Generalized Laplacian approximations in Bayesian inference

This paper presents a new Laplacian approximation to the posterior density of η = g(θ). It has a simpler analytical form than that described by Leonard et al. (1989). The approximation derived by Leonard et al. requires a conditional information matrix R_η to be positive definite for every fixed η. However, in many cases, not all R_η are positive definite. In such cases, the computations of their approximations fail, since the approximation cannot be normalized. However, the new approximation may be modified so that the corresponding conditional information matrix can be made positive definite for every fixed η. In addition, a Bayesian procedure for contingency-table model checking is provided. An example of cross-classification between the educational level of a wife and fertility-planning status of couples is used for explanation. Various Laplacian approximations are computed and compared in this example and in an example of public school expenditures in the context of Bayesian analysis of the multiparameter Fisher-Behrens problem.     

The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

Bayesian analysis of outlier problems using divergence measures

A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling-based approach using a Gibbs or Metropolis-within-Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.     

Two point priors and Γ-minimax estimating in families of uniform distributions

It is shown that when a parameter lying in a sufficiently small interval is to be estimated in a family of uniform distributions, a two point prior is least favourable under squared error loss. The unique Bayes estimator with respect to this prior is minimax. The Γ-minimax estimator is derived for sets Γ of priors consisting of all priors that give fixed probabilities to two specified subintervals of the parameter space if a two point prior is least favourable in Γ.     

India's demand for international reserve and monetary disequilibrium: Reserve adequacy under floating regime

The main aim of this study is to investigate India's demand for international reserve by focusing on the role of national monetary disequilibrium and to present new benchmarks for assessing the adequacy of international reserves. We assessed India's position in terms of reserve adequacy and found that India is well placed and has sufficient stock of international reserves to meet the minimum adequacy requirements. Also, the results reveal that the central bank is holding substantial excess reserves and the related opportunity cost (1.5% of GDP) appears to be quite considerable. Further, the estimates of reserve demand function suggest that scale of foreign trade, uncertainty and profitability considerations play significant role in determining India's long-term reserve demand policies. More importantly, validating the monetary approach to balance of payment, our results show that national monetary disequilibrium does play a crucial role in short-run reserve movements. An excess of money demand (supply) induces an inflow (outflow) of international reserves with an elasticity of 0.56 which also implies that Reserve Bank of India responds to correct the domestic money market disequilibrium; and did not just leave it completely on the mercy of reserve inflows.     

Two-stage Huber estimation

In this paper we propose a new robust estimator in the context of two-stage estimation methods directed towards the correction of endogeneity problems in linear models. Our estimator is a combination of Huber estimators for each of the two stages, with scale corrections implemented using preliminary median absolute deviation estimators. In this way we obtain a two-stage estimation procedure that is an interesting compromise between concerns of simplicity of calculation, robustness and efficiency. This method compares well with other possible estimators such as two-stage least-squares (2SLS) and two-stage least-absolute-deviations (2SLAD), asymptotically and in finite samples. It is notably interesting to deal with contamination affecting more heavily the distribution tails than a few outliers and not losing as much efficiency as other popular estimators in that case, e.g. under normality. An additional originality resides in the fact that we deal with random regressors and asymmetric errors, which is not often the case in the literature on robust estimators.     

On the detection of changes in autoregressive time series I. Asymptotics

Various test statistics are discussed which can be used for detecting changes in the parameters of an autoregressive time series. In this first part of our study, the limiting behavior of the test statistics is derived under the null hypothesis of no change as well as under alternatives. In a forthcoming second part of our investigation, these asymptotic results will be compared to some corresponding bootstrap procedures, and a small simulation study will be conducted.     

Bayesian design in queues: An application to aeronautic maintenance

We exploit Bayesian criteria for designing M/M/c//r$M/M/c//r$ queueing systems with spares. For illustration of our approach we use a real problem from aeronautic maintenance, where the numbers of repair crews and spare planes must be sufficiently large to meet the necessary operational capacity. Bayesian guarantees for this to happen can be given using predictive or posterior distributions.     

On a multiple endpoints testing problem

In a clinical trial comparing drug with placebo, where there are multiple primary endpoints, we consider testing problems where an efficacious drug effect can be claimed only if statistical significance is demonstrated at the nominal level for all endpoints. Under the assumption that the data are multivariate normal, the multiple endpoint-testing problem is formulated. The usual testing procedure involves testing each endpoint separately at the same significance level using two-sample t-tests, and claiming drug efficacy only if each t-statistic is significant. In this paper we investigate properties of this procedure. We show that it is identical to both an intersection union test and the likelihood ratio test. A simple expression for the p-value is given. The level and power function are studied; it is shown that the test may be conservative and that it is biased. Computable bounds for the power function are established.