Simulation-based sequential Bayesian design

We consider simulation-based methods for exploration and maximization of expected utility in sequential decision problems. We consider problems which require backward induction with analytically intractable expected utility integrals at each stage. We propose to use forward simulation to approximate the integral expressions, and a reduction of the allowable action space to avoid problems related to an increasing number of possible trajectories in the backward induction. The artificially reduced action space allows strategies to depend on the full history of earlier observations and decisions only indirectly through a low dimensional summary statistic. The proposed rule provides a finite-dimensional approximation to the unrestricted infinite-dimensional optimal decision rule. We illustrate the proposed approach with an application to an optimal stopping problem in a clinical trial.     

Log-linear models for mutations in the HIV genome

We discuss a general application of categorical data analysis to mutations along the HIV genome. We consider a multidimensional table for several positions at the same time. Due to the complexity of the multidimensional table, we may collapse it by pooling some categories. However, the association between the remaining variables may not be the same as before collapsing. We discuss the collapsibility of tables and the change in the meaning of parameters after collapsing categories. We also address this problem with a log-linear model. We present a parameterization with the consensus output as the reference cell as is appropriate to explain genomic mutations in HIV. We also consider five null hypotheses and some classical methods to address them. We illustrate methods for six positions along the HIV genome, through consideration of all triples of positions.     

Characterizations of distributions through coincidences of semiparametric families

Semiparametric families are families that have both a real parameter and a parameter that is itself a distribution. A number of semiparametric families suitable for lifetime data are introduced: scale, power, frailty (proportional hazards), age, moment, Laplace transform, and convolution parameter families. The coincidence of two families provides a characterization of the underlying distribution. Characterizations of the Weibull, gamma, lognormal, and Gompertz distributions are obtained.     

Riesz inverse Gaussian distributions

The notion of generalized power of a positive definite symmetric matrix and a related notion of generalized Bessel function are used to introduce an extension of the class of matrix generalized inverse Gaussian distributions. The new distributions are shown to arise as conditional distributions of Peirce components of Riesz random matrices. Things are explained in the modern framework of symmetric cones and simple Euclidean Jordan algebra.     

Stochastic volatility modelling in continuous time with general marginal distributions: Inference,prediction and model selection

We compare results for stochastic volatility models where the underlying volatility process having generalized inverse Gaussian (GIG) and tempered stable marginal laws. We use a continuous time stochastic volatility model where the volatility follows an Ornstein–Uhlenbeck stochastic differential equation driven by a Lévy process. A model for long-range dependence is also considered, its merit and practical relevance discussed. We find that the full GIG and a special case, the inverse gamma, marginal distributions accurately fit real data. Inference is carried out in a Bayesian framework, with computation using Markov chain Monte Carlo (MCMC). We develop an MCMC algorithm that can be used for a general marginal model.     

Semiparametric analysis of long-range dependence in nonlinear regression

This paper establishes consistency and asymptotic distribution theory for the least squares estimate of a vector parameter of non-linear regression with long-range dependent noise. A covariance-based estimate of the memory parameter is proposed. The consistency of the estimate is established.     

Private versus public financing of education and endogenous growth

This paper examines interactions between education policy and growth. The analysis is carried out in an OLG model with two types of individuals: skilled and unskilled. An increase in public education reduces private costs of education, increases the proportion of skilled individuals, and tends to promote growth. On the other hand, education spending crowds out physical capital and reduces learning-by-doing. A marginal increase in the education subsidy can lower growth. It is yet shown that pure public education maximizes the long-run growth rate. Importantly, a partial subsidy to education can result in lower growth than pure private education. Received: 7 March 1999/Accepted: 25 November 1999     

A tale of two countries: The Craig–Sakamoto–Matusita theorem

This paper has a long history. Junjiro Ogawa and I have been friends and collaborators for many years. We started this joint paper in the early 1990s and prepared a draft in September 1995. However, we were trying to improve and simplify some of the proofs, and we revised the paper in January 1998. But circumstances were such that we did not submit the paper, but planned to find further simplifications. Junjiro's untimely death in 2003 brought it forth again. Junjiro always liked this topic, and I am pleased to submit this joint paper in his memory. This paper contains both an historical summary as well as several new results. (Ingram Olkin)     

Connections of the Poisson weight function to overdispersion and underdispersion

In this paper, we establish several connections of the Poisson weight function to overdispersion and underdispersion. Specifically, we establish that the logconvexity (logconcavity) of the mean weight function is a necessary and sufficient condition for overdispersion (underdispersion) when the Poisson weight function does not depend on the original Poisson parameter. We also discuss some properties of the weighted Poisson distributions (WPD). We then introduce a notion of pointwise duality between two WPDs and discuss some associated properties. Next, we present some illustrative examples and provide a discussion on various Poisson weight functions used in practice. Finally, some concluding remarks are made.     

Erratum to “Progressively Type-II right censored order statistics from discrete distributions” [J. Statist. Plann. Inference 138 (2008) 845–856]

In this note, we correct the proof of Representation 1 of Balakrishnan and Dembińska [2008. Progressively Type-II right censored order statistics from discrete distributions. J. Statist. Plann. Inference 138, 845–856] which relates the joint distribution of progressively Type-II right censored order statistics corresponding to an arbitrary population to progressively Type-II right censored order statistics from the standard uniform distribution.