially Tilted Empirical Likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys’ method. For regression quantiles we derive the asymptotic form of the posterior density. We also exami...

Classical statistics provides methods to analyze data, from simple descriptive measures to complex and sophisticated models. The available data are processed and then conclusions about a hypothetical population — of which the data available are supposed to be a representative sample — are drawn. It is not hard to imagine situations, however, in which data are not the only available source of in...