TYPOS AND OTHER MINOR ERRORS IN FIRST PRINTING

(1) Page 17, 4th line. Change “2000” to “1996” in “Ning and Finch (2000).” Actually, this report has since been published; the details are: Ning, Y. and Finch, S.J. (2000). The null distribution of the likelihood ratio test for a mixture of two normals after a restricted Box–Cox transformation. Communications in Statistics—Simulation and Computation 29, 449–461.

(2) Page 74, 15th line. Insert “data” after “nuclear.”

(3) Page 82. The divisor in equation (3.4) should be “∑_{j=1}^{n} τ_{ij}^{(k)}” instead of “τ_{ij}^{(k)}.”

(4) Page 95. Delete the second word, “estimate.”

(5) Page 119. The term “p(z | Ψ)” should be deleted from the right-hand side of equations (4.1) and (4.2).

(6) Page 129. Change “1” to “4” in the following: “Section 1.2” (line 2); “(1.27)” (line 18); “Figure 1.1” (lines 30 and 31); “Figure 1.2” (lines 30 and 32).

(7) Page 134, 9th line. The term “\frac{1}{2} | I(Ψ) |” should be “\frac{1}{2} log | I(Ψ) |.”

(8) Page 136. Insert “π_{i}” before “f_{i}(y_{j}; θ_{i})” in the right-hand side of equation (5.1).

(9) Page 156. In the equation on the 6th line, “ℓ_{j}” should be“log ℓ_{j},” and in the equation on the 11th line, “û_{i}/g” should be replaced by “π̂_{i}û_{i}.”

(10) Page 172, 5th line. In the left-hand side of equation (5.64), change “π_{hi}” to “π_{i}.”

(11) Page 173. (a) 9th last line. Insert “(with logit link)” after “multinomial.” (b) Last line. The right-hand side of equation (5.68) should be

∑_{i=1}^{2} π_{i}(x_{j}; α) ∑_{h=1}^{5} π_{hi}(x_{j}; α_{i}) ∏_{v=1}^{10} θ_{vhi}^{y_{vj}}.

(12) Page 202. In equation (6.22), the term “f(w)” should be replaced by “f(w; Ψ̂).”

(13) Page 203. (a) In equation (6.24), the term “b(F)” should be multiplied by “n.” (b) In the first line of Section 6.8.2, “d” should be divided by “n” in the phrase “equal to d.”

(14) Page 204. In equation (6.27), the term “b(F̂_{n})” should be multiplied by ‘n.’

(15) Page 209. (a) In the 1st line, “integrated log likelihood” should be “log integrated likelihood;” (b) on the right-hand side of equation (6.49), “O(d log n)” should be “O(n^{d});” and (c) in the line after equation (6.50), change “as the penalized likelihood to be maximized” to “as twice the negative penalized log likelihood to be minimized.”

(16) Page 229. The last term “u_{j}^{(k)}” in the first line of equation (7.34) should be “u_{ij}^{(k)}”.

(17) Page 232, equation on the 2nd line below equation (7.37). This equation should be

replaced by

ẑ_{ij} = 1, if i = arg max_{h} τ̂_{hj},
= 0, otherwise,

for i = 1, …, g; j = 1, …, n.

(18) Page 234, 4th line of Section 7.8. Change “four” to “five” in “four-dimensional.”

(19) Page 247. In equation (8.28), “ω_{i}^{(k +1/2)}” should be “ω_{i}^{(k)}.”

(20) Page 250, 1st line of Section 8.9. Insert “model” after “ mixtures of PCAs.”

(21) Page 255. In equation (7.14), the term “\frac{1}{2}p log(u_{j})” should be inserted.

(22) Page 270, 7th line. Delete “log” in the right-hand side of the equation.

(23) Page 272, 17th line. In the right-hand side of the equation, “x_{j}” should be“x_{j}^{T}.”

(24) Page 304. (a) Lines 7 to 10. At the start of the sentence before equation (12.4), insert “For the ordinary EM algorithm,” and after equation (12.4), insert, “but with the incremental EM, the current estimate Ψ^{(k)} is used to update the posterior probabilities of component membership for only a single block of observations at a time.”

(b) In the 9th last line, insert “partly” after “expressed” and insert “and previous scan” after “previous iteration.”

(c) 2nd last line. Delete “last iteration of the” before “the previous.”

(25) Page 306, 9th last line. (a) Change the sentence beginning “For convenience ...” to “For convenience, we denote τ_{ij}(y_{j}; Ψ^{(k−1 +(j−1)/n)}) and τ_{ij}(y_{j}; Ψ^{(k +(j−1)/n)}) as τ_{ij} and τ_{ij}^{∗}, respectively, and we write π_{i}^{(k+ (j−1)/n)}, μ_{i}^{(k+ (j−1)/n)}, and Σ_{i}^{(k+ (j−1)/n)} as π_{i}, μ_{i}, and Σ_{i}, respectively.”

(b) In the 6th last line, delete “τ_{ij}^{∗}.”

(26) Page 329. On the right-hand side of equation (13.10) in the last line, “z_{ij}” should be inserted before “f_{i}(y_{j}; θ_{i})” in the last term.

(27) Page 350. In the reference Aitkin et al. (1981), the volume number “B 144” should be “A 144.”

(28) Page 366. In the reference “Genovese and Wasserman (1999), “Mallon” should be “Mellon,” and in “Ghahramani (1995),” the volume number “17” should be “7,”