This function is designed to approximate a density of a bounded (0, 1) function with a beta distribution by equating the mean and variance to the first and second shape parameters. It does do by using the fact that:
μ = α / (α + β)
σ^2 = (α β) / [(α + β)^2 + (α + β + 1)]
The mean of the function to be approximated.
The variance of the function to be approximated.
Some nonsensical answers could be returned if one simply uses the formulas for the first and second shape parameters ourtight, especially concerning beta distributions at the extreme ends of the (0, 1) interval. To account for this, the function handles two cases: (1) if the mean is greater than or equal to 1 or is less than or equal to 0, it is arbitrarily set to 0.99 or 0.01, respectively, and (2) if either of the two shape parameters would be returned as a negative value, the variance is increased for 1,000 iterations to try to force positive shape parameters. After those 1,000 iterations, an error is returned.
The returned values are the first and second shape parameters of the fitted beta distribution, stored in a 2 x 1 vector.
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## Say we have that the tau posterior distribution from EpiBayes_ns() has mean and ## variance 0.01, and 0.015, respectively. The corresponding beta parameters will be: utils_newalphbet(0.01, 0.015) ## If we provide a mean of 1, gives meaningful results utils_newalphbet(1, 1) ## If we provide a mean of 0, gives meaningful results utils_newalphbet(0, 1) ## Not run: ## Returns an error message if shape parameters cannot be coerced to be positive utils_newalphbet(1, -1) ## End(Not run)
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