Prediction intervals with a Dirichlet-process prior distribution

1982 ◽  
Vol 10 (2) ◽  
pp. 103-111 ◽  
Author(s):  
Gregory Campbell ◽  
Myles Hollander
Keyword(s):  
Dirichlet Process ◽  
Prior Distribution ◽  
Prediction Intervals ◽  
Dirichlet Process Prior

scholarly journals Dirichlet Process Prior for Student’s t Graph Variational Autoencoders

2021 ◽  
Vol 13 (3) ◽  
pp. 75
Author(s):  
Yuexuan Zhao ◽  
Jing Huang
Keyword(s):  
Latent Variables ◽  
Dirichlet Process ◽  
Prior Distribution ◽  
Standard Normal Distribution ◽  
Dirichlet Process Prior ◽  
External Relations ◽  
Latent Features ◽  
Standard Normal ◽  
Heavy Tailed ◽  
Student’S T

Graph variational auto-encoder (GVAE) is a model that combines neural networks and Bayes methods, capable of deeper exploring the influential latent features of graph reconstruction. However, several pieces of research based on GVAE employ a plain prior distribution for latent variables, for instance, standard normal distribution (N(0,1)). Although this kind of simple distribution has the advantage of convenient calculation, it will also make latent variables contain relatively little helpful information. The lack of adequate expression of nodes will inevitably affect the process of generating graphs, which will eventually lead to the discovery of only external relations and the neglect of some complex internal correlations. In this paper, we present a novel prior distribution for GVAE, called Dirichlet process (DP) construction for Student’s t (St) distribution. The DP allows the latent variables to adapt their complexity during learning and then cooperates with heavy-tailed St distribution to approach sufficient node representation. Experimental results show that this method can achieve a relatively better performance against the baselines.

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.

scholarly journals Modeling Unobserved Sources of Heterogeneity in Animal Abundance Using a Dirichlet Process Prior

Biometrics ◽  
2008 ◽  
Vol 64 (2) ◽  
pp. 635-644 ◽  
Author(s):  
Robert M. Dorazio ◽  
Bhramar Mukherjee ◽  
Li Zhang ◽  
Malay Ghosh ◽  
Howard L. Jelks ◽  
...  
Keyword(s):  
Dirichlet Process ◽  
Dirichlet Process Prior ◽  
Animal Abundance

scholarly journals A Bayesian Nonparametric Model for Inferring Subclonal Populations from Structured DNA Sequencing Data

2020 ◽  
Author(s):  
Shai He ◽  
Aaron Schein ◽  
Vishal Sarsani ◽  
Patrick Flaherty
Keyword(s):  
Dna Sequencing ◽  
Single Cell ◽  
Dirichlet Process ◽  
Lymphoblastic Leukemia ◽  
Nonparametric Model ◽  
Dirichlet Process Mixture ◽  
Sequencing Data ◽  
Hierarchical Dirichlet Process ◽  
Dirichlet Process Prior

There are distinguishing features or “hallmarks” of cancer that are found across tumors, individuals, and types of cancer, and these hallmarks can be driven by specific genetic mutations. Yet, within a single tumor there is often extensive genetic heterogeneity as evidenced by single-cell and bulk DNA sequencing data. The goal of this work is to jointly infer the underlying genotypes of tumor subpopulations and the distribution of those subpopulations in individual tumors by integrating single-cell and bulk sequencing data. Understanding the genetic composition of the tumor at the time of treatment is important in the personalized design of targeted therapeutic combinations and monitoring for possible recurrence after treatment.We propose a hierarchical Dirichlet process mixture model that incorporates the correlation structure induced by a structured sampling arrangement and we show that this model improves the quality of inference. We develop a representation of the hierarchical Dirichlet process prior as a Gamma-Poisson hierarchy and we use this representation to derive a fast Gibbs sampling inference algorithm using the augment-and-marginalize method. Experiments with simulation data show that our model outperforms standard numerical and statistical methods for decomposing admixed count data. Analyses of real acute lymphoblastic leukemia cancer sequencing dataset shows that our model improves upon state-of-the-art bioinformatic methods. An interpretation of the results of our model on this real dataset reveals co-mutated loci across samples.

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