EMp - The E-M Algorithm in Genetics Biostatistics 666...

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The E-M Algorithm in Genetics Biostatistics 666 Lecture 8
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Maximum Likelihood Estimation of Allele Frequencies z Find parameter estimates which make observed data most likely z General approach, as long as tractable likelihood function exists z Can use all available information z Provides justification for natural estimators
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Today: z The Expectation–Maximization algorithm in Genetics z Frequency estimates for… Recessive alleles A, B, O alleles Haplotype frequencies
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Setting for the E-M Algorithm… z Specific type of incomplete data More possible categories (genotypes) than can be distinguished (phenotypes) z For example, consider disease locus with recessive alleles… What are the possible genotypes? What are the possible phenotypes?
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Setting for the E-M Algorithm. .. z Any problem that is simple to solve for complete data … For example, estimating allele frequencies when all genotypes can be distinguished … z … but the available data is “incomplete” in some way. For example, when disease phenotypes are observed the distinction between homozygotes and heterozygotes is missing.
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The E-M Algorithm z Consider a set of starting parameters z Use these to “estimate” the complete data z Use estimates of complete data to update parameters z Repeat as necessary
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An Example … z A random sample of 100 individuals z 4 express a recessive phenotype Assume the phenotype is controlled by a single gene z Let’s follow E-M algorithm steps …
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Step 1: z Set starting values for parameters z For allele frequency estimation… Equal frequencies are a common choice p rec = 0.5 z Useful to repeat process using different starting point
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Step 2: z Estimate “complete data” z Assign phenotypes to specific genotype categories z Use Bayes’ Theorem
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Step 2 (continued): z
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EMp - The E-M Algorithm in Genetics Biostatistics 666...

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