Convergence of logistic parameters in Bayesian approach
Zhen-Lin Hou · Osaka City University (Osaka City University) · 2000
where jct 's are known real numbers called the observation points. It is sometimes more natural to consider the parameters a and β in the above logistic way than something like e/(l + e)'s. For example, let us cosider a random variable Y on {0, 1} with small P[Y = 1], where the value 1 stands for a serious accident which we must avoid definitely. Since we are sensitive on the value P[Y = 1], we take the measurement log P[Y = 1] instead of the value itself. In this case, the logistic parametrization is suitable. In the same reason, it is natural to assume that the prior distribution a and β is uniform, that is, the joint prior density for (α, β) is given by p(a, β) = 1 on R. Then we discuss the posterior distribution on (α, β) under a set of observations F; = v; (ΐ = l , . . . ,/ i) . By the Bayes formula, the posterior probability density, is given by