Monte Carlo Methods in Bayesian Computation

MING-HUI CHEN, QI-MAN SHAO, AND JOSEPH G. IBRAHIM

Publisher: Springer-Verlag; Publication Date: January, 2000

ERRATA

(1)

On page 30, line -9,

Error:

$$\vartheta_1^\ast, \vartheta_1^\ast, \dots, \vartheta_{k-1}^\ast$$

Correction:

$$\vartheta_1^\ast, \vartheta_2^\ast, \dots, \vartheta_{k-1}^\ast$$

(2)

On page 36, in Equation (2.5.11),

Error:

$$L(\beta,\gamma_2,z\vert D)$$

Correction:

$$L(\beta,\gamma,z\vert D)$$

(3)

On page 41, line -8,

Error: ``Using (2.5.25)"

Correction: ``Using (2.5.26)"

(4)

On page 86, line 16,

Error:

$$\hat{E}_{a}(h)=\sum^n_{i=1} w_i h(\theta_i).$$

Correction:

$$\hat{E}_{a}(h)=\frac{1}{n}\sum^n_{i=1} w_i h(\theta_i).$$

(5)

In Equation (4.3.1) on page 98,

Error:

$$\pi(\theta^{\ast (j)}\vert D)=\int_\Omega \pi( \theta^{\ast (j)}\vert \theta^{(-j)},D) \pi(\theta) d \theta.$$

Correction:

$$\pi(\theta^{\ast (j)}\vert D)=\int_\Omega \pi( \theta^{\ast (j)}\vert \theta^{(-j)},D) \pi(\theta\vert D) d \theta.$$

(6)

In Equation (4.3.3) on page 98 and line -11 on page 99,

Error:

$$w(\theta^{\ast (j)}\vert\theta^{(-j)})$$

Correction:

$$w(\theta^{(j)}\vert\theta^{(-j)})$$

(7)

On page 102, second line of the penultimate paragraph,

Error: ``0For"

Correction: ``For"

(8)

In Equation (8.3.6) on page 251,

Error:

$$B_{12} = {m(D\vert{\cal M}_1)/m(D\vert{\cal M}_r) \over m(D... ...l M}_2)/\pi({\bf\varphi}= 0\vert{\cal M}_2) } \;\;\; (8.3.6)$$

Correction:

$$B_{12} = {m(D\vert{\cal M}_1)/m(D\vert{\cal M}_r) \over m(D... ...M}_2)/\pi({\bf\varphi}=0\vert D,{\cal M}_2) } \;\;\; (8.3.6)$$

(9)

On page 267, line 8 of the first paragraph,

Error: ``... for these models is now ...''

Correction: ``... for these models are now ...''

(10)

On page 301

Error: `` $\pi(\theta_k\vert{\cal M}_k)$'' in Equation (9.5.1) and `` $\pi(k,\theta_k\vert D)$'' in line 21.

Correction: `` $\pi(\theta^{(k)}\vert{\cal M}_k)$'' in Equation (9.5.1) and `` $\pi(k,\theta^{(k)}\vert D)$'' in line 21.

(11)

In Exercise 9-16 on page 306,

Error: ``Metropolized Chib's method"

Correction: ``Metropolized Carlin-Chib's method"

(12)

On page 310, line -11,

Error:

$$\left( \int \frac{1}{f(y_i\vert\theta_l,x_i)} \pi(\theta\vert D) d\theta \right)^{-1}.$$

Correction:

$$\left( \int \frac{1}{f(y_i\vert\theta,x_i)} \pi(\theta\vert D) d\theta \right)^{-1}.$$

(13)

On page 316, line -5,

Error: ``$z_i \sim F$"

Correction: `` $\epsilon_i \sim F$"

(14)

(a) On page 316, line 14; and (b) on page 317, Equations (10.1.26) and (10.1.27),

Error: ``$x_i\beta$"

Correction: ``$x'_i\beta$"

(15)

On page 317, line -15 before Equation (10.1.29),

Error: ``$K > x_i\beta$"

Correction: `` $K> x'_i\beta>0$"

(16)

On page 318, line 11,

Error:

$$\hat{E}[ P( \vert\epsilon_i\vert>K\vert \beta, y_i=1)\vert D ] = {1 \over T}\sum^T_{t=1} \Phi(-K) /\Phi(x_i'\beta_t).$$

Correction:

$$\hat{E}[ P( \vert\epsilon_i\vert>K\vert \beta, y_i=1)\vert D... ...T}\sum^T_{t=1} P( \vert\epsilon_i\vert>K\vert \beta_t, y_i=1).$$

(17)

In Chib, S. and Greenberg, E. (1998) on page 359,

Error: ``Bayesian analysis of multivariate probit models"

Correction: ``Analysis of multivariate probit models"

(18)

In Robert, C.P. (Ed.) (1998) on page 370,

Error: ``New York: Wiley"

Correction: ``New York: Springer-Verlag"

(19)

In Ritter and Tanner (1992) on page 370 and in Tanner and Wong (1987) on page 372,

Error: ``Tanner, T.A."

Correction: ``Tanner, M.A."

Acknowledgments

We would like to thank Steven N. MacEachern and Peter Müller for pointing out some errors in the above list.