By Seymour Geisser (auth.)
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Extra resources for Predictive Inference: An Introduction
Example text
A BAYES IAN PREDICTION 50 If the loss is additive and equal for each component of x
A set of eight observations was generated from an exponential distribution with mean 1. 904. All predicting methods were then plotted on the same graph and all normed so that the area under each curve was unity to make the comparison easier to see (Fig. 2). Two of the methods MLPD and the K-L loss function approach yield the same result. The MLPD /KL result is quite close to the PL method. As expected, the extended FRL exhibits a completely different scaling of the predicted value of a future observable and would yield rather anomalous results, if used.
0, ... , M ( r+s ) r+s(M + N -r-s )N+M-r-s FRL(rls)a M-r r'(M-r) purports to scale the likelihood of future values of r given s. The most "likely" value(s) is(are) achieved by maximizing FRL(rls). This example was given by Fisher and the procedure detailed in the more general form by Kalbfleisch (1971). Its restricted use is exemplified by applying the method to the simple exponential case forM= 1. 9. Let X;, i = 1, ... 3 27 then FRL(x N+! lx (N)) __ iN(N + l)N+l X N+! ---------,-:--:-N_)N+! ( XN+!