Bayesian stable mixture model of state densities of generalized Chua's circuit

In this paper, the probability density functions (PDFs) of the states of Generalized Chua's Circuit (GCC) have been modeled by Finite Mixture α-Stable (FMαS) distributions which is a Bayesian mixture model of α-stable distributions and it provides semiparametric characterization for the distributions of multiscroll chaotic attractors. Fully Bayesian approach has been applied to estimate the mixture parameters of multimodal distributions corresponding to the multiscroll chaotic attractors

Bayesian inference for hedge funds with stable distribution of returns

Recently, a body of academic literature has focused on the area of stable distributions and their application potential for improving our understanding of the risk of hedge funds. At the same time, research has sprung up that applies standard Bayesian methods to hedge fund evaluation. Little or no academic attention has been paid to the combination of these two topics. In this paper, we consider Bayesian inference for alpha-stable distributions with particular regard to hedge fund performance and risk assessment. After constructing Bayesian estimators for alpha-stable distributions in the context of an ARMA-GARCH time series model with stable innovations, we compare our risk evaluation and prediction results to the predictions of several competing conditional and unconditional models that are estimated in both the frequentist and Bayesian setting. We find that the conditional Bayesian model with stable innovations has superior risk prediction capabilities compared with other approaches and, in particular, produced better risk forecasts of the abnormally large losses that some hedge funds sustained in the months of September and October 2008. --

Segmentation of skin lesions in 2D and 3D ultrasound images using a spatially coherent generalized Rayleigh mixture model

This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images