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. --

Bayesian Cointegrated Vector Autoregression models incorporating Alpha-stable noise for inter-day price movements via Approximate Bayesian Computation

We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction model (ECM) framework. This involves developing a novel matrix variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and Alpha-stable errors inter-day in the ECM framework. To achieve this we derive a novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR) representation of Alpha-stable inter-day innovations. These results are generalized to asymmetric models for the innovation noise at inter-day boundaries allowing for skewed Alpha-stable models. Our proposed model and sampling methodology is general, incorporating the current literature on Gaussian models as a special subclass and also allowing for price series level shifts either at random estimated time points or known a priori time points. We focus analysis on regularly observed non-Gaussian level shifts that can have significant effect on estimation performance in statistical models failing to account for such level shifts, such as at the close and open of markets. We compare the estimation accuracy of our model and estimation approach to standard frequentist and Bayesian procedures for CVAR models when non-Gaussian price series level shifts are present in the individual series, such as inter-day boundaries. We fit a bi-variate Alpha-stable model to the inter-day jumps and model the effect of such jumps on estimation of matrix-variate CVAR model parameters using the likelihood based Johansen procedure and a Bayesian estimation. We illustrate our model and the corresponding estimation procedures we develop on both synthetic and actual data.Comment: 30 page

Bayesian analysis of finite mixture distributions using the allocation sampler

Finite mixture distributions are receiving more and more attention from statisticians in many different fields of research because they are a very flexible class of models. They are typically used for density estimation or to model population heterogeneity. One can think of a finite mixture distribution as grouping the observations into components from which they are assumed to have arisen. In certain settings these groups have a physical interpretation. The interest in these distributions has been boosted recently because of the ever increasing computer power available to researchers to carry out the computationally intensive tasks required in their analysis. In order to fit a finite mixture distribution taking a Bayesian approach a posterior distribution has to be evaluated. When the number of components in the model is assumed known this posterior distribution can be sampled from using methods such as Data Augmentation or Gibbs sampling (Tanner and Wong (1987) and Gelfand and Smith (1990)) and the Metropolis-Hastings algorithm (Hastings (1970)). However, the number of components in the model can also be considered an unknown and an object of inference. Richardson and Green (1997) and Stephens (2000a) both describe Bayesian methods to sample across models with different numbers of components. This enables an estimate of the posterior distribution of the number of components to be evaluated. Richardson and Green (1997) define a reversible jump Markov chain Monte Carlo (RJMCMC) sampler while Stephens (2000a) uses a Markov birth-death process approach sample from the posterior distribution. In this thesis a Markov chain Monte Carlo method, named the allocation sampler. This sampler differs from the RJMCMC method reported in Richardson and Green (1997) because the state space of the sampler is simplified by the assumption that the components' parameters and weights can be analytically integrated out of the model. This in turn has the advantage that only minimal changes are required to the sampler for mixtures of components from other parametric families. This thesis illustrates the allocation sampler's performance on both simulated and real data sets. Chapter 1 provides a background to finite mixture distributions and gives an overview of some inferential techniques that have already been used to analyse these distributions. Chapter 2 sets out the Bayesian model framework that is used throughout this thesis and defines all the required distributional results. Chapter 3 describes the allocation sampler. Chapter 4 tests the performance of the allocation sampler using simulated datasets from a collection of 15 different known mixture distributions. Chapter 5 illustrates the allocation sampler with real datasets from a number of different research fields. Chapter 6 summarises the research in the thesis and provides areas of possible future research

Statistical Modeling of SAR Images: A Survey

Statistical modeling is essential to SAR (Synthetic Aperture Radar) image interpretation. It aims to describe SAR images through statistical methods and reveal the characteristics of these images. Moreover, statistical modeling can provide a technical support for a comprehensive understanding of terrain scattering mechanism, which helps to develop algorithms for effective image interpretation and creditable image simulation. Numerous statistical models have been developed to describe SAR image data, and the purpose of this paper is to categorize and evaluate these models. We first summarize the development history and the current researching state of statistical modeling, then different SAR image models developed from the product model are mainly discussed in detail. Relevant issues are also discussed. Several promising directions for future research are concluded at last

The Cross-Section of Investing Skill

Building on insights from the economics of superstars, I develop an efficient method for estimating the skill of mutual fund managers. Outliers are especially helpful for disentangling skill from luck when I explicitly model the cross-sectional distribution of managerial skill using a flexible and realistic function. Forecasted performance is dramatically improved relative to standard regression estimates: an investor selecting (avoiding) the best (worst) decile of funds would improve risk-adjusted performance by 2% (3%) annually. The distribution of skill is found to be fat-tailed and positively skewed, providing a theoretical explanation for the convexity of fund flows