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This paper is concerned with Bayesian analysis of the proportional hazard model with left truncated and right censored data. We use a process neutral to the right as the prior of the baseline survival function and a finite-dimensional prior is placed on the regression coefficient. We then obtain the exact form of the joint posterior distribution of the regression coefficient and the baseline cumulative hazard function. As a by-product, we prove the propriety of the posterior distribution with th

Selection models are appropriate when a datum x enters the sample only with probability or weight w(x). It is typically assumed that the weight function w is monotone, but the precise functional form of the weight function is often unknown. In this article, the Dirichlet process prior, centered on a parametric form, is used as a prior distribution on the weight function. This allows for incorporation of knowledge about the weight function, without restricting it to be of some particular function

Since Ferguson's seminal article on the Dirichlet process, the area of Bayesian nonparametric statistics has seen development of many flexible prior classes. At the center of the development lies the neutral to the right (NTR) process proposed by Doksum. Although the class of NTR processes is very rich in its members and has well-developed theoretical properties, its application has been restricted to very small portions of the class—mainly the Dirichlet, gamma, and beta processes. We believe th

The highly enantioselective aza-Michael reaction of <i>tert</i>-butyl β-naphthylmethoxycarbamate to cyclic enones has been accomplished by using a new <i>cinchona</i> alkaloid derived C(9)-urea ammonium catalyst under phase-transfer catalysis conditions with up to 98% ee at 0 °C. The resulting aza-Michael adducts can be converted to versatile intermediates by selective deprotection and the cyclic 1,3-aminoalcohols by diastereoselective reduction with up to 32:1, which have been widely used as im

Bayesian additive regression trees (BART) is a nonparametric model that is known for its flexibility and strong statistical foundation. To address a robust and flexible approach to analyse ordinal data, we extend BART into an ordered probit regression framework (OPBART). Further, we propose a semiparametric setting for OPBART (semi‐OPBART) to model covariates of interest parametrically and confounding variables nonparametrically. We also provide Gibbs sampling procedures to implement the propose

Abstract Ozonesondes collect data relevant to ozone level at various altitudes. Modeling these data involves a combination of spatial and temporal modeling. The spatial component can be conveniently modeled as a four component mixture of normal distributions. The (relatively few) parameters of this mixture can then be modeled in a time‐dependent fashion, via a dynamic linear model. Computations are carried out via Markov chain Monte Carlo methods. Copyright © 2003 John Wiley &amp; Sons, Ltd.

We review the class of species sampling models (SSM). In particular, we investigate the relation between the exchangeable partition probability function (EPPF) and the predictive probability function (PPF). It is straightforward to define a PPF from an EPPF, but the converse is not necessarily true. In this paper we introduce the notion of putative PPFs and show novel conditions for a putative PPF to define an EPPF. We show that all possible PPFs in a certain class have to define (unnormalized)