[一本引起争议的贝叶斯专著]The Bayesian Core:

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Bayesian Core: A Practical Approach to Computational Bayesian Statistics

Jean-Michel Marin (Author), Christian Robert (Author)

This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book.
Product Details

• Hardcover: 258 pages
• Publisher: Springer; 1st ed. 2007. Corr. 2nd printing 2007 edition (Feb. 18 2007)
• Language: English
• ISBN-10: 0387389792
• ISBN-13: 978-0387389790
• Product Dimensions: 23.6 x 15.5 x 2.3 cm
• Shipping Weight: 295 g
  

Product Description
Review:
"The matching of each computational technique to a real data set allows readers to fully appreciate the Bayesian analysis process, from model formation to prior selection and practical implementation." (Lawrence Joseph from Biometrics, Issue 63, September 2007)

"Recent times have seen several new books introducing Bayesian computing. This book is an introduction on a higher level. ‘The purpose of this book is to provide a self-contained entry to practical & computational Bayesian Statistics using generic examples from the most common models.’ … Many researchers and Ph.D. students will find the R-programs in the book a nice start for their own problems and an innovative source for further developments." (Wolfgang Polasek, Statistical Papers, Vol. 49, 2008)
"This text intentionally focuses on a few fundamental Bayesian statistical models and key computational tools. … Bayesian Core is more than a textbook: it is an entire course carefully crafted with the student in mind. … As an instructor of Bayesian statistics courses, I was pleased to discover this ready- and well-made, self-contained introductory course for (primarily) graduate students in statistics and other quantitative disciplines. I am seriously considering Bayesian Core for my next course in Bayesian statistics." (Jarrett J. Barber, Journal of the American Statistical Association, Vol. 103 (481), 2008)

"The book aims to be a self-contained entry to Bayesian computational statistics for practitioners as well as students at both the graduate and undergraduate level, and has been test-driven in a number of courses given by the authors. … Two particularly attractive aspects of the book are its concise and clear writing style, which is really enjoyable, and its focus on the development of an intuitive feel for the material: the numerous insightful remarks should make the book a real treat … ." (Pieter Bastiaan Ober, Journal of Applied Statistics, Vol. 35 (1), 2008)
"The book is a good, compact and self-contained introduction to the applications of Bayesian statistics and to the use of R to implement the procedures. … a reader with a previous formal course in statistics will enjoy reading this book. … the authors are not shy of presenting such complex models as hidden Markov models and Markov random fields in a simple and direct way. This adds an edge to a compact and useful text." (Mauro Gasparini, Zentralblatt MATH, Vol. 1137 (15), 2008)

"This book’s title captures its focus. It is a textbook covering the core statistical models from both a Bayesian viewpoint and a computational viewpoint. … There is a discussion of choice of priors, along with math to derive the priors. … The book is being actively used as a textbook by a number of university courses. … The course level is graduate or advanced undergraduate. Solutions to the exercises are available to course instructors … . In conclusion, the book does what it does, well." (Rohan Baxter, ACM Computing Reviews, December, 2008)


From the Back CoverThis Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. While R programs are provided on the book website and R hints are given in the computational sections of the book, The Bayesian Core requires no knowledge of the R language and it can be read and used with any other programming language.

The Bayesian Core can be used as a textbook at both undergraduate and graduate levels, as exemplified by courses given at Université Paris Dauphine (France), University of Canterbury (New Zealand), and University of British Columbia (Canada). It serves as a unique textbook for a service course for scientists aiming at analyzing data the Bayesian way as well as an introductory course on Bayesian statistics. The prerequisites for the book are a basic knowledge of probability theory and of statistics. Methodological and data-based exercises are included within the main text and students are expected to solve them as they read the book. Those exercises can obviously serve as assignments, as was done in the above courses. Datasets, R codes and course slides all are available on the book website.

