Adaptive Polar Sampling with an application to a Bayes measure of Value-at-Risk
نویسندگان
چکیده
Adaptive Polar Sampling (APS) is proposed as a Markov chain Monte Carlo method for Bayesian analysis of models with ill-behaved posterior distributions. In order to sample e ciently from such a distribution, a location-scale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a MetropolisHastings algorithm is applied to sample directions and, conditionally on these, distances are generated by inverting the CDF. A sequential procedure is applied to update the location and scale. Tested on a set of canonical models that feature near non-identi ability, strong correlation, and bimodality, APS compares favourably with the standard Metropolis-Hastings sampler in terms of parsimony and robustness. APS is applied within a Bayesian analysis of a GARCH-mixture model which is used for the evaluation of the Value-at-Risk of the return of the Dow Jones stock index. JEL classi cation: C11, C15, C63
منابع مشابه
Core Discussion Paper 9957 Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-risk
Adaptive Polar Sampling (APS) is proposed as a Markov chain Monte Carlo method for Bayesian analysis of models with ill-behaved posterior distributions. In order to sample efficiently from such a distribution, location-scale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a MetropolisHastings algorithm is applied to sample direct...
متن کاملValue at Risk Estimation using the Kappa Distribution with Application to Insurance Data
The heavy tailed distributions have mostly been used for modeling the financial data. The kappa distribution has higher peak and heavier tail than the normal distribution. In this paper, we consider the estimation of the three unknown parameters of a Kappa distribution for evaluating the value at risk measure. The value at risk (VaR) as a quantile of a distribution is one of the import...
متن کاملEstimation of portfolio efficient frontier by different measures of risk via DEA
In this paper, linear Data Envelopment Analysis models are used to estimate Markowitz efficient frontier. Conventional DEA models assume non-negative values for inputs and outputs. however, variance is the only variable in these models that takes non-negative values. Therefore, negative data models which the risk of the assets had been used as an input and expected return was the output are uti...
متن کاملBayes Networks and Fault Tree Analysis Application in Reliability Estimation (Case Study: Automatic Water Sprinkler System)
In this study, the application of Bayes networks and fault tree analysis in reliability estimation have been investigated. Fault tree analysis is one of the most widely used methods for estimating reliability. In recent years, a method called "Bayes Network" has been used, which is a dynamic method, and information about the probable failure of the system components will be updated according to...
متن کاملApplication of adaptive sampling in fishery part 2: Truncated adaptive cluster sampling designs
There are some experiences that researcher come across quite number of time for very large networks in the initial samples such that they cannot finish the sampling procedure. Two solutions have been proposed and used by marine biologists which we discuss in this article: i) Adaptive cluster sampling based on order statistics with a stopping rule, ii) Restricted adaptive cluster sampling. Until...
متن کامل