Probability And Stats Intro2

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Probability And Stats Intro2

  1. 1. Crash course in probability theory and statistics – part 2 Machine Learning, Wed Apr 16, 2008
  2. 2. Motivation All models are wrong, but some are useful. This lecture introduces distributions that have proven useful in constructing models.
  3. 3. Densities, statistics and estimators A probability (density) is any function X a p(X ) that satisfies the probability theory axioms. A statistic is any function of observed data x a f(x). An estimator is a statistic used for estimating a parameter of the probability density x a m.
  4. 4. Estimators Assume D = {x1,x2,...,xN} are independent, identically distributed (i.i.d) outcomes of our experiments (observed data). Desirable properties of an estimator are: for N®¥ and (unbiased)

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