Bayesian Inference in Factor Analysis

Press, S. James; Shigemasu, Kazuo

doi:10.1007/978-1-4612-3678-8_18

Cited by 49 publications

(42 citation statements)

References 5 publications

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“…This is similar to the approach described in Press and Shigemasu (1989) for achieving unique estimates in factor analysis. Informative prior distributions for the source profiles help to "focus" the posterior distribution, and thus allow parameter estimation.…”

Section: Discussionmentioning

confidence: 88%

Compositional receptor modeling

Billheimer

2001

Environmetrics

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Section: Discussionmentioning

confidence: 88%

Compositional receptor modeling

Billheimer

2001

Environmetrics

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“…Of course, this prior knowledge is not deterministic even with the fixed Ψ and this uncertainty is expressed by the covariance matrix H = n 0 I. The interpretation from the Generalized Natural Conjugate Prior (Press (1982), Press and Shigemasu (1989) ) means that n 0 can be interpreted as the number of hypothetical subjects. The concept of generalized Natural Conjugate Density (NCD) do not have such a desirable property as the pure NCD, but it gives meaningful interpretation of the hyperparameters.…”

Section: Prior Distributionsmentioning

confidence: 99%

“…3a Prepare the starting values for Λ and Ψ, which are the estimates given by Press and Shigemasu (1989). 3b Using full conditional distributions for each parameter matrix with all other parameters and observations(X) given, repeat generating random numbers.…”

Section: P(x|b C ⊗ D)mentioning

confidence: 99%

Bayesian Procrustes Solution

Shigemasu

Hoshino

2004

Behaviormetrika

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A new Bayesian method was proposed to obtain the optimal solution when the prior knowledge was given as a target factor pattern matrix. This method (Bayesian Procrustes Solution ) chooses the best target matrix in terms of the posterior probability or Bayes factor when there are two or more possible target matrices. Then the posterior distributions of the relevant parameters are approximated by a sufficient large sample of parameters simulated by the Gibbs sampler. The estimates of the parameters are given as the means of these distributions. The simulation study demonstrated that this method has more robustness with respect to misspecification of the target matrix than the traditional method. Finally, the application of this method to the real data showed the validity of this method.

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“…Many studies on mixture models (Diebolt and Robert, 1994) and factor analysis models (Press and Shigemasu, 1989) employ natural conjugate priors on their parameters, because such priors usually lead to simple Bayesian estimation algorithms.…”

Section: Natural Conjugate Priors On Parametersmentioning

confidence: 99%

Bayesian Analysis of Mixtures of Factor Analyzers

Utsugi

Kumagai

2001

Neural Computation

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For Bayesian inference on the mixture of factor analyzers (MFA), natural conjugate priors on the parameters are introduced and then a Gibbs sampler that generates parameter samples following the posterior is constructed. In addition, a deterministic estimation algorithm is derived by taking modes instead of samples from the conditional posteriors used in the Gibbs sampler. This is regarded as a maximum a posteriori (MAP) estimation algorithm with hyperparameter search. The behaviors of the Gibbs sampler and the deterministic algorithm are compared on a simulation experiment.

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Bayesian Inference in Factor Analysis

Cited by 49 publications

References 5 publications

Compositional receptor modeling

Compositional receptor modeling

Bayesian Procrustes Solution

Bayesian Analysis of Mixtures of Factor Analyzers

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