An iterative Monte Carlo method for nonconjugate Bayesian analysis

The Gibbs sampler has been proposed as a general method for Bayesian calculation in Gelfand and Smith (1990). However, the predominance of experience to date resides in applications assuming conjugacy where implementation is reasonably straightforward. This paper describes a tailored approximate rejection method approach for implementation of the Gibbs sampler when nonconjugate structure is present. Several challenging applications are presented for illustration.     

Modeling heterogeneity for bivariate survival data by the Weibull distribution

We propose bivariate Weibull regression model with heterogeneity (frailty or random effect) which is generated by Weibull distribution. We assume that the bivariate survival data follow bivariate Weibull of Hanagal (Econ Qual Control 19:83–90, 2004). There are some interesting situations like survival times in genetic epidemiology, dental implants of patients and twin births (both monozygotic and dizygotic) where genetic behavior (which is unknown and random) of patients follows a known frailty distribution. These are the situations which motivate to study this particular model. We propose two-stage maximum likelihood estimation for hierarchical likelihood in the proposed model. We present a small simulation study to compare these estimates with the true value of the parameters and it is observed that these estimates are very close to the true values of the parameters.     

Comparison between the rates of convergence of extremes under linear and under power normalization

By using the theory of the second-order regular variation, we study the rates of the weak convergence of the maximum order statistics under power normalization. The exact rates are obtained in the uniform metric and the total variation metric. The relationship between the rates of convergence under linear and under power normalization is derived. Some illustrative examples are given for comparing the rates of convergence.     

Estimating treatment effects on the marginal recurrent event mean in the presence of a terminating event

In biomedical studies where the event of interest is recurrent (e.g., hospitalization), it is often the case that the recurrent event sequence is subject to being stopped by a terminating event (e.g., death). In comparing treatment options, the marginal recurrent event mean is frequently of interest. One major complication in the recurrent/terminal event setting is that censoring times are not known for subjects observed to die, which renders standard risk set based methods of estimation inapplicable. We propose two semiparametric methods for estimating the difference or ratio of treatment-specific marginal mean numbers of events. The first method involves imputing unobserved censoring times, while the second methods uses inverse probability of censoring weighting. In each case, imbalances in the treatment-specific covariate distributions are adjusted out through inverse probability of treatment weighting. After the imputation and/or weighting, the treatment-specific means (then their difference or ratio) are estimated nonparametrically. Large-sample properties are derived for each of the proposed estimators, with finite sample properties assessed through simulation. The proposed methods are applied to kidney transplant data.     

Locally optimal designs for the simple death process

We demonstrate the existence and uniqueness of optimal observation schedules for discrete observation of the simple death process. Optimality is framed in the sense of observing the process at times that maximise the Fisher information for the death rate. We examine the relationship of our designs with those obtained by other authors for the simple birth process. A number of interesting properties are uncovered. Practical considerations in the application of these designs in an experimental setting are investigated, and we examine the performance of some approximately optimal designs that are usually simpler to implement. We will show that our optimal designs are highly robust to mis-specification of the death rate.     

An alternate version of the conceptual predictive statistic based on a symmetrized discrepancy measure

The conceptual predictive statistic, C_p, is a widely used criterion for model selection in linear regression. C_p serves as an estimator of a discrepancy, a measure that reflects the disparity between the generating model and a fitted candidate model. This discrepancy, based on scaled squared error loss, is asymmetric: an alternate measure is obtained by reversing the roles of the two models in the definition of the measure. We propose a variant of the C_p statistic based on estimating a symmetrized version of the discrepancy targeted by C_p. We claim that the resulting criterion provides better protection against overfitting than C_p, since the symmetric discrepancy is more sensitive towards detecting overspecification than its asymmetric counterpart. We illustrate our claim by presenting simulation results. Finally, we demonstrate the practical utility of the new criterion by discussing a modeling application based on data collected in a cardiac rehabilitation program at University of Iowa Hospitals and Clinics.     

Unaliasing of aliased line component frequencies

This paper is concerned with undoing aliasing effects, which arise from discretely sampling a continuous‐time stochastic process. Such effects are manifested in the frequency‐domain relationships between the sampled and original processes. The authors describe a general technique to undo aliasing effects, given two processes, one being a time‐delayed version of the other. The technique is based on the observations that certain phase information between the two processes is unaffected by sampling, is completely determined by the (known) time delay, and contains sufficient information to undo aliasing effects. The authors illustrate their technique with a simulation example. The theoretical model is motivated by the helioseismological problem of determining modes of solar pressure waves. The authors apply their technique to solar radio data, and conclude that certain low‐frequency modes known in the helioseismology literature are likely the result of aliasing effects. The Canadian Journal of Statistics 38: 116–135; 2010 © 2010 Statistical Society of Canada     

Inference on effect size indices from several two-armed experiments

The statistical inference problem on effect size indices is addressed using a series of independent two-armed experiments from k arbitrary populations. The effect size parameter simply quantifies the difference between two groups. It is a meaningful index to be used when data are measured on different scales. In the context of bivariate statistical models, we define estimators of the effect size indices and propose large sample testing procedures to test the homogeneity of these indices. The null and non-null distributions of the proposed testing procedures are derived and their performance is evaluated via Monte Carlo simulation. Further, three types of interval estimation of the proposed indices are considered for both combined and uncombined data. Lower and upper confidence limits for the actual effect size indices are obtained and compared via bootstrapping. It is found that the length of the intervals based on the combined effect size estimator are almost half the length of the intervals based on the uncombined effect size estimators. Finally, we illustrate the proposed procedures for hypothesis testing and interval estimation using a real data set.