# Paper Summary

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Published on April 13, 2008

Author: euler96

Source: slideshare.net

## Description

EM algorithm; Finite mixture model; Generalized linear model; Maximum likelihood.

Paper Summary Maximum Likelihood in a Generalized linear Finite Mixture Model by Using the EM Algorithm Jansen, R.C.; Reinink, K.; Heijden, G.W.A.M. van der (1993) 06/02/09 g9624515 謝宗震

Outline Motivation Introduction Method Application Discuss 06/02/09 g9624515 謝宗震

Motivation

Introduction

Method

Application

Discuss

Motivation Suitable for our topic. Not too difficult. Example in the paper is interesting. 06/02/09 g9624515 謝宗震

Suitable for our topic.

Not too difficult.

Example in the paper is interesting.

Introduction A Generalized Linear Finite Mixture Model. 06/02/09 g9624515 謝宗震

A Generalized Linear Finite Mixture Model.

Method Likelihood equation can be solved by applying the EM algorithm, (Dempster et al., 1977). 06/02/09 g9624515 謝宗震

Likelihood equation can be solved by applying the EM algorithm,

(Dempster et al., 1977).

Method 06/02/09 g9624515 謝宗震 Likelihood equation can be split in two terms, (Everitt and Hand, 1981).

Likelihood equation can be split in two terms, (Everitt and Hand, 1981).

Method Since likelihood equation can be split in two terms. Therefore the estimators { θ , p} are separated in the iterative scheme . M-step for the mixture problem can be split into two M-steps for standard non-mixture problems. 06/02/09 g9624515 謝宗震

Since likelihood equation can be split in two terms.

Therefore the estimators { θ , p} are separated in the iterative scheme .

M-step for the mixture problem can be split into two M-steps for standard non-mixture problems.

Method The first problem is solved by fitting a GLM for multinomial or Poisson data to the &quot;data&quot; p j|i . The second problem is solved by fitting a GLM to the response variable by using weights p j|i . 06/02/09 g9624515 謝宗震

The first problem is solved by fitting a GLM for multinomial or Poisson data to the &quot;data&quot; p j|i .

The second problem is solved by fitting a GLM to the response variable by using weights p j|i .

Application 06/02/09 g9624515 謝宗震

06/02/09 g9624515 謝宗震

06/02/09 g9624515 謝宗震

Application 06/02/09 g9624515 謝宗震

Application 06/02/09 g9624515 謝宗震 Results of fitting a generalized linear finite mixture model of ten and two Weibull distributions to a mutant and a control mouse, respectively.

Application 06/02/09 g9624515 謝宗震

Discuss For traditional EM algorithm and our result, which one would be better? Why mixture Weibull distributions model? Do you have any other idea to construct the model? 06/02/09 g9624515 謝宗震

For traditional EM algorithm and our result, which one would be better?

Why mixture Weibull distributions model?

Do you have any other idea to construct the model?

Reference Dempster, A. P., N. M. Laird, and D. B. Rubin (1977) Maximum likelihood from incomplete data via the E-M algorithm (with discussion). Journal of the Royal Statistical Society, Ser. B., 39, 1-38. Everitt, B. S. and Hand, D. J. (1981). Finite Mixture Distributions. London: Chapman and Hall. 06/02/09 g9624515 謝宗震

Dempster, A. P., N. M. Laird, and D. B. Rubin (1977) Maximum likelihood from incomplete data via the E-M algorithm (with discussion). Journal of the Royal Statistical Society, Ser. B., 39, 1-38.

Everitt, B. S. and Hand, D. J. (1981). Finite Mixture Distributions. London: Chapman and Hall.

Thank you for your listening. 06/02/09 g9624515 謝宗震

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