## Emails I cannot reply to

I received this email yesterday from a reader of The Bayesian Choice (still selling on Amazon at a bargain price of  \$32.97!)

if x has gamma distribution with shap parameter alpha and scale parameter tetha , and tetha has gamma distribution  with “v ” and “x0” parameters as shape and scale parameters show that bayes estimatore of tetha under Hellinger loss function is of the form of “k/(x+x0)”
if  we calculate Hellinger loss function for this distribution we see a loss function with nearly beta distribution.
i tried to earn this answer for bayes estimator ,but i could not  see this answer, can u give me a hint for this question?

Alas (?) I obviously cannot reply without providing the answer…. Of course, if there is a problem with this exercise, just let me know! But once you write down the Hellinger loss as

$\text{L}(\theta,\delta) = 1 - \int \sqrt{ f_\theta(x) \,f_\delta(x) } \,\text{d}x$

the remainder of the exercise is sheer calculus…

### 6 Responses to “Emails I cannot reply to”

1. Is there a Figure 1.1.6 in this book? Are there Errata?

• No there should be no Figure 1,1,6! Where did you spot this typo?

There is an errata on my book webpage, to be updated.

• Pages 5, under equation 1.1.2, specifically “… this modeling considerably smoothes the histogram (see Figure 1.1.6), but also allows a description of the image through five parameters.” Also, page 4, “For instance, Figure 1.1.6 ….” It’s probable the intended reference is 1.1.2 in both instances, but it seems that 1.1.2 should then have a histogram backdrop in addition to the trace of the two-component mixture model.

• I have just spent the afternoon compiling the typos discussed on this blog for all my books. It is now available in pdf format.

2. Sebastian Nowozin Says:

The price really is a bargain. This low price is possible due to Springers print-on-demand process they now apply to many of their scientific text books.

On the downside the process is not perfect yet and although it has improved in the past year there are still artifacts. In your book for example, a large number of horizontal lines in fractions (between numerator and denumerator) are missing, especially in free standing equations (eg page 23, 64, 174, 257, ..). It is still quite readable. An earlier print-on-demand version of your Robert/Casella Monte Carlo book was unreadable due to many algorithm environments being completely missing (blanked out) and Figures being rasterized at incredibly low resolutions, making it impossible to distinguish different line styles (dashed, dotted, etc.). I hope Springer can find a way to avoid these issues in the future.

• Thank you. The Chinese printing I mentioned a while ago is of a much worse quality (which makes sense given the price!)…

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