- Date:26 Jul 2020
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Introduction Bayes Estimation Empirical Bayes Books Books Summary. Bayesian and Frequentist Representatives, Rev Thomas Bayes FRS 1702 1761 Sir Ronald Fisher FRS 1890 1962. English Mathematician English Statistician, Presbyterian Minister Evolutionary Biologist Geneticist. P H E Let the data speak for itself, Arthur Berg Standing Between a Bayesian and a Frequentist 2 27. Introduction Bayes Estimation Empirical Bayes Books Books Summary. Bayes Estimator as a Convex Combination,1st Goal List the top 250 movies of all time. Movies are rated on a scale of 1 to 10, Some movies are rated by many people and some by only a few.

Movies with fewer than 3000 votes are not considered. All movies have an average rating of C 6 9, i represents the mean rating by everyone who has seen movie i. The real goal is to construct the best estimate of i then pick the top 250. The frequentist approach uses only X i the average rating for movie i. The Bayesian approach shrinks X i towards C with more shrinking. applied when the number of votes for movie i is small. i X i 1 i C where i 0 1, Arthur Berg Standing Between a Bayesian and a Frequentist 3 27. Introduction Bayes Estimation Empirical Bayes Books Books Summary. Internet Movie Database Top 250,Rank WR R Title Votes. 1 9 2 9 2 The Shawshank Redemption 1994 546 155,2 9 1 9 2 The Godfather 1972 427 961. 3 9 0 9 0 The Godfather Part II 1974 257 643, 4 8 9 9 0 The Good the Bad and the Ugly 1966 170 045.

5 8 9 9 0 Pulp Fiction 1994 436 456,6 8 9 8 9 Inception 2010 265 531. 7 8 9 8 9 Schindler s List 1993 289 170,8 8 9 8 9 12 Angry Men 1957 126 983. 9 8 8 8 9 One Flew Over the Cuckoo s Nest 1975 225 419. 10 8 8 8 9 The Dark Knight 2008 487 800,85 8 5 8 7 Black Swan 2010 20 326. 142 8 2 8 3 Avatar 2009 285 005,240 8 0 8 5 True Grit 2010 6 444. Arthur Berg Standing Between a Bayesian and a Frequentist 4 27. Introduction Bayes Estimation Empirical Bayes Books Books Summary. IMDb Weighted Ranking a true Bayesian estimate,vi m vi m vi m.

Ri average rating of the movie i X i,vi total number of votes from regular voters. m minimum of votes to make the list 3000, C grand mean across all movies in the database 6 9. Arthur Berg Standing Between a Bayesian and a Frequentist 5 27. Introduction Bayes Estimation Empirical Bayes Books Books Summary. A Bayesian Calculation, Xi Xi 1 Xi vi represents the vi ratings of movie i. prior i N 0 02,conditional Xi j i N i 2 j 1 vi,vi 2 02 vi 2 02. Ri C 0 C m 2 02, Arthur Berg Standing Between a Bayesian and a Frequentist 6 27.

ction Error,Does shrinking really help,2 How much to shrink by i. Prediction Error i i 2, Introduction Bayes Estimation Empirical Bayes Books Books Summary. Standing Between a Bayesian and a Frequentist, In 1956 Charles Stein proved the existence of an estimator better than. the sample mean under certain assumptions, In 1961 Willard James and Charles Stein explicitly constructed such an. Arthur Berg Standing Between a Bayesian and a Frequentist 8 27. Introduction Bayes Estimation Empirical Bayes Books Books Summary. The James Stein Estimator n 4,i N 0 02 Xi i N i 2 i 1 n.

Bayes E i Xi Xi,n 3 2 n 3 2,Xi X 2 Xi X 2,In practice if 2 is unknown an estimate is used. Arthur Berg Standing Between a Bayesian and a Frequentist 9 27. Introduction Bayes Estimation Empirical Bayes Books Books Summary. Predicting Batting Averages, 2nd Goal Predict final batting averages from pre season performances. Pre season batting averages for 18 major league players are provided. Season final batting averages for the same players are also recorded. Data is from the 1970 season and is published in JASA 1975 and. Scientific American 1977 by Efron and Morris, The frequentist approach uses only Xi the pre season batting average. for player i Xi, The Emperical Bayes approach shrinks Xi towards X by some. empirically determined amount,Xi 1 X where 0 1, Arthur Berg Standing Between a Bayesian and a Frequentist 10 27.

Introduction Bayes Estimation Empirical Bayes Books Books Summary. Name hits AB pre season ML season final,1 Clemente 18 45 0 400 0 346. 2 Robinson 17 45 0 378 0 298,3 Howard 16 45 0 356 0 276. 4 Johnstone 15 45 0 333 0 222,5 Berry 14 45 0 311 0 273. 6 Spencer 14 45 0 311 0 270,7 Kessinger 13 45 0 289 0 263. 8 Alvarado 12 45 0 267 0 210,9 Santo 11 45 0 244 0 269.

10 Swoboda 11 45 0 244 0 230,11 Unser 10 45 0 222 0 264. 12 Williams 10 45 0 222 0 256,13 Scott 10 45 0 222 0 303. 14 Petrocelli 10 45 0 222 0 264,15 Rodriguez 10 45 0 222 0 226. 16 Campaneris 9 45 0 200 0 286,17 Munson 8 45 0 178 0 316. 18 Alvis 7 45 0 156 0 200, Arthur Berg Standing Between a Bayesian and a Frequentist 11 27.

Introduction Bayes Estimation Empirical Bayes Books Books Summary. Batting Average 1977,Batting Averages Dataset Efron. pre season,season final,Batting Average,1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18. Arthur Berg Standing Between a Bayesian and a Frequentist 12 27. Introduction Bayes Estimation Empirical Bayes Books Books Summary. James Stein Estimation of Batting Averages,1977 Batting Averages Dataset Efron. pre season,season final,Batting Average,1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18. Arthur Berg Standing Between a Bayesian and a Frequentist 13 27. Introduction Bayes Estimation Empirical Bayes Books Books Summary. Ranking Bias Emperical Bayes Order Statistics,1977 Batting Averages Dataset Efron.

pre season,season final,Genome wide association studies. Batting Average,SNPS AA Aa aa or 0 1 2,1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18. ranking bias estimator,part frequentist part Bayesian. with robust properties,Applied to 2 GWAS studies with. Estimated effects of the top SNPs,2 000 cases and 3 000 controls.

are biased up winner s curse,Crohn s Disease,Type 1 Diabetes. Arthur Berg Standing Between a Bayesian and a Frequentist 14 27. Introduction Bayes Estimation Empirical Bayes Books Books Summary. Williams College Book Survey, In the summer of 2009 Williams faculty members were asked to list. three books they felt that students should read,150 faculty members responded. 25 departments are represented,394 different books were recommended. The original publication dates were added wikipedia openlibrary org. Books with unknown publication dates 13 in total were approximated. Arthur Berg Standing Between a Bayesian and a Frequentist 15 27. Classics Asian Stud Anth amp Soc Religion Humanities Political Sci Philosophy Geosciences Music Math amp Stat English Art Astronomy Comp Sci Psychology History Theater Ger amp Rus Biology Economics Amer Stud Physics Comp Lit Chemistry Rom Lang 3 3 5 4 2 3 3 2 1 5 8 4 3 2 6 3 6 5 10 111810 10 1112 l l l l l l l l l l l l l l l l l l l l l l l l l

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