Bayesian Nonparametric Analysis for a Generalized Dirichlet Process Prior

2005 ◽  
Vol 8 (3) ◽  
pp. 283-309 ◽  
Author(s):  
Antonio Lijoi ◽  
Ramsés H. Mena ◽  
Igor Prünster
Keyword(s):  
Dirichlet Process ◽  
Nonparametric Analysis ◽  
Bayesian Nonparametric ◽  
Dirichlet Process Prior ◽  
Generalized Dirichlet

scholarly journals Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis

2018 ◽  
Vol 11 (3) ◽  
pp. 52 ◽  
Author(s):  
Mark Jensen ◽  
John Maheu
Keyword(s):  
Dirichlet Process ◽  
Joint Distribution ◽  
Nonparametric Model ◽  
Bayesian Nonparametric ◽  
Excess Returns ◽  
Dirichlet Process Prior ◽  
Stock Market Returns ◽  
Conditional Mean ◽  
Risk Return ◽  
Volatility Feedback

In this paper, we let the data speak for itself about the existence of volatility feedback and the often debated risk–return relationship. We do this by modeling the contemporaneous relationship between market excess returns and log-realized variances with a nonparametric, infinitely-ordered, mixture representation of the observables’ joint distribution. Our nonparametric estimator allows for deviation from conditional Gaussianity through non-zero, higher ordered, moments, like asymmetric, fat-tailed behavior, along with smooth, nonlinear, risk–return relationships. We use the parsimonious and relatively uninformative Bayesian Dirichlet process prior to overcoming the problem of having too many unknowns and not enough observations. Applying our Bayesian nonparametric model to more than a century’s worth of monthly US stock market returns and realized variances, we find strong, robust evidence of volatility feedback. Once volatility feedback is accounted for, we find an unambiguous positive, nonlinear, relationship between expected excess returns and expected log-realized variance. In addition to the conditional mean, volatility feedback impacts the entire joint distribution.

scholarly journals Experience rating with Poisson mixtures

2015 ◽  
Vol 9 (2) ◽  
pp. 304-321 ◽  
Author(s):  
Garfield O. Brown ◽  
Winston S. Buckley
Keyword(s):  
Life Insurance ◽  
Dirichlet Process ◽  
Posterior Probability ◽  
Mixture Distribution ◽  
Reversible Jump ◽  
Dirichlet Process Prior ◽  
Poisson Mixtures ◽  
Group Life ◽  
Insurance Portfolio ◽  
Poisson Mixture Model

AbstractWe propose a Poisson mixture model for count data to determine the number of groups in a Group Life insurance portfolio consisting of claim numbers or deaths. We take a non-parametric Bayesian approach to modelling this mixture distribution using a Dirichlet process prior and use reversible jump Markov chain Monte Carlo to estimate the number of components in the mixture. Unlike Haastrup, we show that the assumption of identical heterogeneity for all groups may not hold as 88% of the posterior probability is assigned to models with two or three components, and 11% to models with four or five components, whereas models with one component are never visited. Our major contribution is showing how to account for both model uncertainty and parameter estimation within a single framework.

A matrix-variate dirichlet process to model earthquake hypocentre temporal patterns

2020 ◽  
pp. 1471082X2093976
Author(s):  
Meredith A. Ray ◽  
Dale Bowman ◽  
Ryan Csontos ◽  
Roy B. Van Arsdale ◽  
Hongmei Zhang
Keyword(s):  
Dirichlet Process ◽  
Temporal Pattern ◽  
Temporal Trends ◽  
Temporal Patterns ◽  
The United States ◽  
Seismic Zone ◽  
Clustering Methods ◽  
Dirichlet Process Prior ◽  
And Performance ◽  
Over Time

Earthquakes are one of the deadliest natural disasters. Our study focuses on detecting temporal patterns of earthquakes occurring along intraplate faults in the New Madrid seismic zone (NMSZ) within the middle of the United States from 1996–2016. Based on the magnitude and location of each earthquake, we developed a Bayesian clustering method to group hypocentres such that each group shared the same temporal pattern of occurrence. We constructed a matrix-variate Dirichlet process prior to describe temporal trends in the space and to detect regions showing similar temporal patterns. Simulations were conducted to assess accuracy and performance of the proposed method and to compare to other commonly used clustering methods such as Kmean, Kmedian and partition-around-medoids. We applied the method to NMSZ data to identify clusters of temporal patterns, which represent areas of stress that are potentially migrating over time. This information can then be used to assist in the prediction of future earthquakes.

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