Transcription of Reading 10b: Maximum Likelihood Estimates
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Reading 10b: Maximum Likelihood Estimates
Maximum Likelihood EstimatesClass 10, Orloff and Jonathan Bloom1 Learning Goals1. Be able to define the Likelihood function for a parametric model given Be able to compute the Maximum Likelihood estimate of unknown parameter(s).2 IntroductionSuppose we know we have data consisting of valuesx1,..,xndrawn from an exponentialdistribution. The question remains: which exponential distribution?!We have casually referred totheexponential distribution orthebinomial distribution orthenormal distribution. In fact the exponential distribution exp( ) is not a single distributionbut rather a one-parameter family of distributions. Each value of defines a different dis-tribution in the family, with pdff (x) = e xon [0, ). Similarly, a binomial distributionbin(n,p) is determined by the two parametersnandp, and a normal distributionN( , 2)is determined by the two parameters and 2(or equivalently, and ). Parameterizedfamilies of distributions are often calledparametric distributionsorparametric are often faced with the situation of having random data which we know (or believe)is drawn from a parametric model, whose parameters we do not know.]
Maximum Likelihood Estimates Class 10, 18.05 Jeremy Orlo and Jonathan Bloom 1 Learning Goals 1. Be able to de ne the likelihood function for a parametric model given data.
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