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4 results on '"Constrained posterior prior"'

1. Equality and inequality constrained multivariate linear models: Objective model selection using constrained posterior priors

Author

Mulder, Joris, Hoijtink, Herbert, and Klugkist, Irene

Subjects
*LINEAR statistical models, *MULTIVARIATE analysis, *CONSTRAINED optimization, *BAYESIAN analysis, *MATHEMATICAL inequalities, *MATHEMATICAL statistics
Abstract

Abstract: In objective Bayesian model selection, a well-known problem is that standard non-informative prior distributions cannot be used to obtain a sensible outcome of the Bayes factor because these priors are improper. The use of a small part of the data, i.e., a training sample, to obtain a proper posterior prior distribution has become a popular method to resolve this issue and seems to result in reasonable outcomes of default Bayes factors, such as the intrinsic Bayes factor or a Bayes factor based on the empirical expected-posterior prior. In this paper, it will be illustrated that such default methods may not result in sensible outcomes when evaluating inequality constrained models that are supported by the data. To resolve this issue, a default method is proposed for constructing so-called constrained posterior priors, which are inspired by the symmetrical intrinsic priors discussed by for a simple inequality constrained model selection problem. The resulting Bayes factors can be called “balanced” because model complexity of inequality constrained models is incorporated according to a specific definition that is presented in this paper. [Copyright &y& Elsevier]

Published
2010
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2. Bayesian model selection of informative hypotheses for repeated measurements

Author

Mulder, Joris, Klugkist, Irene, van de Schoot, Rens, Meeus, Wim H.J., Selfhout, Maarten, and Hoijtink, Herbert

Subjects
*BAYESIAN analysis, *MATHEMATICAL models, *DEVELOPMENTAL psychology, *SIMULATION methods & models, *TECHNICAL specifications, *MEASUREMENT
Abstract

Abstract: When analyzing repeated measurements data, researchers often have expectations about the relations between the measurement means. The expectations can often be formalized using equality and inequality constraints between (i) the measurement means over time, (ii) the measurement means between groups, (iii) the means adjusted for time-invariant covariates, and (iv) the means adjusted for time-varying covariates. The result is a set of informative hypotheses. In this paper, the Bayes factor is used to determine which hypothesis receives most support from the data. A pivotal element in the Bayesian framework is the specification of the prior. To avoid subjective prior specification, training data in combination with restrictions on the measurement means are used to obtain so-called constrained posterior priors. A simulation study and an empirical example from developmental psychology show that this prior results in Bayes factors with desirable properties. [Copyright &y& Elsevier]

Published
2009
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3. Bayesian model selection of informative hypotheses for repeated measurements

Author

Mulder, Joris, Klugkist, I.G., Schoot, Rens van de, Meeus, W.H.J., Selfhout, Maarten, Hoijtink, Herbert, Adolescent development: Characteristics and determinants, Methodology and statistics for the behavioural and social sciences, Afd methoden en statistieken, and Dep Educatie & Pedagogiek

Subjects
Constrained posterior prior, Training data, International (English), Sociale Wetenschappen, Bayesian model selection, Repeated measurements
Abstract

When analyzing repeated measurements data, researchers often have expectations about the relations between the measurement means. The expectations can often be formalized using equality and inequality constraints between (i) the measurement means over time, (ii) the measurement means between groups, (iii) the means adjusted for time-invariant covariates, and (iv) the means adjusted for time-varying covariates. The result is a set of informative hypotheses. In this paper, the Bayes factor is used to determine which hypothesis receives most support from the data. A pivotal element in the Bayesian framework is the specification of the prior. To avoid subjective prior specification, training data in combination with restrictions on the measurement means are used to obtain so-called constrained posterior priors. A simulation study and an empirical example from developmental psychology show that this prior results in Bayes factors with desirable properties.

Published
2010

4. Bayesian model selection of informative hypotheses for repeated measurements

Subjects
Constrained posterior prior, Training data, Bayesian model selection, Repeated measurements
Abstract

When analyzing repeated measurements data, researchers often have expectations about the relations between the measurement means. The expectations can often be formalized using equality and inequality constraints between (i) the measurement means over time, (ii) the measurement means between groups, (iii) the means adjusted for time-invariant covariates, and (iv) the means adjusted for time-varying covariates. The result is a set of informative hypotheses. In this paper, the Bayes factor is used to determine which hypothesis receives most support from the data. A pivotal element in the Bayesian framework is the specification of the prior. To avoid subjective prior specification, training data in combination with restrictions on the measurement means are used to obtain so-called constrained posterior priors. A simulation study and an empirical example from developmental psychology show that this prior results in Bayes factors with desirable properties.

Published
2010

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