CSE 221: Probabilistic Analysis of Computer SystemsIntroduction and motivationIntroduction and motivationTypes of inference problemsParameter estimationParameter estimation: Bernoulli trialsSlide 7Parameter estimation: Binomial distributionParameter estimation: Binomial distribution (contd..)Parameter estimation: Binomial distribution (contd..)Slide 11Irreducible chainsIrreducible chains (contd..)Irreducible chains (contd..)CSE 221: Probabilistic Analysis of Computer SystemsTopics covered:Statistical inferenceIntroduction and motivation Practical application of probability models: Observations:Population: Sample:Introduction and motivation What is inference?Representativeness of the sample:Types of inference problems Parameter estimation:Determination of the distribution:Hypothesis testing:Parameter estimationMaximum likelihood:Parameter estimation: Bernoulli trials Parameters to be estimated:Observations:Likelihood function:Parameter estimation: Bernoulli trials Maximum likelihood estimate:Example:Parameter estimation: Binomial distributionParameter to be estimated:Observations:Parameter estimation: Binomial distribution (contd..) Likelihood function:Parameter estimation: Binomial distribution (contd..)Maximum likelihood estimate:Parameter estimation: Binomial distribution (contd..)Example:Irreducible chainsExample:Definition: Steady-state or equilibrium state:Irreducible chains (contd..)Computation of steady-state probabilities:Irreducible chains (contd..)
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