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typosIMCR - Typos from the Og Christian P Robert...

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Typos from the ’Og Christian P. Robert October 10, 2011 Introducing Monte Carlo Methods with R 1. (Thanks to Kazue Ishida, Japanese translator of the book) The demos for chapters 2 and 5 do not work, due to an upgrade of R that invalidated my (much) older syntax. The demos should be fixed within the package mcsm any time soon. 2. (Thanks to Jerry Sin) On page 11, matrix summation in the matrix com- mands of Figure 1.2 should be matrix multiplication. 3. (Thanks to Liaosa Xu from Virginia Tech) On page 20, when we mention the uniform over the set ( a, b ) : y i ( a + bx i ) > log u i 1 - u i this set is missing (a) an intersection sign before the curly bracket and (b) a ( - 1) y i instead of the y i . It should be n \ i =1 ( a, b ) : ( - 1) y i ( a + bx i ) > log u i 1 - u i 4. (Thanks to Matthieu Gomez) In formula (2.1), the transform for the gamma G ) α, β ) distribution assumes β is a scale parameter, while the remainder of the book takes the opposite convention. 5. In Exercise 2.17, page 58, question d. should be d. Show that the maximum of b - a (1 - b ) a - α is attained at b = a/α . 6. In Exercise 2.21, page 59, in item (ii), || θ || should be replaced by λ and question b. should be removed. 7. On page 71, due to the late inclusion of an extra-exercise in the book, the above exercise in Exercise 3.5 actually means Exercise 3.3. 8. (Thanks to Brad McNeney, Simon Fraser University) The end of Example 3.6 (page 75) is missing a marginal estimate, i.e. there is a x (1 - x ) missing from m ( x ). It should have been obvious from the estimates we derived, 19 and 16, which do not even appear on the support of the posterior distribution represented on Figure 3.5. The R code is given as > mean(y[,1]*apply(y,1,f)/den)/mean(apply(y,1,h)/den) [1] 19.33745 > mean(y[,2]*apply(y,1,f)/den)/mean(apply(y,1,h)/den) [1] 16.54468 1
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and should have been view source > mean(y[,1]*f(y)/den)/mean(f(y)/den) [1] 94.08314 > mean(y[,2]*f(y)/den)/mean(f(y)/den) [1] 80.42832 A similar modification applies to the remark after eqn. (3.7) (page 76): mean(apply(y,1,h)/den) should be mean(f(y)/den) 9. In Exercise 3.11, page 86, question c, a line got commented by mistake in the L A T E Xfile and it should read Explore the gain in efficiency from this method. Take a = 4 . 5 in part (a) and run an experiment to determine how many normal N (0 , 1) random variables would be needed to calculate P ( Z > 4 . 5) to the same accuracy obtained from using 100 random variables in this importance sampler. 10. (Thanks to Edward Kao, University of Houston) In Exercise 3.17, page 88, question b, it should be X | Y ∼ G a (1 , y ), not X | Y ∼ G a ( y, 1). 11. (Thanks to Kazue Ishida, Japanese translator of the book) In Example 4.4, the R code cannot run as provided and contains several mistakes. (a) in the remark of page 98, the second line of code should be > wachd[wachd<10^(-10)]=10^(-10) in order to eliminate all zeroes (b) in the code page 100, the negative log-perplexities should be put to zero: > plex[plex>0]=0 > plech[plech>0]=0 (this should come right after their definition)
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