A markov regression model for the analysis of the postpartum lactational amenorrhea

Failure time data represent a particular case of binary longitudinal data. The corresponding analysis of the effect of explanatory covariates repeatedly collected over time on the failure rate has been largely facilitated by the Cox semi-parametric regression model. However, neither the interpretation of the estimated parameters associated with time-dependent covariates is straight-forward, nor does this model fully account for the dynamics of the effect of a covariate over time. Markovian regression models appear as complementary tools to address these specific issues from the predictive point of view. We illustrate these aspects using data from the WHO multicenter study, which was designed to analyze the relation between the duration of postpartum lactational amenorrhea and the breastfeeding pattern. One of the main advantage of this approach applied to the field of reproductive epidemiology was to provide a flexible tool, easily and directly understood by clinicians and fieldworkers, for simulating situations, which were still unobserved, and to predict their effects on the duration of amenorrhea.     

Monte Carlo Methods for Bayesian Inference on the Linear Hazard Rate Distribution

The Bayesian estimation and prediction problems for the linear hazard rate distribution under general progressively Type-II censored samples are considered in this article. The conventional Bayesian framework as well as the Markov Chain Monte Carlo (MCMC) method to generate the Bayesian conditional probabilities of interest are discussed. Sensitivity of the prior for the model is also examined. The flood data on Fox River, Wisconsin, from 1918 to 1950, are used to illustrate all the methods of inference discussed in this article.     

Bayesian Estimation of the Parameters of Bivariate Exponential Distributions

In this article, we develop an empirical Bayesian approach for the Bayesian estimation of parameters in four bivariate exponential (BVE) distributions. We have opted for gamma distribution as a prior for the parameters of the model in which the hyper parameters have been estimated based on the method of moments and maximum likelihood estimates (MLEs). A simulation study was conducted to compute empirical Bayesian estimates of the parameters and their standard errors. We use moment estimators or MLEs to estimate the hyper parameters of the prior distributions. Furthermore, we compare the posterior mode of parameters obtained by different prior distributions and the Bayesian estimates based on gamma priors are very close to the true values as compared to improper priors. We use MCMC method to obtain the posterior mean and compared the same using the improper priors and the classical estimates, MLEs.     

Online change detection of Markov chains with unknown post-change transition probabilities

ABSTRACT

In this paper, we investigate the performance of cumulative sum (CUSUM) stopping rules for the online detection of unknown change point in a time homogeneous Markov chain. Under the condition that the post-change transition probabilities are unknown, we proposed two CUSUM type schemes for the detection. The first scheme is based on the maximum likelihood estimates of the post-change transition probabilities. This scheme is limited by its computation burden, which is mitigated by another scheme based on the reference transition probabilities selected from a prior known region. We give the bounds of the mean delay time and the mean time between false alarms to illustrate the effectiveness of the proposed schemes. The results of the simulation also demonstrate the feasibility of the proposed schemes.     

Minimizing Upper Bound of Ruin Probability Under Discrete Risk Model with Markov Chain Interest Rate

This article focuses on minimal upper bound of ruin probability for a discrete time risk model with Markov chain interest rate and stochastic investment return. The interest rate of bond market is assumed to be a stationary Markov chain, and the return process of a stock market can be negative. This article presents two kinds of methods for minimizing the upper bound of ruin probability. One method relies on recursive equations for finite time ruin probabilities and inductive approach, the other one depends on martingale approach. Numerical examples show that the martingale approach is better than the inductive one.     

Comparison of Shared Frailty Models for Kidney Infection Data under Exponential Power Baseline Distribution

Shared frailty models are often used to model heterogeneity in survival analysis. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, four shared frailty models with frailty distribution gamma, inverse Gaussian, compound Poisson, and compound negative binomial with exponential power as baseline distribution are proposed. These models are fitted using Markov Chain Monte Carlo methods. These models are illustrated with a real life bivariate survival data set of McGilchrist and Aisbett (1991) related to kidney infection, and the best model is suggested for the data using different model comparison criteria.     

A transitional Markov switching autoregressive model

ABSTRACT

This paper is concerned with properties of a transitional Markov switching autoregressive (TMSAR) model, together with its maximum-likelihood estimation and inference. We extend existing MSAR models by allowing dependence of AR parameters on hidden states at time points prior to the current time t. A stationary solution is given and expressions for the theoretical autocovariance function are derived. Two time series are analyzed and the new model outperforms two existing MSAR models in terms of maximized log-likelihood, residual correlations, and one-step-ahead forecasting performance. The new model also gives more regime changes in agreement with real events.     

A Bayesian random effects model for analyzing mixed negative binomial and continuous longitudinal responses

ABSTRACT

A general Bayesian random effects model for analyzing longitudinal mixed correlated continuous and negative binomial responses with and without missing data is presented. This Bayesian model, given some random effects, uses a normal distribution for the continuous response and a negative binomial distribution for the count response. A Markov Chain Monte Carlo sampling algorithm is described for estimating the posterior distribution of the parameters. This Bayesian model is illustrated by a simulation study. For sensitivity analysis to investigate the change of parameter estimates with respect to the perturbation from missing at random to not missing at random assumption, the use of posterior curvature is proposed. The model is applied to a medical data, obtained from an observational study on women, where the correlated responses are the negative binomial response of joint damage and continuous response of body mass index. The simultaneous effects of some covariates on both responses are also investigated.     

Penalized maximum likelihood estimation for Gaussian hidden Markov models

ABSTRACT

The likelihood function of a Gaussian hidden Markov model is unbounded, which is why the maximum likelihood estimator (MLE) is not consistent. A penalized MLE is introduced along with a rigorous consistency proof.