ENGG2430A Probability and Statistics for Engineers lassical Instructor: Shengyu Zhang
Instructor: Shengyu Zhang
Preceding chapter: Bayesian inference Preceding chapter: Bayesian approach to inference a Unknown parameters are modeled as random variables a Work within a single, fully-specified probabilistic model a Compute posterior distribution by judicious application of Bayes rule
Preceding chapter: Bayesian inference ◼ Preceding chapter: Bayesian approach to inference. ❑ Unknown parameters are modeled as random variables. ❑ Work within a single, fully-specified probabilistic model. ❑ Compute posterior distribution by judicious application of Bayes' rule
This chapter: classical inference We view the unknown parameter 0 as a deterministic(not random! )but unknown quantit ity a The observation x is random and its distribution Px(x; 0)if X is discrete a x(x; 0)if X is continuous depends on the value of 0
This chapter: classical inference ◼ We view the unknown parameter 𝜃 as a deterministic (not random!) but unknown quantity. ◼ The observation 𝑋 is random and its distribution ❑ 𝑝𝑋 𝑥; 𝜃 if 𝑋 is discrete ❑ 𝑓𝑋 𝑥; 𝜃 if 𝑋 is continuous depends on the value of 𝜃
Classical inference Deal simultaneously with multiple candidate models, one model for each possible value of a"good "hypothesis testing or estimation procedure will be one that possesses certain desirable properties under every candidate model o i.e. for every possible value of 0
Classical inference ◼ Deal simultaneously with multiple candidate models, one model for each possible value of 𝜃. ◼ A ''good" hypothesis testing or estimation procedure will be one that possesses certain desirable properties under every candidate model. ❑ i.e. for every possible value of 𝜃
a Bayesian Prior pe HObservation H Posterior Pe(I X=r); Point Estimates i Process Calculation E rror Analysis Conditional et Pxe Classical Px(; I Point estimates Observation Hypothesis selection P rocess Confidence intervals i etc
◼ Bayesian: ◼ Classical: