Errata (excluding minor typos) for the 1st printing of Bayesian Data Analysis. If you find any other errors, please e-mail to gelman@stat.columbia.edu p. 16, 5th line from bottom: "317/659 = 0.48" should be "308/655 = 0.47". p. 26, Exercise 2: "(2.7) and (2.8) hold if theta is a vector parameter" should be "(1.6) and (1.7) hold if u is a vector". p. 31, 11th line from bottom: "241,925" should be "241,945". p. 45, line 5: tau^2 should be tau_0^2. p. 47, lines 12-13: "precision-weighted average" should be "degrees-of-freedom-weighted average". p. 60, Exercise 9: also cite Jeffreys (1961) and Lee (1989). p. 61, exercise 12(a): "normal approximation to the Poisson" should be "normal approximation to the gamma and Poisson". p. 61, Exercise 12(b): "8000 million" should be "8 x 10^11". p. 61, 2nd line from the bottom: "per million" should be "per 100 million". p. 76, 14th-13rd lines from the bottom: "can be interpreted as containing equivalent information to" should be "is mathematically equivalent to a likelihood resulting from". p. 79, top equation: "(y-mu)^T(Sigma^(-1))(y-mu)" should be "sum_{i=1}^{n} (y_i-mu)^T(Sigma^(-1))(y_i-mu)". p. 79, last equation: 2nd "Lambda_n^{12}" should be "Lambda_n^{21}". p. 80, 2nd line of 2nd pair of equations: "= E(Lambda_n|y) + var(mu|y) = Lambda_n + Sigma" should be "= E(Sigma|y) + var(mu|y) = Sigma + Lambda_n". p. 80, 15th line from bottom: "mu|Sigma" should be "mu|Sigma,y". p. 88, Exercise 1: The second sentence ("Also suppose . . .") should be "Also suppose that theta=(theta_1,...,theta_J) has a Dirichlet prior distribution." p. 89, Exercise 3(a): "In both cases, assume a uniform prior distribution on (mu, log sigma)" should be "Assume a uniform prior distribution on (mu_c, mu_t, log sigma_c, log sigma_t)". p. 95, 2 lines above the example: "I(theta) is positive" should be "I(theta-hat) is positive". p. 95, 4th equation from bottom: (((n-1)/n) s^2) should be (sqrt((n-1)/n) s). p. 95, 2nd line from bottom: this cross-derivative is not zero in general (only zero at the mode). The right side of the equation should be: -2n(y-bar - mu)/(sigma^2). p. 95, last equation: -1/(2 sigma^2) should be -2/sigma^2. p. 96, line 6: sigma-hat^2 = ((n-1)/(n+1)) s^2 should be sigma-tilde^2 = (n/(n+2)) sigma-hat^2. p. 96, line 8: sigma-hat^2 should be sigma-tilde^2. p. 96, line 8: 2 sigma-hat^4/n should be 2 sigma-tilde^4/(n+2). p. 103, line 10: "theta_1" should be "mu_1". p. 130, 2nd line from bottom: log(alpha/beta) should be log(alpha+beta). p. 131, 2nd paragraph: "Jacobians yield" should be "Jacobian yields". p. 131, middle: both instances of "10^{-10}" should be "-10^{10}". p. 140, equation: proportionality should be equality. p. 157, exercise 5(a): "1/(1+beta)" should be "beta/(1+beta)". p. 158, exercise 7(c): "improper" should be "proper". p. 158, exercise 7(c): last two lines should be "0 < y_j < n_j for at least one experiment j". p. 163, line just below 3rd equation: "arcsin(theta_j)" should be "2 sqrt(45) arcsin(sqrt(theta_j))". Also note in second full paragraph on p. 185 that Efron and Morris (1975) use a slightly different analysis. p. 165, line 11: "too far" should be omitted. p. 176, 1st full paragraph: "0.25/1.0" should be "1.0/0.25", and the next "0.25" should be "4". p. 181, 7th line from bottom: 20 should be 28. p. 184, 2nd paragraph: After Gelfand, Day, and Chang (1992), include a reference to Bernardo and Smith (1994). p. 187, 3rd line of Exercise 7b: "posterior" should be "prior". p. 188, end of Exercise 11: "Section 6.6" should be "Exercise 6.12". p. 218, 12th line from bottom: "N - N lambda_2" should be "N - N lambda_1". p. 239, line 3: "E(y-tilde|y)" should be "E(y-tilde|sigma^2,y)". p. 239, 17th line from bottom: "center beta-hat" should be "center X-tilde beta-hat". p. 245, table: The numbers in the table are wrong. They should be: 2.5% 25% median 75% 97.5% Incumbency 0.084 0.103 0.114 0.124 0.144 Vote proportion in 1986 0.576 0.627 0.654 0.680 0.731 Incumbent party -0.014 -0.009 -0.007 -0.004 0.001 Constant term 0.066 0.106 0.127 0.148 0.188 sigma (residual sd) 0.061 0.064 0.066 0.068 0.071 p. 256, first line of (8.13): "p(beta|Sigma_y)" should be "p(beta|Sigma_y,y)". p. 256, second line of (8.13): "N(beta|X beta-hat,V_beta)" should be "N(beta|beta-hat,V-beta)". p. 256, equation (8.14): right side of equation should also include a factor of |Sigma_y|^(-1/2). p. 258, line 2: "Q_y^{-1/2}" should be "Q_y^{-1}". p. 258, 6th line from bottom: "Q_y^{-1}" should be "Q_y". p. 290, Table 9.3: The bottom numbers on the two rightmost columns should be "-61.832", not "-63.832". (The marginal posterior density for the EM algorithm increases at every step!) p. 296, lines 6-7: "the Cholesky factor of V_{gamma}(tau)" should be "an upper-triangular