Journal of Data Science

Abstract: A Bayesian hierarchical model is developed for multiple com parisons in mixed models with missing values where the population means satisfy a simple order restriction. We employ the Gibbs sampling and Metropolis-within-Gibbs sampling techniques to obtain parameter estimates and estimates of the posterior probabilities of the equality of the mean pairs. The latter estimates are used to test whether any two means are significantly different, and to test the global hypothesis of the equality of all means. The performance of the model is investigated in simulations by means of both multiple imputations and ignoring missingness. We also illustrate the utility of the model in a real data set. The results show that the proposed hierarchical model can effectively unify parameter estimation, multiple imputations, and multiple comparisons in one setting.

In this paper an attempt has been made to analyze the child mortality by use of a hazard model in Bayesian environment, family effect through multiplicative random effect is also incorporated in the model. For fitting this model real data has taken from District Level Household and Facility Survey (DLHS)-3. The largest state (in population) of India i.e. Uttar Pradesh data is taken for analysis. Deviance information criteria are used for comparison of models. It found that the model with family frailty gives better fit. All the analysis is performed in winBUGS software, which is used Markov chain monte carlo simulation under gibbs sampling.

Abstract: This paper discusses a comprehensive statistical approach that will be useful in answering health-related questions concerning mortality and incidence rates of chronic diseases such as cancer and hypertension. The developed spatio-temporal models will be useful to explain the patterns of mortality rates of chronic disease in terms of environmental changes and social-economic conditions. In addition to age and time effects, models include two components of normally distributed residual effects and spatial effects, one to represent average regional effects and another to represent changes of subgroups within region over time. Numerical analysis is based on male lung cancer mortality data from the state of Missouri. Gibbs sampling is used to obtain the posterior quantities. As a result, all models discussed in this article fit well in stabilizing the mortality rates, especially in the less populated areas. Due to the richness of hierarchical settings, easy interpretation of parameters and ease of implementation, any models proposed in this paper can be applied generally to other sets of data.

Abstract: We have extended some previous works by applying the product partition model (PPM) to identify multiple change points in the variance of normal data sequence assuming mean equal to zero. This type of problem is very common in applied economics and finance. We consider the Gibbs sampling scheme proposed in the literature to obtain the posterior estimates or product estimates for the variance and the posterior distributions for the instants when changes take place and also for the number of change points in the sequence. The PPM is used to obtain the posterior behavior of the volatility (measured as the variance) in the series of returns of four important Latin American stock indexes (MERVAL-Argentina, IBOVESPABrazil, IPSA-Chile and IPyC-Mexico). The posterior number of change point as well as the posterior most probable partition for each index series are also obtained.