Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig
11.4. Modern Bayesian Methods 685 (c)Using parts (a) and (b) and assuming squared-error loss, write the Gibbs sampler algorithm ...
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Appendix A Mathematical Comments A.1 RegularityConditions These are the regularity conditions referred to in Sections 6.4 and 6. ...
688 Mathematical Comments A.2 Sequences The following is a short review of sequences of real numbers. In particular the liminf a ...
A.2. Sequences 689 Theorem A.2.3.Let{an}be a nondecreasing sequence of real numbers; i.e., for alln,an≤an+1.Suppose{an}is bounde ...
690 Mathematical Comments Suppose{an}is defined by an= { 1+n^1 ifnis even 2+n^1 ifnis odd. Then{bn}is the sequence{ 3 ,2+(1/3) ...
A.2. Sequences 691 A.2.3.Let{an}and{dn}be sequences of real numbers. Show that lim n→∞ (an+dn)≥ lim n→∞ an+ lim n→∞ dn. A.2.4.Le ...
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Appendix B RPrimer The package R can be downloaded at CRAN (https://cran.r-project.org/). It is freeware and there are versions ...
694 R Primer [1] 523.5988 > 2*pi*5 # The circumference of a sphere with radius 5 [1] 31.41593 Results can be saved for later ...
B.1. Basics 695 c1 c2 [1,] 7 8 [2,] 15 20 [3,] 23 32 [4,] 31 44 Brackets are also used to refer to elements of matrices. Letamat ...
696 R Primer 02468 0 500 1000 1500 2000 r Vol Simple Plot 02468 0 500 1000 1500 2000 Radius Volume Volume vs Radius 02468 0 500 ...
B.2. Probability Distributions 697 [1] 0.08801633 rnorm(6,70,4) # sample of size 6 on X [1] 72.12486 75.25811 71.26661 63.3646 ...
698 R Primer > pbinom(55,100,.6) # Probability of at most 55 successes [1] 0.1789016 > dbinom(55,100,.6) # Probability of ...
B.4. Loops 699 hence, the sample mean for the sequencex 1 ,...,xn+1can be expressed as a linear combination of the sample mean a ...
700 R Primer B.5 Input and Output Many texts on R, including the references cited above, have information on input and output (I ...
B.6. Packages 701 robust and nonparametric procedures. There are thousands of free packages avail- able to users at the site CRA ...
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Appendix C Lists of Common Distributions In this appendix, we provide a short list of common distributions. For each distribu- t ...
704 Common Distributions List of Common Discrete Distributions Bernoulli (3.1.1) 0 <p< 1 p(x)=px(1−p)^1 −x,x=0, 1 μ=p, σ^2 ...
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