A Bayesian predictive approach to determining the number of components in a mixture distribution

Dey, Dipak K.; Kuo, Lynn; Sahu, Sujit K.

doi:10.1007/bf00162502

Cited by 32 publications

(19 citation statements)

References 28 publications

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“…Based on theoretical results by De Vore e Lorenz (1993) and Asmussen (1987), Wiper et al (2001) used mixtures of Gamma densities to approximate any density defined over [0, ∞). See also Dalal and Hall (1983) and Dey et al (1995) for related work.…”

Section: Nonparametric Estimation Of Curvesmentioning

confidence: 98%

A semiparametric Bayesian approach to extreme value estimation

2011

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This paper is concerned with extreme value density estimation. The generalized Pareto distribution (GPD) beyond a given threshold is combined with a nonparametric estimation approach below the threshold. This semiparametric setup is shown to generalize a few existing approaches and enables density estimation over the complete sample space. Estimation is performed via the Bayesian paradigm, which helps identify model components. Estimation of all model parameters, including the threshold and higher quantiles, and prediction for future observations is provided. Simulation studies suggest a few useful guidelines to evaluate the relevance of the proposed procedures. They also provide empirical evidence about the improvement of the proposed methodology over existing approaches. Models are then applied to environmental data sets. The paper is concluded with a few directions for future work.

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Section: Nonparametric Estimation Of Curvesmentioning

confidence: 98%

A semiparametric Bayesian approach to extreme value estimation

2011

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“…If Θ denotes the entire parameter space of our model and Z pr denotes the predictive data vector, then the posterior predictive distribution (p.p.d) is given by:

p false(z_{italicpr} ∣ z false) = italic\int p false(z_{italicpr} ∣ Θ false) p false(Θ ∣ z false) d Θ

where predictive data are easily obtained from converged posterior samples. The basis for our model selection is the conditional predictive ordinate (CPO) statistics, a widely used tool for Bayesian model diagnostic and assessment [47, 48, 49]. Importantly, it is useful in evaluating model fit when the Bayesian deviance information criteria (DIC)[59] is difficult to calculate.…”

Section: Bayesian Inferencementioning

confidence: 99%

Hidden Markov models for zero‐inflated Poisson counts with an application to substance use

DeSantis

Bandyopadhyay

2011

Statistics in Medicine

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Paradigms for substance abuse cue-reactivity research involve short term pharmacological or stressful stimulation designed to elicit stress and craving responses in cocaine-dependent subjects. It is unclear as to whether stress induced from participation in such studies increases drug-seeking behavior. We propose a 2-state Hidden Markov model to model the number of cocaine abuses per week before and after participation in a stress- and cue-reactivity study. The hypothesized latent state corresponds to ‘high’ or ‘low’ use. To account for a preponderance of zeros, we assume a zero-inflated Poisson model for the count data. Transition probabilities depend on the prior week’s state, fixed demographic variables, and time-varying covariates. We adopt a Bayesian approach to model fitting, and use the conditional predictive ordinate statistic to demonstrate that the zero-inflated Poisson hidden Markov model outperforms other models for longitudinal count data.

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“…, n} and {h, W}. Therefore, we introduce a latent variable z i as in Dey et al (1995). The latent variable z i can be simulated independently from the Bernoulli distribution B(1, p i ) where (13) We then consider the joint density of (b i , z i ) that is useful in deriving the conditional density of the hyperparameters.…”

Section: Modelmentioning

confidence: 99%

Forecasting stock prices using a hierarchical Bayesian approach

Ying

Kuo

2005

J. Forecast.

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The Ohlson model is evaluated using quarterly data from stocks in the Dow Jones Index. A hierarchical Bayesian approach is developed to simultaneously estimate the unknown coefficients in the time series regression model for each company by pooling information across firms. Both estimation and prediction are carried out by the Markov chain Monte Carlo (MCMC) method. Our empirical results show that our forecast based on the hierarchical Bayes method is generally adequate for future prediction, and improves upon the classical method. Copyright © 2005 John Wiley & Sons, Ltd.

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A Bayesian predictive approach to determining the number of components in a mixture distribution

Cited by 32 publications

References 28 publications

A semiparametric Bayesian approach to extreme value estimation

A semiparametric Bayesian approach to extreme value estimation

Hidden Markov models for zero‐inflated Poisson counts with an application to substance use

Forecasting stock prices using a hierarchical Bayesian approach

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