To calculate the credible region for the odds ratio&nbsp;θ1−θ. This is part of a bigger problem where I have already calculated&nbsp;90%&nbsp;credible region for random variable&nbsp;θ:P(θ≤0.30)=0.05P(θ≤0.52)=0.95P(0.30≤θ≤0.52)=0.9.

You should be careful in that your manipulation only works if θ≤1. You say that θ comes from a beta distribution though, so you're good.You have a small algebra mistake: it should beP(θ1−θ≤a)=P(θ≤a1+a)=0.05which impliesa=0.42 and similarlyP(θ1−θ≤b)=P(θ≤b1+b)=0.95which impliesb=1.08

Question: "To calculate the credible region for the odds..."

College
Statistics and Probability
College Statistics
Confidence intervals

zdebe5l8

Answered question

2022-04-11

To calculate the credible region for the odds ratio $\frac{θ}{1 - θ}$ . This is part of a bigger problem where I have already calculated $90 %$ credible region for random variable $θ$ :
$P (θ \leq 0.30) = 0.05$
$P (θ \leq 0.52) = 0.95$
$P (0.30 \leq θ \leq 0.52) = 0.9 .$

Answer & Explanation

szkliwiakinrd

Beginner2022-04-12Added 10 answers

You should be careful in that your manipulation only works if

θ \leq 1

. You say that

θ

comes from a beta distribution though, so you're good.
You have a small algebra mistake: it should be

P (\frac{θ}{1 - θ} \leq a) = P (θ \leq \frac{a}{1 + a}) = 0.05

which implies

a = 0.42

and similarly

P (\frac{θ}{1 - θ} \leq b) = P (θ \leq \frac{b}{1 + b}) = 0.95

which implies

b = 1.08

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