A Constructive Definition of Dirichlet Priors

Sethuraman, Jayaram

doi:10.21236/ada238689

Cited by 1,223 publications

(1,571 citation statements)

References 6 publications

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“…(15). If our method works well, the relevant local contexts would have high ranks in the ranked list.…”

Section: Experiments Resultsmentioning

confidence: 96%

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Modeling Content Structures of Domain-Specific Texts with RUP-HDP-HSMM and Its Applications

Okada

Nitta

2017

IEICE Trans. Inf. & Syst.

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SUMMARYWe propose a novel method, built upon the hierarchical Dirichlet process hidden semi-Markov model, to reveal the content structures of unstructured domain-specific texts. The content structures of texts consisting of sequential local contexts are useful for tasks, such as text retrieval, classification, and text mining. The prominent feature of our model is the use of the recursive uniform partitioning, a stochastic process taking a view different from existing HSMMs in modeling state duration. We show that the recursive uniform partitioning plays an important role in avoiding the rapid switching between hidden states. Remarkably, our method greatly outperforms others in terms of ranking performance in our text retrieval experiments, and provides more accurate features for SVM to achieve higher F1 scores in our text classification experiments. These experiment results suggest that our method can yield improved representations of domainspecific texts. Furthermore, we present a method of automatically discovering the local contexts that serve to account for why a text is classified as a positive instance, in the supervised learning settings.

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“…(15). If our method works well, the relevant local contexts would have high ranks in the ranked list.…”

Section: Experiments Resultsmentioning

confidence: 96%

“…where GEM denotes a stick breaking process [15] and DP(α 0 , β) denotes a Dirichlet process with a base probability distribution β and a strength parameter α 0 [5]. According to this generative process, The hidden variables involved include {β, π, φ, T, a}; hidden topics z in Fig.…”

Section: Rup-hdp-hsmmmentioning

confidence: 99%

Modeling Content Structures of Domain-Specific Texts with RUP-HDP-HSMM and Its Applications

Okada

Nitta

2017

IEICE Trans. Inf. & Syst.

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“…Realizations from the PoissonDirichlet prior of W (u) are generated by using the Ferguson and Sethuraman stickbreaking algorithm (Sethuraman, 1994;Phadia, 2013).…”

Section: Logistic Generalized Gamma Convolution Priormentioning

confidence: 99%

The current duration design for estimating the time to pregnancy distribution: a nonparametric Bayesian perspective

et al. 2015

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This paper was inspired by the studies of Niels Keiding and co-authors on estimating the waiting time-to-pregnancy (TTP) distribution, and in particular on using the current duration design in that context. In this design, a cross-sectional sample of women is collected from those who are currently attempting to become pregnant, and then by recording from each the time she has been attempting. Our aim here is to study the identifiability and the estimation of the waiting time distribution on the basis of current duration data. The main difficulty in this stems from the fact that very short waiting times are only rarely selected into the sample of current durations, and this renders their estimation unstable. We introduce here a Bayesian method for this estimation problem, prove its asymptotic consistency, and compare the method to some variants of the non-parametric maximum likelihood estimators (NPMLE), which have been used previously in this context. The properties of the Bayesian estimation method are studied also empirically, using both simulated data and TTP data on current durations collected by Slama et al. (2012).

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“…Employing Sethuraman (1994) representation of DP (α, G 0 ), G will almost surely be equal to the discrete distribution…”

Section: Modelmentioning

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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A Constructive Definition of Dirichlet Priors

Cited by 1,223 publications

References 6 publications

Modeling Content Structures of Domain-Specific Texts with RUP-HDP-HSMM and Its Applications

Modeling Content Structures of Domain-Specific Texts with RUP-HDP-HSMM and Its Applications

The current duration design for estimating the time to pregnancy distribution: a nonparametric Bayesian perspective

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

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