Probability Day 2

Probability Day 2 - Probability and Statistics Part 2. More...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Probability and Statistics Part 2. More Probability, Statistics and their Application Chang-han Rhee Stanford University Sep 20, 2011 / CME001 1 Outline Statistics Estimation Concepts Estimation Strategies More Probability Expectation and Conditional Expectation Interchange of Limit Transforms Simulation Monte Carlo Method Rare Event Simulation Further Reference Classes at Stanford Books 2 Outline Statistics Estimation Concepts Estimation Strategies More Probability Expectation and Conditional Expectation Interchange of Limit Transforms Simulation Monte Carlo Method Rare Event Simulation Further Reference Classes at Stanford Books 3 Probability and Statistics Probability Statistics Model Data 4 Estimation Making best guess of an unknown parameter out of sample data. eg. Average height of west african giraffe 5 Estimator An estimator (statistic) is a rule of estimation: ˆ θ n = g ( X 1 , . . . , X n ) 6 Quality of an Estimator I Bias E ˆ θ- θ I Variance var ( ˆ θ ) I Mean Square Error (MSE) E [ ˆ θ- θ ] 2 = ( bias ) 2 + ( var ) 7 Confidence Interval Consider the sample mean estimator ˆ θ = 1 n S n . From the CLT, S n- n E X 1 √ n D → σ N ( , 1 ) Rearranging terms, (note: this is not a rigorous argument) 1 n S n D ≈ E X 1 + σ √ n N ( , 1 ) 8 Outline Statistics Estimation Concepts Estimation Strategies More Probability Expectation and Conditional Expectation Interchange of Limit Transforms Simulation Monte Carlo Method Rare Event Simulation Further Reference Classes at Stanford Books 9 Maximum Likelihood Estimation Finding most likely explanation. ˆ θ n = arg max θ f ( x 1 , x 2 , . . . , x n | θ ) = f ( x 1 | θ ) · f ( x 2 | θ ) · f ( x n | θ ) I Gold Standard: Gueranteed to be I Often computationally challenging 10 Method of Moments Matching the sample moment and the parametric moments.Matching the sample moment and the parametric moments....
View Full Document

This note was uploaded on 10/01/2011 for the course EE 221 taught by Professor Ee221a during the Spring '08 term at Berkeley.

Page1 / 35

Probability Day 2 - Probability and Statistics Part 2. More...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online