STAT231 Lecture Notes - Lecture 7: Random Variable, Partial Derivative, Statistical Model
15 Jan 2018
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Syllabus for the midterm: <= end of this week + stat 230; fall 2015 midterm and practice problems posted (solutions will be posted this friday) Today: overview of statistical modelling, estimatation and the mle calculation, likelihood functions and the mle for continuous r. v. s, special case -> uniform distribution. Paul the octopus problem: toss a coin 100 times. Data points are not just numbers, but outcomes of a random experiment: we need to construct a statistical model (assuption on the distribution y) Statistical model: construct the likelihood function, l(pi) = c^100_70 pi^70(1-pi)^30, find the mle(we choose pi hat which maximizes l(pi)), pi hat = 0. 7, we choose that value of the parameter that maximizes the chance of what we observed. Formal definition: yi = f(theta;yi), i=1, ,n, f=distribution function, yi"s are independent, L(theta;y1,y2, ,yn) = n pi i=1 f(theta;yi) product of the distribution functions evaluated at the sample points.
