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

By Yasui Y.

Read or Download A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono PDF

Best probability books

A First Course in Probability Models and Statistical Inference

Welcome to new territory: A path in likelihood versions and statistical inference. the concept that of likelihood isn't new to you after all. you've gotten encountered it given that early life in video games of chance-card video games, for instance, or video games with cube or cash. and also you find out about the "90% likelihood of rain" from climate studies.

Additional info for A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono

Example text

Thus limsupk^oo Qk(Qt)^2/n for each n. This last implies that the family of stationary measures {Qk} is tight on [0,1]. As noted earlier, this means the family {Qk} is tight in Ms((l). Thus, if Q is any limit point, we must have Q e A n A,*, since A H Aoo is closed, and also Q e G since G is closed. Hence, we have contradicted the assumption. , J(A)S= -infQ6AH(Q), but only under the additional hypothesis that the family AM of one-dimensional marginals of Q as Q varies over A forms a tight family of measures in X.

For each f > 0 and each xeX, we use this mapping to induce a probability measure Ttx on Ms(£l) by defining Ftx = P0>XR^, i-e-> if B<^MS(CI), then If P0x is ergodic with invariant measure v(dx) on X, and if Q&Ms(fl) is the stationary Markov process with v as its marginal distribution, then, by the ergodic theorem, as t —» °o, a4 SECTION 9 Here, 8\$ is the Dirac measure on Ms(fl) concentrated at Q. We are concerned with the probabilities of large deviations for the measure Ft x. In Section 10 we define, for any Q&Ms(fy, the entropy, H(Q), of the stationary process O with respect to the Markov process P0>x.

E(£l)<= Ms(Cl) be the subset of Ms(£l) consisting of the ergodic measures. ME(fl) is the set of extremals of Ms(fl). It follows from an argument of Oxtoby [11] that there exist a subset ft0c=ft which is ^o°° measurable and a ^o°° measurable map TT^: fto —>ME(ty with the following properties: O(ft0) = 1 for all QeMs(fl) and Q{o>: ir« = Q}= 1 for all QME(fl). d. of Q given &Q°°. d. can always be selected so that it is jointly measurable in Q and w. We define the desired ^ by R^ = R^, o>). Then, for all Qe^ E (ft), SOME PROPERTIES OF ENTROPY 39 But, R^ = R^v, «) is indepenednt of Q, and so we have a linear relation true for extremals and hence true for QeJ(s(ft).