• Title/Summary/Keyword: Dirichlet prior

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Empirical Bayes Nonparametric Estimation with Beta Processes Based on Censored Observations

  • Hong, Jee-Chang;Kim, Yongdai;Inha Jung
    • Journal of the Korean Statistical Society
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    • v.30 no.3
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    • pp.481-498
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    • 2001
  • Empirical Bayes procedure of nonparametric estiamtion of cumulative hazard rates based on censored data is considered using the beta process priors of Hjort(1990). Beta process priors with unknown parameters are used for cumulative hazard rates. Empirical Bayes estimators are suggested and asymptotic optimality is proved. Our result generalizes that of Susarla and Van Ryzin(1978) in the sensor that (i) the cumulative hazard rate induced by a Dirichlet process is a beta process, (ii) our empirical Bayes estimator does not depend on the censoring distribution while that of Susarla and Van Ryzin(1978) does, (iii) a class of estimators of the hyperprameters is suggested in the prior distribution which is assumed known in advance in Susarla and Van Ryzin(1978). This extension makes the proposed empirical Bayes procedure more applicable to real dta sets.

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Variational Expectation-Maximization Algorithm in Posterior Distribution of a Latent Dirichlet Allocation Model for Research Topic Analysis

  • Kim, Jong Nam
    • Journal of Korea Multimedia Society
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    • v.23 no.7
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    • pp.883-890
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    • 2020
  • In this paper, we propose a variational expectation-maximization algorithm that computes posterior probabilities from Latent Dirichlet Allocation (LDA) model. The algorithm approximates the intractable posterior distribution of a document term matrix generated from a corpus made up by 50 papers. It approximates the posterior by searching the local optima using lower bound of the true posterior distribution. Moreover, it maximizes the lower bound of the log-likelihood of the true posterior by minimizing the relative entropy of the prior and the posterior distribution known as KL-Divergence. The experimental results indicate that documents clustered to image classification and segmentation are correlated at 0.79 while those clustered to object detection and image segmentation are highly correlated at 0.96. The proposed variational inference algorithm performs efficiently and faster than Gibbs sampling at a computational time of 0.029s.

Bayesian pooling for contingency tables from small areas

  • Jo, Aejung;Kim, Dal Ho
    • Journal of the Korean Data and Information Science Society
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    • v.27 no.6
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    • pp.1621-1629
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    • 2016
  • This paper studies Bayesian pooling for analysis of categorical data from small areas. Many surveys consist of categorical data collected on a contingency table in each area. Statistical inference for small areas requires considerable care because the subpopulation sample sizes are usually very small. Typically we use the hierarchical Bayesian model for pooling subpopulation data. However, the customary hierarchical Bayesian models may specify more exchangeability than warranted. We, therefore, investigate the effects of pooling in hierarchical Bayesian modeling for the contingency table from small areas. In specific, this paper focuses on the methods of direct or indirect pooling of categorical data collected on a contingency table in each area through Dirichlet priors. We compare the pooling effects of hierarchical Bayesian models by fitting the simulated data. The analysis is carried out using Markov chain Monte Carlo methods.

EMPIRICAL BAYES ESTIMATION OF RESIDUAL SURVIVAL FUNCTION AT AGE

  • Liang, Ta-Chen
    • Journal of the Korean Statistical Society
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    • v.33 no.2
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    • pp.191-202
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    • 2004
  • The paper considers nonparametric empirical Bayes estimation of residual survival function at age t using a Dirichlet process prior V(a). Empirical Bayes estimators are proposed for the case where both the function ${\alpha}$(0, $\chi$] and the size a(R$\^$+/) are unknown. It is shown that the proposed empirical Bayes estimators are asymptotically optimal at a rate n$\^$-1/, where n is the number of past data available for the present estimation problem. Therefore, the result of Lahiri and Park (1988) in which a(R$\^$+/) is assumed to be known and a rate n$\^$-1/ is achieved, is extended to a(R$\^$+/) unknown case.

