Journal of Data Science

Abstract: The concept of frailty provides a suitable way to introduce random effects in the model to account for association and unobserved heterogeneity. In its simplest form, a frailty is an unobserved random factor that modifies multiplicatively the hazard function of an individual or a group or cluster of individuals. In this paper, we study positive stable distribution as frailty distribution and two different baseline distributions namely Pareto and linear failure rate distribution. We estimate parameters of proposed models by introducing Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique. In the present study a simulation is done to compare the true values of parameters with the estimated value. We try to fit the proposed models to a real life bivariate survival data set of McGrilchrist and Aisbett (1991) related to kidney infection. Also, we present a comparison study for the same data by using model selection criterion, and suggest a better model.

Abstract: While conducting a social survey on stigmatized/sensitive traits, obtaining efficient (truthful) data is an intricate issue and estimates are generally biased in such surveys. To obtain trustworthy data and to reduce false response bias, a technique, known as randomized response technique, is now being used in many surveys. In this study, we performed a Bayesian analysis of a general class of randomized response models. Suitable simple Beta prior and mixture of Beta priors are used in a common prior structure to obtain the Bayes estimates for the proportion of a stigmatized/sensitive attributes in the population of interest. We also extended our proposal to stratified random sampling. The Bayes and the maximum likelihood estimators are compared. For further understanding of variability, we have also compared the prior and posterior distributions for different values of the design constants through graphs and credible intervals. The condition to develop a new randomized response model is also discussed.

This article discusses the estimation of the Generalized Power Weibull parameters using the maximum product spacing (MPS) method, the maximum likelihood (ML) method and Bayesian estimation method under squares error for loss function. The estimation is done under progressive type-II censored samples and a comparative study among the three methods is made using Monte Carlo Simulation. Markov chain Monte Carlo (MCMC) method has been employed to compute the Bayes estimators of the Generalized Power Weibull distribution. The optimal censoring scheme has been suggested using two different optimality criteria (mean squared of error, Bias and relative efficiency). A real data is used to study the performance of the estimation process under this optimal scheme in practice for illustrative purposes. Finally, we discuss a method of obtaining the optimal censoring scheme.

Abstract: This article concerns the Bayesian estimation of interest rate mod els based on Euler-Maruyama approximation. Assume the short term inter est rate follows the CIR model, an iterative method of Bayesian estimation is proposed. Markov Chain Monte Carlo simulation based on Gibbs sam pler is used for the posterior estimation of the parameters. The maximum A-posteriori estimation using the genetic algorithm is employed for finding the Bayesian estimates of the parameters. The method and the algorithm are calibrated with the historical data of US Treasury bills.

Abstract: In this paper, we propose a nonparametric approach using the Dirichlet processes (DP) as a class of prior distributions for the distribution G of the random effects in the hierarchical generalized linear mixed model (GLMM). The support of the prior distribution (and the posterior distribution) is large, allowing for a wide range of shapes for G. This provides great flexibility in estimating G and therefore produces a more flexible estimator than does the parametric analysis. We present some computation strategies for posterior computations involved in DP modeling. The proposed method is illustrated with real examples as well as simulations.