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Bayesian skew selection for multivariate models

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Title: Bayesian skew selection for multivariate models
Authors: Panagiotelis, Anastasios1, Smith, Michael2 mike.smith@mbs.edu
Source: Computational Statistics & Data Analysis. Jul2010, Vol. 54 Issue 7, p1824-1839. 16p.
Subjects: Bayesian analysis, Multivariate analysis, Distribution (Probability theory), Mathematical symmetry, Division rings, Markov processes, Monte Carlo method
Abstract: Abstract: We develop a Bayesian approach for the selection of skew in multivariate skew distributions constructed through hidden conditioning in the manners suggested by either or . We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether there is symmetry, or skew, in each dimension. We adopt a proper beta prior on each non-zero skew coefficient, and derive the corresponding prior on the skew parameters. In both distributions we show that as the degrees of freedom increases, the prior smoothly bounds the non-zero skew parameters away from zero and identifies the posterior. We estimate the model using Markov chain Monte Carlo (MCMC) methods by exploiting the conditionally Gaussian representation of the skew distributions. This allows for the search through the posterior space of all possible combinations of skew and symmetry in each dimension. We show that the proposed method works well in a simulation setting, and employ it in two multivariate econometric examples. The first involves the modeling of foreign exchange rates and the second is a vector autoregression for intra-day electricity spot prices. The approach selects skew along the original coordinates of the data, which proves insightful in both examples. [Copyright &y& Elsevier]
Copyright of Computational Statistics & Data Analysis is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: <searchLink fieldCode="DE" term="%22Bayesian+analysis%22">Bayesian analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Multivariate+analysis%22">Multivariate analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+symmetry%22">Mathematical symmetry</searchLink><br /><searchLink fieldCode="DE" term="%22Division+rings%22">Division rings</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink>
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  Data: Abstract: We develop a Bayesian approach for the selection of skew in multivariate skew distributions constructed through hidden conditioning in the manners suggested by either or . We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether there is symmetry, or skew, in each dimension. We adopt a proper beta prior on each non-zero skew coefficient, and derive the corresponding prior on the skew parameters. In both distributions we show that as the degrees of freedom increases, the prior smoothly bounds the non-zero skew parameters away from zero and identifies the posterior. We estimate the model using Markov chain Monte Carlo (MCMC) methods by exploiting the conditionally Gaussian representation of the skew distributions. This allows for the search through the posterior space of all possible combinations of skew and symmetry in each dimension. We show that the proposed method works well in a simulation setting, and employ it in two multivariate econometric examples. The first involves the modeling of foreign exchange rates and the second is a vector autoregression for intra-day electricity spot prices. The approach selects skew along the original coordinates of the data, which proves insightful in both examples. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Computational Statistics & Data Analysis is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1016/j.csda.2010.02.004
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 1824
    Subjects:
      – SubjectFull: Bayesian analysis
        Type: general
      – SubjectFull: Multivariate analysis
        Type: general
      – SubjectFull: Distribution (Probability theory)
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      – SubjectFull: Mathematical symmetry
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      – SubjectFull: Division rings
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      – SubjectFull: Markov processes
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      – SubjectFull: Monte Carlo method
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              M: 07
              Text: Jul2010
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              Y: 2010
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