What This Document Is
This document presents a detailed exploration of the Expectation-Maximization (EM) algorithm, a powerful iterative technique used for finding maximum likelihood estimates of parameters in statistical models, particularly when dealing with incomplete data or latent variables. It focuses on illustrating the application of the EM algorithm through a series of carefully selected examples drawn from the field of statistical genetics. The material originates from a lecture delivered at the University of California, Berkeley (Statistics 246, Spring 2002).
Why This Document Matters
This resource is ideal for students and researchers studying statistical genetics, biostatistics, or advanced statistical modeling. It’s particularly beneficial for those seeking a deeper understanding of how the EM algorithm can be applied to real-world genetic problems. It serves as a valuable supplement to coursework or independent study, offering a practical perspective on a conceptually challenging topic. Those preparing to implement EM algorithms in their own research will find the examples insightful.
Topics Covered
* Application of the EM algorithm to genetic linkage analysis
* Estimation of recombination rates between linked loci
* Modeling phenotypic frequencies from genotypic data
* Incomplete data formulations and likelihood estimation
* Historical context of statistical methods in genetics (Fisher & Balmukand, 1928)
* Utilizing the multinomial distribution in statistical genetics
What This Document Provides
* A detailed examination of three distinct examples showcasing the EM algorithm.
* A discussion of the challenges and considerations involved in parameter estimation with incomplete data.
* A historical perspective on the development of statistical methods in genetics.
* A framework for understanding how to formulate genetic problems within the EM algorithm structure.
* References to seminal work in the field, allowing for further exploration of the topic.