matrix square root of V_{gamma}(tau)". p. 297, 6th line from bottom: tau=0 and tau=infinity should be switched. p. 306, "approximation of E(h(theta)|y)": "|-(hp)''(theta_0)|^{1/2}" should be "(2 pi)^{-d/2} |-u''(theta_0)|^{-1/2}", where d is the dimension of theta and u(theta)=log(h(theta)p(theta|y)). Correction to the correction: "-d/2" should be "d/2" just above. p. 307, definitions of w(theta) (below equations 10.3 and 10.4): these should be w(theta^l), to be consistent with the right sides of the equations. p. 309, second displayed equation: "p(gamma)p(phi|gamma)p(y|phi,gamma)" should be "p(phi)p(gamma|phi)p(y|gamma,phi)". p. 313, Figure 10.2(b): horizontal axis label "sigma" should be "tau". p. 317, Exercise 4a: "p(y|theta)" should be "p(theta|y)". p. 339, unnumbered displayed equation: there should also be a factor of |Sigma_y|^(-1/2) on the right side of the equation. p. 339, immediately before "A computational method based on EM and the Gibbs sampler": sigma_I^2 should be sigma_i^2. p. 340, lines 14, 15: Sigma^2 should be Sigma. p. 341, line 3: Sigma^2 should be Sigma. p. 350, two equations: right side of first equation should be "N(mu,V_i)"; right side of second equation should be "Inv-chi^2(nu,sigma^2)". p. 361, equation below (12.6): "nu" in denominator should be "nu sigma^2 old". p. 368, "Intraclass correlation": not quite correct as written since sigma is used twice with different meanings in the original and random effects models. To fix: - In the 2nd sentence of the "Intraclass correlation" paragraph, change "sigma" to "eta" in both places. - In the 4th sentence, just after "occurs when", add "eta^2 = sigma^2 + sigma^2_beta and". p. 378, second full paragraph: the dimension of beta is 70, not 75, because the five regional variables associated with specific years (see Table 13.1) have been removed. p. 378, beginning of last paragraph: "Sections 11.7 and 15.2" should be "Section 11.7, using the above parameterization as an augmented linear regression". p. 385, equation (14.1): "p(y|X,beta)" should be "p(y|X,beta,phi)". p. 394, 2nd equation: should be theta_{il} (not theta_{ij}) in denominator and y_{ij} (not y_{il}) outside the parentheses, where y_{ij} is the j-th element of the multinomial variable y_i. p. 396, line 16: "implicitly impose" should be "allow us to impose". p. 396, 8th line from bottom: "An implication of this coding is that the parameters A_ij will be estimated in such a manner to insure that" should be "In simulating from the posterior distribution the parameters A_ij will not be sampled but instead used to insure that". p. 429, long equation: E_old(zeta_ij) and (1-E_old(zeta_ij)) should be switched. p. 429, long equation: The following term is missing and should be added to the formula on the right side of the equation: sum_{j=1}^{17} sum_{i=1}^{30} S_j (log(lambda) E_old(zeta_ij) + log(1-lambda) (1-E_old(zeta_ij))) p. 429, long equation, and p. 430, first full paragraph: "E_old(p(zeta,theta|y))" should be "E_old(log(p(zeta,theta|y)))". p. 432, item 3: beta distribution parameters should be (h+1, 180-h+1), not (h, 180-h), because of the uniform prior distribution on lambda. p. 449, table caption: last word should be `attendance', not `secession'. p. 449, "Crude estimates": "we ignore the DK responses" should be followed by "for these two questions". p. 457, 4th line from bottom: "iid" should be "independent". p. 468, 5th line from bottom: "lack of discussion" should be followed by "in this book". p. 477, density function of Beta-binomial distribution: a and b should be alpha and beta. p. 478: 2nd full paragraph: "sum of two normal random variables" should be "sum of two independent normal random variables" (and similarly for the convolution properties of independent multivariate normal, gamma, chi-square, Poisson, and binomial random variables). p. 479, equation (A.2): "mu_j" should be "theta_j-mu_j". p. 479, equation (A.2): "(Sigma^-1)_ii" should be "1/(Sigma^-1)_ii". p. 485: In the two equations (B.1), log(p/f) should be log(f/p). (That is, we mistakenly switched the sign of the K-L information.) Then, three lines below (B.1), "maximizer" should be "minimizer"; in pp. 485-487, "maximize" should be "minimize" throughout. p. 485, last line: "H(theta)-H(theta_0)" should be "H(theta_0)-H(theta)". p. 487, 15th line from bottom: "second derivative" should be "negative second derivative". We thank Patrick Aboyoun, Adriano Azevedo, Victor De Oliveira, David Draper, Yuri Goegebeur, Chuanpu Hu, Zaiying Huang, Yoon-Sook Jeon, Tom Little, Xiao-Li Meng, Radford Neal, Phil Price, Thomas Richardson, Charles Russell, Scott Schmidler, Francis Tuerlinckx, Iven Van Mechelen, and Mark Vangel for finding some of these. This list was last changed on 29 August 2003.