Exploring trends in blockchain publications with topic modeling: Implications for forecasting the emergence of industry applications

  • Jeongho Lee;Hangjung Zo;Tom Steinberger
    • ETRI Journal
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    • v.45 no.6
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    • pp.982-995
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    • 2023
  • Technological innovation generates products, services, and processes that can disrupt existing industries and lead to the emergence of new fields. Distributed ledger technology, or blockchain, offers novel transparency, security, and anonymity characteristics in transaction data that may disrupt existing industries. However, research attention has largely examined its application to finance. Less is known of any broader applications, particularly in Industry 4.0. This study investigates academic research publications on blockchain and predicts emerging industries using academia-industry dynamics. This study adopts latent Dirichlet allocation and dynamic topic models to analyze large text data with a high capacity for dimensionality reduction. Prior studies confirm that research contributes to technological innovation through spillover, including products, processes, and services. This study predicts emerging industries that will likely incorporate blockchain technology using insights from the knowledge structure of publications.

Bayesian Inference for Multinomial Group Testing

  • Heo, Tae-Young;Kim, Jong-Min
    • Communications for Statistical Applications and Methods
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    • v.14 no.1
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    • pp.81-92
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    • 2007
  • This paper consider trinomial group testing concerned with classification of N given units into one of k disjoint categories. In this paper, we propose Bayesian inference for estimating individual category proportions using the trinomial group testing model proposed by Bar-Lev et al. (2005). We compared a relative efficience (RE) based on the mean squared error (MSE) of MLE and Bayes estimators with various prior information. The impact of different prior specifications on the estimates is also investigated using selected prior distribution. The impact of different priors on the Bayes estimates is modest when the sample size and group size we large.

A Hierarchical Bayesian Model for Survey Data with Nonresponse

  • Han, Geunshik
    • Journal of the Korean Statistical Society
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    • v.30 no.3
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    • pp.435-451
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    • 2001
  • We describe a hierarchical bayesian model to analyze multinomial nonignorable nonresponse data. Using a Dirichlet and beta prior to model the cell probabilities, We develop a complete hierarchical bayesian analysis for multinomial proportions without making any algebraic approximation. Inference is sampling based and Markove chain Monte Carlo methods are used to perform the computations. We apply our method to the dta on body mass index(BMI) and show the model works reasonably well.

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A Bayes Reliability Estimation from Life Test in a Stress-Strength Model

  • Park, Sung-Sub;Kim, Jae-Joo
    • Journal of the Korean Statistical Society
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    • v.12 no.1
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    • pp.1-9
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    • 1983
  • A stress-strength model is formulated for s out of k system of identical components. We consider the estimation of system reliability from survival count data from a Bayesian viewpoint. We assume a quadratic loss and a Dirichlet prior distribution. It is shown that a Bayes sequential procedure can be established. The Bayes estimator is compared with the UMVUE obtained by Bhattacharyya and with an estimator based on Mann-Whitney statistic.

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Bayesian Conjugate Analysis for Transition Probabilities of Non-Homogeneous Markov Chain: A Survey

  • Sung, Minje
    • Communications for Statistical Applications and Methods
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    • v.21 no.2
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    • pp.135-145
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    • 2014
  • The present study surveys Bayesian modeling structure for inferences about transition probabilities of Markov chain. The motivation of the study came from the data that shows transitional behaviors of emotionally disturbed children undergoing residential treatment program. Dirichlet distribution was used as prior for the multinomial distribution. The analysis with real data was implemented in WinBUGS programming environment. The performance of the model was compared to that of alternative approaches.

Semiparametric Bayesian Hierarchical Selection Models with Skewed Elliptical Distribution (왜도 타원형 분포를 이용한 준모수적 계층적 선택 모형)

  • 정윤식;장정훈
    • The Korean Journal of Applied Statistics
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    • v.16 no.1
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    • pp.101-115
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    • 2003
  • Lately there has been much theoretical and applied interest in linear models with non-normal heavy tailed error distributions. Starting Zellner(1976)'s study, many authors have explored the consequences of non-normality and heavy-tailed error distributions. We consider hierarchical models including selection models under a skewed heavy-tailed e..o. distribution proposed originally by Chen, Dey and Shao(1999) and Branco and Dey(2001) with Dirichlet process prior(Ferguson, 1973) in order to use a meta-analysis. A general calss of skewed elliptical distribution is reviewed and developed. Also, we consider the detail computational scheme under skew normal and skew t distribution using MCMC method. Finally, we introduce one example from Johnson(1993)'s real data and apply our proposed methodology.