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Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed‐effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed‐effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed‐effects state‐space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew‐t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG‐315) clinical trial data set. [ABSTRACT FROM AUTHOR]

In this article, we introduce a likelihood-based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood-based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high-dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a robust extension of the three-factor model of Diebold and Li ( J. Econometrics, 130: 337-364, 2006) using the class of symmetric scale mixtures of normal distributions. Specific distributions examined include the multivariate normal, Student- t, slash, and variance gamma distributions. In the presence of non-normality in the data, these distributions provide an appealing robust alternative to the routine use of the normal distribution. Using a Bayesian paradigm, we developed an efficient MCMC algorithm for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. Our results reveal that the Diebold-Li models based on the Student- t and slash distributions provide significant improvement in in-sample fit and out-of-sample forecast to the US yield data than the usual normal-based model. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Bivariate clustered (correlated) data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model (LMM) framework with underlying normality assumptions of the random effects and within-subject errors. However, such normality assumptions might be questionable if the data set particularly exhibits skewness and heavy tails. Using a Bayesian paradigm, we use the skew-normal/independent (SNI) distribution as a tool for modeling clustered data with bivariate non-normal responses in an LMM framework. The SNI distribution is an attractive class of asymmetric thick-tailed parametric structure which includes the skew-normal distribution as a special case. We assume that the random effects follow multivariate SNI distributions and the random errors follow SNI distributions which provides substantial robustness over the symmetric normal process in an LMM framework. Specific distributions obtained as special cases, viz. the skew- t, the skew-slash and the skew-contaminated normal distributions are compared, along with the default skew-normal density. The methodology is illustrated through an application to a real data which records the periodontal health status of an interesting population using periodontal pocket depth (PPD) and clinical attachment level (CAL). Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The modified mixture model with Markov switching volatility specification is introduced to analyze the relationship between stock return volatility and trading volume. We propose to construct an algorithm based on Markov chain Monte Carlo simulation methods to estimate all the parameters in the model using a Bayesian approach. The series of returns and trading volume of the British Petroleum stock will be analyzed. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]