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Activity Number:
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505
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Type:
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Contributed
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Date/Time:
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Thursday, August 10, 2006 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #306149 |
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Title:
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Application of Randomized Spherical-Radial Integration to the E-step of the Monte Carlo Expectation Maximization Algorithm for Generalized Linear Mixed Models
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Author(s):
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Vadim Zipunnikov*+ and James Booth
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Companies:
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Cornell University and Cornell University
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Address:
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Department of Statistical Science, Ithaca, NY, 14853,
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Keywords:
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MCEM ; IRSL ; randomized quadratures ; spherical radial rule ; salamander data
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Abstract:
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Very often in practice the E-step of the EM algorithm applied to GLMM involves analytically intractable integrals. We show how the randomized spherical-radial (SR) integration can be used in such cases. After a standardizing transformation, a change to polar coordinates allows to represent an integral as a double integral consisting of a one dimensional integral on the real line and a multivariate integral on the surface of a unit sphere. Randomized quadratures are used to approximate both of them. An attractive feature of the randomized SR rule is that its implementation requires only generating from standard probability distributions. Another advantage of the randomized rules is a direct way to construct MC error estimates. The resulting approximation has a form of a fixed effects GLM likelihood and a standard iteratively reweighted least squares procedure may be utilized for M-step.
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