chapter14.md

#Simple applicatons of decision theory.

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Comments on 14.1 and 14.2

On p. 428 Jaynes seems to be describing a simple probabilistic graphical model (and is making some analogy between belief propagation in a PGM and Huygens principle).

$Y$ --- $V$ --- $D$

Then $V$ screens $D$ from $Y$ and also screens $Y$ from $D$.

See also this on Kevin Van Horn's page.

Comments on 14.4

Small nitpick: There is a discrepancy between the caption of Fig 14.1 and the text ($L_a=2, L_r=1$ gives $L_a=2L_r$ and not $L_a=(3/2)L_r$).

A key point seems to be that (in the example at hand) both the minimax and Neyman-Pearson decision rules are reproduced by a Bayesian decision rule with appropriate prior. It would be interesting to know how general this phenomenon is. I guess by Wald's theorem one only needs to show that minimax/Neyman-Pearson is an dmissible decision rule, as Jaynes says: "Wald showed in great generality what we have just illustrated by one simple example".

Comments on 14.7

Seems like in the real world the fact that an order for 40 green widgets came -- 4 times the average daily order size! -- in may indicate that the green widget shortage is looming (or something like that). This might give one some impetus to make green ones after all...