September 2012
Intermediate to advanced
486 pages
10h 41m
English
Content preview from Bayesian Statistics: An Introduction, 4th Edition
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7.9 Exercises on Chapter 7
1. Show that in any experiment E in which there is a possible value y for the random variable 
such that 
, then if z is any other possible value of 
, the statistic t=t(x) defined by
is sufficient for θ given x. Hence, show that if 
is a continuous random variable, then a naïve application of the weak sufficiency principle as defined in Section 7.1 would result in 
for any two possible values y and z of 
.
such that , then if z is any other possible value of , the statistic t=t(x) defined by
is sufficient for θ given x. Hence, show that if is a continuous random variable, then a naïve application of the weak sufficiency principle as defined in Section 7.1 would result in for any two possible values y and z of .
2. Consider an experiment 
. We say that censoring (strictly speaking, fixed censoring) occurs with censoring mechanism g (a known function of x) when, instead of 
. We say that censoring (strictly speaking, fixed censoring) occurs with censoring mechanism g (a known function of x) when, instead of