Jean-Michel Marin is currently senior researcher at INRIA, the French Computer Science research institute, and located at Université Paris-Sud, Orsay. He has previously been Assistant Professor at Université Paris Dauphine for four years. He has written numerous papers on Bayesian methodology and computing, and is currently a member of the council of the French Statistical Society.

Christian Robert is Professor of Statistics at Université Paris Dauphine and Head of the Statistics Research Laboratory at CREST-INSEE, Paris. He has written over a hundred papers on Bayesian Statistics and computational methods and is the author or co-author of seven books on those topics, including The Bayesian Choice (Springer, 2001), winner of the ISBA DeGroot Prize in 2004. He is a Fellow and member of the council of the Institute of Mathematical Statistics, and a Fellow and member of the research committee of the Royal Statistical Society. He is currently co-editor of the Journal of the Royal Statistical Society, Series B, after taking part in the editorial boards of the Journal of the American Statistical Society, the Annals of Statistics, Statistical Science, andBayesian Analysis. He is also the winner of the Young Statistician prize of the Paris Statistical Society in 1996 and a recipient of an Erskine Fellowship from the University of Canterbury (NZ) in 2006.

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关键词：Bayesian Bayes core baye cor Christian available intended provides standard

1. # CHAPTER 2: R COMMANDS
   
2. # 19/12/2006
   
3. 
   
4. ################################################################################
   
5. 
   
6. # normaldata DATASET IMPLEMENTATION AND GRAPHS
   
7. 
   
8. normaldata=scan("normaldata")
   
9. hist(normaldata,nclass=20,col="blue")
   
10. 
    
11. ################################################################################
    
12. 
    
13. # CMBdata DATASET IMPLEMENTATION AND GRAPHS
    
14. 
    
15. CMBdata=scan("CMBdata")
    
16. CMBdatamat=matrix(CMBdata,800,800,byrow=TRUE)
    
17. image(CMBdatamat,col=grey(1:1000/1000))
    
18. hist(CMBdata,nclass=100,col="red",prob=TRUE)
    
19. f=function(x){dnorm(x,mean(CMBdata),sd(CMBdata))}
    
20. curve(f,-0.2,0.8,add=TRUE,col="blue")
    
21. 
    
22. ################################################################################
    
23. 
    
24. # normaldata DATASET COMPUTATION OF EACH PREDICTIVE CDF
    
25. 
    
26. n=length(normaldata)
    
27. outl=rep(0,n)
    
28. outf=outl
    
29. for (i in 1:n)
    
30. {
    
31. outl[i]=pt((normaldata[i]-mean(normaldata[normaldata[]!=normaldata[i]]))/
    
32. (sd(normaldata[normaldata[]!=normaldata[i]])*sqrt(91/90)),90)
    
33. outf[i]=dt((normaldata[i]-mean(normaldata[normaldata[]!=normaldata[i]]))/
    
34. (sd(normaldata[normaldata[]!=normaldata[i]])*sqrt(91/90)),90)/
    
35. (sd(normaldata[normaldata[]!=normaldata[i]])*sqrt(91/90))
    
36. }
    
37. 
    
38. plot(c(0,1),c(0,1),lwd=2,ylab="Predictive",xlab="Uniform",type="l")
    
39. points(seq(1/91,90/91,length=90),sort(outl),pch=19,col="steelblue3")
    
40. points(seq(1/91,90/91,length=90),sort(runif(90)),pch=21,col="tomato")
    
41. 
    
42. ################################################################################

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1. # CHAPTER 3: R COMMANDS
   
2. # 19/12/2006
   
3. 
   
4. ################################################################################
   
5. 
   
6. # caterpillar DATASET IMPLEMENTATION
   
7. 
   
8. source("#3.R")
   
9. processio=read.table("caterpillar")
   
10. y=log(processio$V11)
    
11. X=as.matrix(cbind(rep(1,33),processio[,1:10]))
    
12. n=length(y)
    
13. k=dim(X)[2]
    
14. 
    
