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815.worksheet09 - 2 1 2 1 2 1 π(The product should be...

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Biostatistics 615/815 Problem Set 8 Due November 24, 2004 1. Consider the following set of 20 observations drawn from a mixture of two normal distributions. -2.876 -0.877 0.728 1.670 -2.527 -0.645 0.737 1.826 -1.213 0.151 0.819 1.867 -1.111 0.246 0.998 2.107 -1.034 0.409 1.602 2.618 Assuming that the two distributions have unit variance and symmetric means and – , the likelihood function for these data is: + = + i x x i i e e L 2 2
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Unformatted text preview: ) ( 2 1 ) ( 2 1 2 1 ) ( π (The product should be calculated over all observations). Write a program that: a) Brackets the maximum of the log-likelihood function. b) Using the golden-section optimization strategy, finds the MLE for ∆ . c) Using an optimization strategy based on parabolic interpolation, finds the MLE of ∆ . d) How many function evaluations did you need for steps a), b) and c) above?...
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  • Fall '10
  • Abecasis
  • probability density function, Maximum likelihood, Likelihood function, optimization strategy, golden-section optimization strategy

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