Bayesian Density Estimation and Inference Using Mixtures

Escobar, Michael; West, Mike

doi:10.2307/2291069

Cited by 875 publications

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“…To sample from p(θ , φ, σ 2 1 , σ 2 2 , ψ 1 , ψ 2 | data), we use an MCMC algorithm that combines techniques from Escobar and West (1995) and Neal (2000). Regarding the MCMC updates for θ and φ, note that based on (4), the prior full conditional for each θ i , p(θ i | {θ r : r = i}, ψ 1 ), i = 1, ..., n 1 +n 2 , has point masses (α 1 +n 1 +n 2 −1) −1 at θ r , r = i, and continuous mass α 1 (α 1 +n 1 +n 2 −1) −1 on the N(μ 1 , τ 2 1 ) distribution.…”

Section: Appendix B: Mcmc Posterior Simulation Methodsmentioning

confidence: 99%

“…In particular, once all the updates above for the θ i , i = 1, ..., n 1 , and for the (θ n 1 + j , φ j ), j = 1, ..., n 2 , are completed, we obtain the number of and values of the distinct components in θ and φ. Denote these by n * θ (≤ n 1 + n 2 ) and {θ * k : k = 1, ..., n * θ } for vector θ, and by n * φ (≤ n 2 ) and {φ (φ * k − μ 2 ) 2 ) distribution. The DP precision parameters α 1 and α 2 are updated using the data augmentation technique from Escobar and West (1995).…”

Section: Appendix B: Mcmc Posterior Simulation Methodsmentioning

confidence: 99%

“…This approach was discussed in Gelfand and Kuo (1991), developed in Gelfand and Kottas (2001), and also used in Kottas et al (2002) and Hanson et al (2008). Now, the choice of the Dirichlet process (DP) prior (Ferguson 1973) for G 1 and G 2 becomes attractive as it yields a DP mixture structure for F 1 and F 2 (Antoniak 1974;Escobar and West 1995). We will use the generic notation G ∼ DP(α, G 0 ) to indicate that a DP prior is assigned to random distribution G, where α is the DP precision parameter and G 0 is the DP centering distribution.…”

Section: The Modeling Approachmentioning

confidence: 99%

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Bayesian semiparametric modeling for stochastic precedence, with applications in epidemiology and survival analysis

Kottas

2010

Lifetime Data Anal

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We propose a prior probability model for two distributions that are ordered according to a stochastic precedence constraint, a weaker restriction than the more commonly utilized stochastic order constraint. The modeling approach is based on structured Dirichlet process mixtures of normal distributions. Full inference for functionals of the stochastic precedence constrained mixture distributions is obtained through a Markov chain Monte Carlo posterior simulation method. A motivating application involves study of the discriminatory ability of continuous diagnostic tests in epidemiologic research. Here, stochastic precedence provides a natural restriction for the distributions of test scores corresponding to the non-infected and infected groups. Inference under the model is illustrated with data from a diagnostic test for Johne's disease in dairy cattle. We also apply the methodology to the comparison of survival distributions associated with two distinct conditions, and illustrate with analysis of data on survival time after bone marrow transplantation for treatment of leukemia.

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Section: Appendix B: Mcmc Posterior Simulation Methodsmentioning

confidence: 99%

Section: Appendix B: Mcmc Posterior Simulation Methodsmentioning

confidence: 99%

Section: The Modeling Approachmentioning

confidence: 99%

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Bayesian semiparametric modeling for stochastic precedence, with applications in epidemiology and survival analysis

Kottas

2010

Lifetime Data Anal

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“…The two step algorithm of Escobar and West (1995) is used to sample the ASV-DPM model's precision parameter α. When the mixture order, k, identifying vector, s, and locations {Σ j }, are all known, the posterior of α will only depend on k. Assuming a gamma prior, Γ(a, b),…”

Section: Sampler Of αmentioning

confidence: 99%

“…where α is the draw from the previous sweep and k is the number of clusters from the current sweep (see Escobar and West (1995) for the formula of the likelihood function, π(k|α, n)).…”

Section: Asv-dpm Asvmentioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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In this paper, we extend the parametric, asymmetric, stochastic volatility model (ASV), where returns are correlated with volatility, by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically. Its novelty is in modeling the joint, conditional, return-volatility distribution with an infinite mixture of bivariate Normal distributions with mean zero vectors, but having unknown mixture weights and covariance matrices. This semiparametric ASV model nests stochastic volatility models whose innovations are distributed as either Normal or Student-t distributions, plus the response in volatility to unexpected return shocks is more general than the fixed asymmetric response with the ASV model. The unknown mixture parameters are modeled with a Dirichlet process prior. This prior ensures a parsimonious, finite, posterior mixture that best represents the distribution of the innovations and a straightforward sampler of the conditional posteriors. We develop a Bayesian Markov chain Monte Carlo sampler to fully characterize the parametric and distributional uncertainty. Nested model comparisons and out-ofsample predictions with the cumulative marginal-likelihoods, and one-day-ahead, predictive logBayes factors between the semiparametric and parametric versions of the ASV model shows the semiparametric model projecting more accurate empirical market returns. A major reason is how volatility responds to an unexpected market movement. When the market is tranquil, expected volatility reacts to a negative (positive) price shock by rising (initially declining, but then rising when the positive shock is large). However, when the market is volatile, the degree of asymmetry and the size of the response in expected volatility is muted. In other words, when times are good, no news is good news, but when times are bad, neither good nor bad news matters with regards to volatility. JEL classification: C11, C14, C53, C58

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Bayesian Methods for Microarray Data

Lewin

Richardson

2007

Handbook of Statistical Genetics

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Bayesian Density Estimation and Inference Using Mixtures

Cited by 875 publications

References 0 publications

Bayesian semiparametric modeling for stochastic precedence, with applications in epidemiology and survival analysis

Bayesian semiparametric modeling for stochastic precedence, with applications in epidemiology and survival analysis

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Bayesian Methods for Microarray Data

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