The Calculation of Posterior Distributions by Data Augmentation

Tanner, Martin A.; Wong, Wing Hung

doi:10.1080/01621459.1987.10478458

Cited by 2,714 publications

(638 citation statements)

References 10 publications

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“…Consequently, no closed form can be available for the posterior p θ, δ, QjY ðÞ . This problem can be addressed via the data augmentation idea in Tanner and Wong [25]. Data augmentation technique treats the latent quantities Ω; Z fg as the hypothetical missing data and augments them with the observed data to form complete data.…”

Section: Gibbs Sampling Scheme and Posterior Analysismentioning

confidence: 99%

Bayesian Analysis for Hidden Markov Factor Analysis Models

Xia¹,

Zeng²,

Tang³

2018

New Insights Into Bayesian Inference

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Section: Gibbs Sampling Scheme and Posterior Analysismentioning

confidence: 99%

Bayesian Analysis for Hidden Markov Factor Analysis Models

Xia¹,

Zeng²,

Tang³

2018

New Insights Into Bayesian Inference

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show abstract

“…Under the SIR model, data augmentation techniques (Tanner and Wong, 1987) cannot be applied directly because of the difficulties in obtaining conditional expectations of the numbers of subjects in each of the three classes. To avoid such difficulties, Cauchemez and Ferguson (2008) approximated the SIR model with a diffusion process, but their approach assumed a large population size and would not be suitable for data collected in small communities or households.…”

Section: Jmssmentioning

confidence: 99%

Approximation of Estimates in the Susceptible-Infectious-Removed Epidemic Model

Oh¹

2013

Journal of Mathematics and Statistics

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In this note, a simple approximation for the maximum likelihood estimates of infection and removal parameters used in the Susceptible-Infectious-Removed (SIR) epidemic model is presented. This approximation can be applied when the numbers of susceptible and infected individuals are observable only at discrete points in time. Since, in such cases, a closed form of the likelihood function is generally too complicated to obtain, the proposed approximation method represents an important advance. Simulation results show that the method yields approximations quite close to the maximum likelihood estimates obtained under continuous observation.

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“…In order to calculate the posterior distribution, we use the data augmentation technique (Tanner, Wong 1987) and we introduce the non-positive latent variables λ = {λ ij ; j∈{1, …, n i }: h ij = 0; I = 1, …, N}. We also define λ ij = h ij for j∈{1, …, n i }: h ij > 0.…”

Section: Posterior Distributionmentioning

confidence: 99%

Towards a Dynamic Analysis of Multiple-Store Shopping: Evidence From Spanish Panel Data

Martínez-Caraballo

Salvador

Berné

et al. 2013

Journal of Business Economics and Management

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Abstract. This paper aims to determine why consumer purchasing of fast moving consumer goods varies over time in Spain. More specifically, our objective is to explain multiple-store shopping in the households belonging to the Spanish Nielsen Homescan consumer panel that provides information about household shopping decisions between April 2003 and April 2004. In order to achieve this purpose, a Bayesian Dynamic Tobit model is used. The results allow us to confirm the influence of several demographical and geographical variables on household multiple-store shopping during the sample period.

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The Calculation of Posterior Distributions by Data Augmentation

Cited by 2,714 publications

References 10 publications

Bayesian Analysis for Hidden Markov Factor Analysis Models

Bayesian Analysis for Hidden Markov Factor Analysis Models

Approximation of Estimates in the Susceptible-Infectious-Removed Epidemic Model

Towards a Dynamic Analysis of Multiple-Store Shopping: Evidence From Spanish Panel Data

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