A note on the posterior inference for the Yule–Simon distribution

The Yule–Simon distribution has been out of the radar of the Bayesian community, so far. In this note, we propose an explicit Gibbs sampling scheme when a Gamma prior is chosen for the shape parameter. The performance of the algorithm is illustrated with simulation studies, including count data regression, and a real data application to text analysis. We compare our proposal to the frequentist counterparts showing better performance of our algorithm when a small sample size is considered.     

The relationship of trauma exposure to sex offending behavior among male juvenile offenders

The most common type of adult and juvenile sex offender treatment utilizes a Relapse Prevention (RP) model. In RP clients learn about their offense cycle with an emphasis on recognizing high-risk situations and negative emotional states that can be precursors or triggers to offending behavior. This study identifies ways that traumatic experiences and trauma-associated feelings can be offense triggers for juvenile sex offenders. Researchers interviewed the treating clinicians of 40 male juvenile sex offenders who received at least six months of RP sex offender treatment. Results showed that 95% of the youths had experienced a Post Traumatic Stress Disorder (PTSD) Criterion A traumatic event and that 65% met criteria for PTSD based on clinician judgments. Overall, clinicians identified prior trauma exposure as being related to the offense triggers in 85% of offenders. Specifically, the following trauma-related feelings were identified as offense triggers: intense fear in 37.5% of sex offenders, helplessness in 55%, and horror in 20%. Implications for sex offender treatment programs are discussed.     

Loss-based approach to two-piece location-scale distributions with applications to dependent data

Two-piece location-scale models are used for modeling data presenting departures from symmetry. In this paper, we propose an objective Bayesian methodology for the tail parameter of two particular distributions of the above family: the skewed exponential power distribution and the skewed generalised logistic distribution. We apply the proposed objective approach to time series models and linear regression models where the error terms follow the distributions object of study. The performance of the proposed approach is illustrated through simulation experiments and real data analysis. The methodology yields improvements in density forecasts, as shown by the analysis we carry out on the electricity prices in Nordpool markets.

     

A Bootstrap Likelihood Approach to Bayesian Computation

There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the problems with these algorithms is that their performance depends on the appropriate choice of summary statistics, distance measure and tolerance level. To circumvent this problem, an alternative method based on the empirical likelihood has been introduced. This method can be easily implemented when a set of constraints, related to the moments of the distribution, is specified. However, the choice of the constraints is sometimes challenging. To overcome this difficulty, we propose an alternative method based on a bootstrap likelihood approach. The method is easy to implement and in some cases is actually faster than the other approaches considered. We illustrate the performance of our algorithm with examples from population genetics, time series and stochastic differential equations. We also test the method on a real dataset.     

Interacting multiple try algorithms with different proposal distributions

We introduce a new class of interacting Markov chain Monte Carlo (MCMC) algorithms which is designed to increase the efficiency of a modified multiple-try Metropolis (MTM) sampler. The extension with respect to the existing MCMC literature is twofold. First, the sampler proposed extends the basic MTM algorithm by allowing for different proposal distributions in the multiple-try generation step. Second, we exploit the different proposal distributions to naturally introduce an interacting MTM mechanism (IMTM) that expands the class of population Monte Carlo methods and builds connections with the rapidly expanding world of adaptive MCMC. We show the validity of the algorithm and discuss the choice of the selection weights and of the different proposals. The numerical studies show that the interaction mechanism allows the IMTM to efficiently explore the state space leading to higher efficiency than other competing algorithms.