Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models

Basu, Sanjib; Chib, Siddhartha

doi:10.1198/01621450338861947

Cited by 124 publications

(128 citation statements)

References 36 publications

(63 reference statements)

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“…We should mention that this paper does not delve into the problem of comparing the proposed model with parametric alternatives. Such a comparison is now possible for the ÿrst time using the methods that have been developed by Basu and Chib (2001). An application of the latter methods to the current problem will be considered in future work.…”

Section: Resultsmentioning

confidence: 99%

Semiparametric Bayes analysis of longitudinal data treatment models

Chib

Hamilton

2002

Journal of Econometrics

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This paper is concerned with the problem of determining the e ect of a binary treatment variable on a continuous outcome given longitudinal observational data and non-randomly assigned treatments. A general semiparametric Bayesian model (based on Dirichlet process mixing) is developed which contains potential outcomes and subject level outcome-speciÿc random e ects. The model is subjected to a fully Bayesian analysis based on Markov chain Monte Carlo simulation methods. The methods are used to compute the posterior distribution of the parameters and potential outcomes. The sampled posterior output from the simulation is also used to construct treatment e ect distributions at the unit level (and at other levels of aggregation), marginalized over all unknowns of the model, including the unknown distribution of responses and treatments, and treatment e ects matched by treatment probability. A real data example, dealing with the wage premium associated with union membership, is considered in detail where quantities such as the average treatment e ect, the treatment e ect on the treated, and matched treatment e ects are derived and illustrated.

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Section: Resultsmentioning

confidence: 99%

Semiparametric Bayes analysis of longitudinal data treatment models

Chib

Hamilton

2002

Journal of Econometrics

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“…(6) is unknown, and is modeled by a Dirichlet process (DP) prior, as will be described in Section 4, resulting in a DP mixture (DPM) model. Although new to the GARCH literature, DPM models have an extensive literature in Bayesian analysis and provide a broad and flexible class of distributions in many different settings, see, for instance, Ishwaran and Zarepour (2002), Basu and Chib (2003) and Ghosh, Basu and Tiwari (2009) and the references therein. In what follows, the model defined in Eqs.…”

Section: Introductionmentioning

confidence: 99%

A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation

Ausín

Galeano

Ghosh

2014

European Journal of Operational Research

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Financial time series analysis deals with the understanding of data collected on financial markets. Several parametric distribution models have been entertained for describing, estimating and predicting the dynamics of financial time series. Alternatively, this article considers a Bayesian semiparametric approach. In particular, the usual parametric distributional assumptions of the GARCH-type models are relaxed by entertaining the class of location-scale mixtures of Gaussian distributions with a Dirichlet process prior on the mixing distribution, leading to a Dirichlet process mixture model. The proposed specification allows for a greater exibility in capturing both the skewness and kurtosis frequently observed in financial returns. The Bayesian model provides statistical inference with finite sample validity. Furthermore, it is also possible to obtain predictive distributions for the Value at Risk (VaR), which has become the most widely used measure of market risk for practitioners. Through a simulation study, we demonstrate the performance of the proposed semiparametric method and compare results with the ones from a normal distribution assumption. We also demonstrate the superiority of our proposed semiparametric method using real data from the Bombay Stock Exchange Index (BSE-30) and the Hang Seng Index (HSI). In particular, the usual parametric distributional assumptions of the GARCH-type models are relaxed by entertaining the class of location-scale mixtures of Gaussian distributions with a Dirichlet process prior on the mixing distribution, leading to a Dirichlet process mixture model. The proposed specification allows for a greater flexibility in capturing both the skewness and kurtosis frequently observed in financial returns. The Bayesian model provide statistical inference with finite sample validity. Furthermore, it is also possible to obtain predictive distributions for the Value at Risk (VaR), which has become the most widely used measure of market risk for practitioners. Through a simulation study, we demonstrate the performance of the proposed semiparametric method and compare results with the ones from a normal distribution assumption. We also demonstrate the superiority of our proposed semiparametric method using real data from the Bombay Stock Exchange Index (BSE-30) and the Hang Seng Index (HSI).

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“…Recently, Ray and Mallick (2006) developed a semiparametric wavelet model with parameters distributed according to a Dirichlet process. They took a marginal likelihood approach, proposed by Basu and Chib (2003), to choose a partition of the data. Other relevant work, by Heard et al (2006) and by Heller and Gharamani (2005), will be discussed in Section 3.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Model-Based Clustering Procedures

Lau¹,

Green

2007

Journal of Computational and Graphical Statistics

195

187

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This article establishes a general formulation for Bayesian model-based clustering, in which subset labels are exchangeable, and items are also exchangeable, possibly up to covariate effects. The notational framework is rich enough to encompass a variety of existing procedures, including some recently discussed methods involving stochastic search or hierarchical clustering, but more importantly allows the formulation of clustering procedures that are optimal with respect to a specified loss function. Our focus is on loss functions based on pairwise coincidences, that is, whether pairs of items are clustered into the same subset or not.Optimization of the posterior expected loss function can be formulated as a binary integer programming problem, which can be readily solved by standard software when clustering a modest number of items, but quickly becomes impractical as problem scale increases. To combat this, a new heuristic item-swapping algorithm is introduced. This performs well in our numerical experiments, on both simulated and real data examples. The article includes a comparison of the statistical performance of the (approximate) optimal clustering with earlier methods that are model-based but ad hoc in their detailed definition.

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Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models

Cited by 124 publications

References 36 publications

Semiparametric Bayes analysis of longitudinal data treatment models

Semiparametric Bayes analysis of longitudinal data treatment models

A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation

Bayesian Model-Based Clustering Procedures

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