Keying Ye

Approximatereference priors in the presence of latent structures

Objective Bayesian Inference with Applications.- Bayesian Decision Based Estimation and Predictive Inference.- Bayesian Model Selection and Hypothesis Tests.- Bayesian Inference for Complex Computer Models.- Bayesian Nonparametrics and Semi-parametrics.- Bayesian Influence and Frequentist Interface.- Bayesian Clinical Trials.- Bayesian Methods for Genomics, Molecular and Systems Biology.- Bayesian Data Mining and Machine Learning.- Bayesian Inference in Political Science, Finance, and Marketing Research.- Bayesian Categorical Data Analysis.- Bayesian Geophysical, Spatial and Temporal Statistics.- Posterior Simulation and Monte Carlo Methods.

Bayesian Decision Based Estimation and Predictive Inference

Shrinkage estimation is a traditional research topic in Bayesian analysis. The three sections in this chapter convincingly argue that this venerable topic remains a current research frontier with many open problems. The chapter starts with a review of the current state of research and concludes with an insightful discussion of a very specific form of shrinkage estimation arising in recent work on inference in gene-environment interaction studies.

Bayesian Model Selection and Hypothesis Tests

Model comparison remains an active research frontier in Bayesian analysis. The chapter introduces related specific research problems, including the selection of a number of components in a mixture model and the choice of a training sample size when using virtual simulated training samples. The chapter also discusses an intriguing general property that sets Bayesian testing apart from frequentist testing, by effectively rewarding honest choice of an alternative hypothesis. Cheating does not pay.

Bayesian Inference in Political Science, Finance, and Marketing Research

Many current research challenges in Bayesian analysis arise in applications. A beauty of the Bayesian approach is that it facilitates principled inference in essentially any well-specified probability model or decision problem. In principle one could consider arbitrarily complicated priors, probability models and decision problems. However, not even the most creatively convoluted mind could dream up the complexities, wrinkles and complications that arise in actual applications. In this chapter we discuss typical examples of such challenges, ranging from prior constructions in political science applications, to model based data transformation for the display of multivariate marketing data, to challenging posterior simulation for state space models in finance and to expected utility maximization for portfolio selection.

Bayesian Clinical Trials

Innovative clinical trial design is one of the currently most exciting and high impact frontiers in a Bayesian analysis. The increasingly complex nature of clinical study designs and the increasing pressures for efficient and ethical design naturally lead to Bayesian approaches. In this chapter we discuss some examples of specific research problems, including adaptive and sequential trial design, sample size choice determination for longitudinal studies, and subgroup analysis.

Bayesian Influence and Frequentist Interface

Under the Bayesian paradigm to statistical inference the posterior probability distribution contains in principle all relevant information. All statistical inference can be deduced from the posterior distribution by reporting appropriate summaries. This coherent nature of Bayesian inference can give rise to problems when the implied posterior summaries are unduly sensitive to some detail choices of the model. This chapter discusses summaries and diagnostics that highlight such sensitivity and ways to choose a prior probability model to match some desired (frequentist) summaries of the implied posterior inference.

Bayesian Geophysical, Spatial and Temporal Statistics

Spatio-temporal models give rise to many challenging research frontiers in Bayesian analysis. One simple reason is that the spatial and/or time series nature of the data implies complicated dependence structures that require modeling and lead to often challenging inference problems. The power of the Bayesian approach comes to bear especially when inference is desired on aspects of the model that are removed from the data by various levels in the hierarchical model. In this chapter we discuss two examples of such problems and also review the use of non-informative priors in spatial models.

Bayesian Categorical Data Analysis

Some interesting research challenges for Bayesian inference arise from binary and categorical data, including more traditional inference problems like contingency tables with sparse data and case-control studies as well as more recent research frontiers like non-standard link function for binary data regression.

Bayesian Data Mining and Machine Learning

Researchers in machine learning have developed methods for largely automated inference with large data sets. With increasingly more powerful computing resources and ever increasing needs for statistical inference for massive data sets, similar methods are also being developed by researchers in Bayesian analysis. The distinction between machine learning and Bayesian analysis is starting to blur. This chapter discusses several examples of such research.

Bayesian Nonparametrics and Semi-parametrics

One of the fastest growing research areas in Bayesian inference is the study of prior probability models for random distributions, also known as nonparametric Bayesian models. While the literature goes back to the 1970s, nonparametric Bayes remained a highly specialized field until the 1990s when new computational methods facilitated the use of such models for actual data analysis. This eventually led to a barrage of new nonparametric Bayesian literature over the last 10 years. In this chapter we highlight some of the current research challenges in nonparametric Bayes.