# A statistical method for the estimation of window-period by Yasui Y.

By Yasui Y.

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In our parametric framework an inference on the parameters. As mentioned above, the choice of the prior distribution is delicate, but its determination should be incorporated into the statistical process in parallel with the determination of the distribution of the observation. Indeed, a prior distribution is the best way to include residual information into the model. In addition, Bayesian statistical analysis provides natural tools to incorporate the uncertainty associated with this information in the prior distribution (possibly through a hierarchical modeling, see Chapter 10).

A natural conﬁdence region is then C = = {θ; π(θ|x) > k} 10 θ; θ − x > k 11 . We can also associate a conﬁdence level α with this region in the sense that, if zα/2 is the α/2 quantile of N (0, 1), Cα = 10 x − zα/2 11 10 10 , x + zα/2 11 11 10 11 has a posterior probability (1 − α) of containing θ. We will see in Chapter 10 that a posterior distribution can sometimes be decomposed into several levels according to a hierarchical structure, the parameters of the ﬁrst levels being treated as random variables with additional prior distributions.

Conditionality Principle If two experiments on the parameter θ, E1 and E2 , are available and if one of these two experiments is selected with probability p, the resulting inference on θ should only depend on the selected experiment. This principle seems diﬃcult to reject when the selected experiment is known, as shown by the following example. 5, or through a less precise but always available machine, which gives x2 ∼ N (θ, 10). The machine being selected at random, depending on the availability of the more precise machine, the inference on θ when it has been selected should not depend on the fact that the alternative machine could have been selected.