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A Clinical Trial. The clinical trial introduced in Example 2.1.4 was concerned with

how likely patients are to avoid relapse while under various treatments. For each i,

let\({X_i} = 1\)if patient i in the imipramine group avoids relapse and\({X_i} = 0\)otherwise.

Let P stand for the proportion of patients who avoid relapse out of a large group

receiving imipramine treatment.

If P is unknown, we can model\({X_1},{X_2}...\)as iid. Bernoulli random variables with parameter p conditional on\(P = p\)

The patients in the imipramine column of Table 2.1 should provide us with some information that changes our uncertainty about P. A statistical inference would consist of making a probability statement about the data and/or P, and what the data and P tell usabout each other. For instance, in Example 4.7.8, we assumed that P had the uniform distribution on the interval\(\left( {0,1} \right)\)and we found the conditional distribution of P given the observed results of the study. We also computed the conditional mean of P given the study results as well as the M.S.E. for trying to predict P both before and after observing the results of the study.

A statistical model consists of an identification of random variables of interest (both observable and only hypothetically observable),a specification of a joint distribution for the observable random variables, the identification of any parameter of those distribution that are assumed unknown and possibly hypothetically observable, and a specification for a joint distribution for a unknown parameters.

From the given information and the definition of statistical model the component of statistical model is:

The random variables of interest are the observables\({X_1},{X_2}...\)and the hypothetically observable (parameter) P. The \({X_i}'s\) are i.i.d. Bernoulli with parameter p given \(P = p\)