Find the posterior mean for α and π by using the formula for the total probability P(yi = 1).

Suppose a binary response has true prevalence Pr(Y = 1) = π but that observed responses are subject to misclassification with probabilities α0 = Pr(y = 1|Y = 0), and α1 = Pr(y = 0|Y = 1). Assuming α0 = α1 = α, state the total probability P(yi = 1) in terms of the true prevalence probabilities P(Y = 1) and P(Y = 0) and the conditional probabilities P(y = 1|Y = 1) and p(y = 1|Y = 0). Winkler and Gaba (1990, p. 307) note that high values of α are unlikely and provide observed data on a juvenile survey question ‘have you beaten up on someone’, with r = 21 and n = 104. They assume π ∼ Beta(2, 8) and α ∼ Beta(2, 18) consistent with a prior misclassification rate of 10%. Find the posterior mean for α and π by using the formula for the total probability P(yi = 1).

What are the multiple correlations of three sets of predictors and overall state of health?

What are the multiple correlations of three sets of predictors and overall state of health? The first set of predictors contains demographic variables (age and years of education). The second….

What conclusions might you draw from these data?

According to the Death Penalty Information Center, death penalty states record higher murder rates than non-deathpenalty states. On January 1, 2014, the average murder rate among death penalty states was….

How would you defend these reforms to persons who advocate for tough-on-crime approaches?

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