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16 - Estimation of alpha and beta Parameters for Prior Beta distributions

This program calculates the alpha and beta parameters for prior Beta distributions used in the Bayesian analyses, based on the values specified for the mode and 5th or 95th percentile of the distribution. The mode and percentiles can be estimated either from existing data or from expert opinion.

For this analysis, two estimates were calculated. The first for a distribution with a mode of 0.9 (90%) and a 5th percentile of 0.75 (75%), and the second is for a distribution with a mode at 0.75 and the 95th percentile at 0.9. Input values and results are summarised below.

Distribution	Mode	5/95 percentile	Alpha value	Beta value
1	0.9	0.75	22.99	3.44
2	0.75	0.9	7.39	3.13

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Contents
1	Fixed pool size and perfect tests
2	Fixed pool size and tests with known sensitivity and specificity
3	Fixed pool size and tests with uncertain sensitivity and specificity
4	Variable pool size and perfect test
5	Pooled prevalence using a Gibbs sampler
6	Estimated true prevalence using one test (unpooled) with a Gibbs sampler
7	Estimated true prevalence using two tests (unpooled) with a Gibbs sampler
8	Sample size calculation for fixed pool size and perfect tests
9	Sample size calculation for fixed pool size and tests with known sensitivity and specificity
10	Sample size calculation for fixed pool size and tests with uncertain sensitivity and specificity
11	Simulate sampling for fixed pool size and assumed perfect test
12	Simulate sampling for fixed pool size and test with known sensitivity and specificity
13	Simulate sampling for fixed pool size and test with uncertain sensitivity and specificity
14	Simulate sampling for variable pool size and assumed perfect test
15	Demonstration of freedom using pooled testing with tests of known sensitivity and fixed pool size
16	Estimation of alpha and beta Parameters for Prior Beta distributions
17	Estimation of Beta probability distributions for specified alpha and beta parameters