15. ################################################################################
    
16. 
    
17. # caterpillar DATASET: ORDINARY LEAST SQUARE ESTIMATION OF beta
    
18. 
    
19. betahat=inv(t(X)%*%X,tol=10e-20)%*%t(X)%*%y
    
20. betahat
    
21. 
    
22. ################################################################################
    
23. 
    
24. # caterpillar DATASET: UNBIASED ESTIMATION OF sigma2
    
25. 
    
26. S2=t(y-X%*%betahat)%*%(y-X%*%betahat)
    
27. sigma2hat=S2/(n-k)
    
28. sigma2hat
    
29. 
    
30. ################################################################################
    
31. 
    
32. # caterpillar DATASET: ESTIMATION OF THE VARIANCE OF betahat
    
33. 
    
34. diag(as.real(sigma2hat)*inv(t(X)%*%X))
    
35. 
    
36. ################################################################################
    
37. 
    
38. # CONJUGATE PRIOR ANALYSIS
    
39. 
    
40. a=2.1
    
41. b=2
    
42. 
    
43. # PRIOR MEAN OF sigma2
    
44. 
    
45. 2/(2.1-1)
    
46. 
    
47. # PRIOR VARIANCE OF sigma2
    
48. 
    
49. 2^2/((2.1-1)^2*(2.1-2))
    
50. 
    
51. # caterpillar DATASET: POSTERIOR MEANS OF sigma2 FOR DIFFERENT c
    
52. 
    
53. # c=0.1
    
54. 
    
55. M=10*diag(11)
    
56. T=inv(inv(M)+inv(t(X)%*%X))
    
57. (2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)
    
58. 
    
59. # c=1
    
60. 
    
61. M=diag(11)
    
62. T=inv(inv(M)+inv(t(X)%*%X))
    
63. (2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)
    
64. 
    
65. # c=10
    
66. 
    
67. M=0.1*diag(11)
    
68. T=inv(inv(M)+inv(t(X)%*%X))
    
69. (2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)
    
70. 
    
71. # c=100
    
72. 
    
73. M=0.01*diag(11)
    
74. T=inv(inv(M)+inv(t(X)%*%X))
    
75. (2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)
    
76. 
    
77. # c=1000
    
78. 
    
79. M=0.001*diag(11)
    
80. T=inv(inv(M)+inv(t(X)%*%X))
    
81. (2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)
    
82. 
    
83. # caterpillar DATASET: POSTERIOR MEANS OF beta FOR DIFFERENT c
    
84. 
    
85. # c=0.1
    
86. 
    
87. M=10*diag(11)
    
88. b1beta=inv(M+t(X)%*%X)%*%t(X)%*%y
    
89. b1beta[1]
    
90. 
    
91. # c=1
    
92. 
    
93. M=diag(11)
    
94. b2beta=inv(M+t(X)%*%X)%*%t(X)%*%y
    
95. b2beta[1]
    
96. 
    
97. # c=10
    
98. 
    
99. M=0.1*diag(11)
    
100. b3beta=inv(M+t(X)%*%X)%*%t(X)%*%y
     
101. b3beta[1]
     
102. 
     
103. # c=100
     
104. 
     
105. M=0.01*diag(11)
     
106. b4beta=inv(M+t(X)%*%X)%*%t(X)%*%y
     
107. b4beta[1]
     
108. 
     
109. # c=1000
     
110. 
     
111. M=0.001*diag(11)
     
112. b5beta=inv(M+t(X)%*%X)%*%t(X)%*%y
     
113. b5beta[1]
     
114. 
     
115. # caterpillar DATASET: POSTERIOR VARIANCES OF THE FIRST COMPONENT OF beta
     
116. # FOR DIFFERENT c
     
117. 
     
118. # c=0.1
     
119. 
     
