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In general we would have two tables of this kind when setting up our function g x,one for estimating the parameters associated with P x w 1 and one for P x w 2
...The estimates shown above are examples of point estimates
...Two basic assumptions made in deriving any estimation rule through Bayesian decision theory are:1 the form of the prior distribution on the parameter space,i
...probability distribution on the possible values of the binomial parameter;and 2 the form of the loss function used to measure the error made in estimating the parameter
...Once these two assumptions are made explicit by defining the form of the distribution and loss function,then,together with Bayes Principle which seeks to minimise the posterior conditional expected loss given the observations,we can derive a number of different estimation rules
...where x is the number of successes in n trials,and a and b are parameters dictated by the particularcombination of prior and loss |
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function
...One important reason for having estimation rules different from the simple x n,is that this is rather unrealistic for small samples
...0 <p <1
...This is really as much as I wish to say about estimation rules,and therefore I shall not push the technical discussion on this points any further;the interested reader should consult the readily accessible statistical literature
...Recapitulation At this point I should like to summarise the formal argument thus far so that we may reduce it to simple English
...The first point to make then,is that,we have been trying to estimate P relevance document,that is,the probability of relevance for a given document
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