Exact and approximate sum representations for the Dirichlet process

Ishwaran, Hemant; Zarepour, Mahmoud

doi:10.2307/3315951

Cited by 207 publications

(147 citation statements)

References 42 publications

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“…Also, a Pólya urn structure was considered in the collapsed cluster sampling method and the "no-gaps" algorithm for nonconjugate DPM models, proposed respectively by MacEachern (1994) and MacEachern and Müller (1998). On the other hand, Sethuraman and Tiwari (1982) and Sethuraman (1994) proposed an alternative characterization of Dirichlet process mixtures in terms of a "stick-breaking" construction, which was furthermore extended by Ishwaran and Zarepour (2002) and James (2001, 2003) and, more recently, by Walker (2007) and Papaspiliopoulos and Roberts (2008). Using this stick-breaking representation, the distribution of the auxiliary variable, ξ t , introduced above, can be described hierarchically as ,…”

Section: Bayesian Inference For the Garch-dpm Modelmentioning

confidence: 99%

“…(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%

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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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Section: Bayesian Inference For the Garch-dpm Modelmentioning

confidence: 99%

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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“…It can be shown that the following finite, hierarchical mixture model converges in distribution to the HDP as L → ∞ (Ishwaran and Zarepour [2002], Teh et al [2006]):…”

Section: Background: Dirichlet Processes and The Sticky Hdp-hmmmentioning

confidence: 99%

Nonparametric Bayesian Identification of Jump Systems with Sparse Dependencies

Fox¹,

Sudderth²,

Jordan³

et al. 2009

IFAC Proceedings Volumes

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Many nonlinear dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such Markov jump linear systems: the switching linear dynamical system (SLDS) and the switching vector autoregressive (S-VAR) process. In this paper, we present a nonparametric Bayesian approach to identifying an unknown number of persistent, smooth dynamical modes by utilizing a hierarchical Dirichlet process prior. We additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies. The utility and flexibility of our models are demonstrated on synthetic data and a set of honey bee dances.

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“…The parameters θ i 's are usually chosen as in the Sethuraman's representation, that is i.i.d. G. Iswaran and Zarepour (2002a) studied convergence properties of these random measures. For the choice α j,k = M/k, the limiting measure is Dir(M, G).…”

Section: Priors Obtained From Random Series Representationmentioning

confidence: 99%