NSF-CBMS Regional Conference Series in Probability and Statistics

NSF-CBMS Regional Conference Series in Probability and Statistics

Series information

Nonparametric Bayesian Inference

These notes arose out of a short course at UC Santa Cruz in summer 2010. Like the course, the notes provide an overview of some popular Bayesian nonparametric (BNP) probability models. The discussion follows a logical development of many commonly used nonparametric Bayesian models as generalizations of the Dirichlet process (DP) in different directions, including Pólya tree (PT) models, species sampling models (SSM), dependent DP (DDP) models and product partition models (PPM).

Group Invariance in Applications in Statistics

These lecture notes are a result of the NSF ICBMS Regional Conference held at the University of Michigan, 15-19 June 1987. Topics in invariance with applications in statistics were discussed in a series of eighteen 45 minute lectures.

Empirical Processes

These notes grew from lectures the author gave at the University of Iowa in July of 1988, as part of the NSF-CBMS Regional Conference Series. The aim has been to introduce just enough technique to handle typical nontrivial asymptotic problems in statistics and econometrics. The four substantial examples that represent the applications part of the lectures do not exhaust the possible uses for the theory; they cleanly illustrate specific aspects of the theory.

Stochastic Curve Estimation

These notes are based on a regional set of lectures on curve estimation in the context of independent and dependent observations given at the University of California, Davis during June 1989. Much of these lectures is concerned with probability density or regression function estimation when observations are independent. The character of the asymptotic results (at least locally) is qualitatively the same if the observations are those of a dependent stationary sequence with short-range dependence.

Higher Order Asymptotics

This monograph is based on the author’s CBMS-NSF lectures in August, 1991 at Chapel Hill, North Carolina. Higher order asymptotics itself, like all mathematical tools, is philosophically neutral, and can be effectively used by both Bayesians and frequentists. The frequentist results here concentrate on optimality, but the theory can, in principle, be applied to parametric robustness studies also.

Mixture Models

The mixture model has long been a challenge to the statistician, whether beginner, practitioner or theoretician. Recent times have seen great advances in our understanding of the some basic mathematical features of this model, and these notes are meant to be a unification of the work I have carried out, jointly with many wonderful collaborators, in this area. Based on lectures given in 1993 at a regional conference of the Conference Board of the Mathematical Sciences, the notes are directed toward a mixed audience of advanced graduate students and research workers in this and related areas.

Statistical Inference from Genetic Data on Pedigrees

This monograph is based primarily on material presented at the CBMS Summer Course on Inferences from genetic data on pedigrees given at Michigan Technical University, Houghton, Michigan, in July 1999.

Generalized Linear Mixed Models

This monograph is a fairly accurate account of the lectures the author gave at the CBMS conference with a bit of updating, especially in the bibliographic notes sections that follow each of the later chapters. Compared to the author’s other books, this monograph has much more of a research focus. This monograph is written assuming familiarity with linear models and matrix algebra and some exposure to mixed models and logistic regression. References are given to more standard texts that cover some of the basic material in more depth.

Analysis of Longitudinal and Cluster-Correlated Data

The analysis of data with outcomes measured repeatedly on each subject has experienced several transforming developments in the last twenty years. This monograph presents a unified treatment of modern methods for longitudinal and/or correlated data that have developed during this period.

Bayesian Inference and Computing for Spatial Point Patterns

This monograph results from a CBMS short course given by Alan Gelfand at the University of California at Santa Cruz the week of August 14-18, 2017. It extracts a portion of the lecture material which focuses on spatial point patterns and substantially expands it, in addition to providing introductory material (Chapter 1). The decision to focus on spatial point pattern models reflects the fact that this area of spatial analysis has, arguably, received the least attention in the literature and, even less within the Bayesian community. At this point, the other, more mainstream spatial and spatio-temporal material is discussed and readily available in many books. The monograph provides a forum for presentation of novel Bayesian inference and model fitting material which has been very recently developed by Gelfand and collaborators. This material is predicated on an assumption which currently drives much Bayesian work: if you can fit a Bayesian model and if you can simulate realizations of the model, you can do full Bayesian inference under the model.