120. M=10*diag(11)
     
121. T=inv(inv(M)+inv(t(X)%*%X))
     
122. E=as.real(2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)*inv(M+t(X)%*%X)
     
123. E[1,1]
     
124. 
     
125. # c=1
     
126. 
     
127. M=diag(11)
     
128. T=inv(inv(M)+inv(t(X)%*%X))
     
129. E=as.real(2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)*inv(M+t(X)%*%X)
     
130. E[1,1]
     
131. 
     
132. # c=10
     
133. 
     
134. M=0.1*diag(11)
     
135. T=inv(inv(M)+inv(t(X)%*%X))
     
136. E=as.real(2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)*inv(M+t(X)%*%X)
     
137. E[1,1]
     
138. 
     
139. # c=100
     
140. 
     
141. M=0.01*diag(11)
     
142. T=inv(inv(M)+inv(t(X)%*%X))
     
143. E=as.real(2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)*inv(M+t(X)%*%X)
     
144. E[1,1]
     
145. 
     
146. # c=1000
     
147. 
     
148. M=0.001*diag(11)
     
149. T=inv(inv(M)+inv(t(X)%*%X))
     
150. E=as.real(2*b+S2+t(betahat)%*%T%*%betahat)/(n+2*a-2)*inv(M+t(X)%*%X)
     
151. E[1,1]
     
152. 
     
153. ################################################################################
     
154. 
     
155. # NON-INFORMATIVE PRIOR ANALYSIS
     
156. 
     
157. # caterpillar DATASET: 0.95 HPD LOWER BOUND OF beta
     
158. 
     
159. betahat-qt(0.95,22)*sqrt(diag(as.real(sigma2hat)*inv(t(X)%*%X)))
     
160. 
     
161. # caterpillar DATASET: 0.95 HPD UPPER BOUND OF beta
     
162. 
     
163. betahat+qt(0.95,22)*sqrt(diag(as.real(sigma2hat)*inv(t(X)%*%X)))
     
164. 
     
165. ################################################################################
     
166. 
     
167. # ZELLNER INFORMATIVE G-PRIOR ANALYSIS
     
168. 
     
169. # caterpillar DATASET: POSTERIOR MEAN OF beta FOR c=100
     
170. 
     
171. 100/101*betahat
     
172. 
     
173. # caterpillar DATASET: POSTERIOR VARIANCE OF beta FOR c=100
     
174. 
     
175. diag(100/(33*101)*as.real(S2+t(betahat)%*%t(X)%*%X%*%betahat/101)*inv(t(X)%*%X))
     
176. 
     
177. # BAYES FACTOR
     
178. 
     
179. X0=X[,-c(8,9)]
     
180. P0=X0%*%inv(t(X0)%*%X0)%*%t(X0)
     
181. lulu0=101^(-9/2)*(t(y)%*%y-100/101*t(y)%*%P0%*%y)^(-33/2)
     
182. 
     
183. P=X%*%inv(t(X)%*%X)%*%t(X)
     
184. lulu=101^(-11/2)*(t(y)%*%y-100/101*t(y)%*%P%*%y)^(-33/2)
     
185. 
     
186. log10(lulu0/lulu)
     
187. 
     
188. ################################################################################
     
189. 
     
190. # caterpillar DATASET: ZELLNER NON-INFORMATIVE G-PRIOR ANALYSIS
     
191. 
     
192. cc=1:100000
     
193. sum(cc/(cc+1)*betahat[1]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
194. sum(cc/(cc+1)*betahat[2]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
195. sum(cc/(cc+1)*betahat[3]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
196. sum(cc/(cc+1)*betahat[4]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
197. sum(cc/(cc+1)*betahat[5]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
198. sum(cc/(cc+1)*betahat[6]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
199. sum(cc/(cc+1)*betahat[7]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
200. sum(cc/(cc+1)*betahat[8]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
201. sum(cc/(cc+1)*betahat[9]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
202. sum(cc/(cc+1)*betahat[10]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
203. sum(cc/(cc+1)*betahat[11]*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
204. 
     
