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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Efficient methods for the estimation of the multinomial parameter for the two-trait group testing model.

Gregory Haber1, Yaakov Malinovsky2

  • 1Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, NIH, Bethesda, MD 20892, USA.

Electronic Journal of Statistics
|July 16, 2021
PubMed
Summary
This summary is machine-generated.

This study addresses estimating joint probabilities for two traits using group testing. It introduces the expectation-maximization (EM) algorithm and closed-form estimators for accurate multinomial likelihood maximization.

Keywords:
EM algorithmgroup testingmultinomial samplingrestricted parameter space

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Area of Science:

  • Statistics
  • Bioinformatics
  • Epidemiology

Background:

  • Group testing efficiently estimates single parameters using pooled samples.
  • Recent interest focuses on estimating joint probabilities of correlated traits via multinomial models.
  • Existing literature lacks sufficient methods for maximum likelihood estimation (MLE) in these complex scenarios.

Purpose of the Study:

  • To develop and evaluate methods for estimating joint probabilities of two correlated traits using group testing.
  • To address the gap in the literature regarding maximum likelihood estimators (MLE) for multinomial group testing.
  • To provide alternative estimators that minimize bias and mean square error.

Main Methods:

  • Reformulating the MLE problem as maximizing a restricted multinomial likelihood.
  • Applying the Expectation-Maximization (EM) algorithm, guaranteeing global convergence.
  • Developing two closed-form estimators to optimize bias and mean square error.

Main Results:

  • The EM algorithm effectively finds the global maximizer for the multinomial likelihood, even at parameter space boundaries.
  • Closed-form estimators offer alternatives for bias and mean square error reduction.
  • Demonstrated application in estimating joint transmission prevalence of two Potato virus Y strains.

Conclusions:

  • The proposed EM algorithm and closed-form estimators provide robust solutions for joint probability estimation in group testing.
  • These methods enhance the application of group testing for complex biological and epidemiological studies.
  • The study advances statistical methodologies for analyzing correlated traits in pooled sample data.