205. sum((S2+t(betahat)%*%t(X)%*%X%*%betahat/(cc+1))/(n-2)*cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))/sum(cc^(-1)*(cc+1)^(-11/2)*(t(y)%*%y-cc/(cc+1)*t(y)%*%P%*%y)^(-33/2))
     
206. 
     
207. ################################################################################
     
208. 
     
209. # VARIABLE SELECTION
     
210. 
     
211. library(combinat)
     
212. GAMPRO=matrix(0,1024,10)
     
213. qq=cumsum(c(choose(10,0:10)))
     
214. for (k in 1:10)
     
215. {
     
216. tab=t(combn(10,k))
     
217. GAMPRO[(qq[k]+1):qq[k+1],]=t(apply(tab,1,invt1,p=10))
     
218. }
     
219. rm(qq,tab)
     
220. 
     
221. # caterpillar DATASET: CACULATION OF THE MODEL POSTERIOR PROBABILITIES
     
222. # UNDER ZELLNER NON-INFORMATIVE G-PRIOR
     
223. 
     
224. yp=y
     
225. Xp=as.matrix(X[,2:11])
     
226. 
     
227. PRO1NIP=rep(0,1024)
     
228. for (k in 1:1024) {PRO1NIP[k]=lpostwnoinf(GAMPRO[k,],yp,Xp); print(k)}
     
229. PRO1NIP=exp(PRO1NIP-max(PRO1NIP))
     
230. PRO1NIP=PRO1NIP/sum(PRO1NIP)
     
231. MONIP=order(PRO1NIP)[1024:1005]
     
232. TOPPRO1NIP=cbind(apply(GAMPRO[MONIP,],1,newt1),PRO1NIP[MONIP])
     
233. rm(MONIP)
     
234. 
     
235. # caterpillar DATASET: GIBBS SAMPLING UNDER ZELLNER NON-INFORMATIVE G-PRIOR
     
236. 
     
237. GIBBSPRO1NIP=gibbsNIP2(20000,yp,Xp,PRO1NIP)
     
238. RGIBBSPRO1NIP=apply(GIBBSPRO1NIP[10001:20000,],1,newt1)
     
239. RGIBBSPRO1NIP=summary(as.factor(RGIBBSPRO1NIP))/10000
     
240. 
     
241. # caterpillar DATASET: CACULATION OF THE MODEL POSTERIOR PROBABILITIES
     
242. # UNDER ZELLNER INFORMATIVE G-PRIOR
     
243. 
     
244. PRO1IP2=rep(0,1024)
     
245. for (k in 1:1024) {PRO1IP2[k]=lpostw(GAMPRO[k,],yp,Xp,rep(0,11),100); print(k)}
     
246. PRO1IP2=exp(PRO1IP2-max(PRO1IP2))
     
247. PRO1IP2=PRO1IP2/sum(PRO1IP2)
     
248. MOIP2=order(PRO1IP2)[1024:1005]
     
249. TOPPRO1IP2=cbind(apply(GAMPRO[MOIP2,],1,newt1),PRO1IP2[MOIP2])
     
250. rm(MOIP2)
     
251. 
     
252. # caterpillar DATASET: GIBBS SAMPLING UNDER ZELLNER INFORMATIVE G-PRIOR
     
253. 
     
254. GIBBSPRO1IP2=gibbsIP(20000,yp,Xp,rep(0,11),100)
     
255. RGIBBSPRO1IP2=apply(GIBBSPRO1IP2[10001:20000,],1,newt1)
     
256. RGIBBSPRO1IP2=summary(as.factor(RGIBBSPRO1IP2))/10000
     
257. 
     
258. ################################################################################

复制代码

Bayesian Core: A Practical Approach to Computational Bayesian Statistics

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https://www.ceremade.dauphine.fr/~xian/BCS/