An R version of Wes Johnson and Chun-Lung Su's Betabuster
A function to return shape1 and shape2 parameters for a beta distribution, based on expert elicitation.
epi.betabuster(mode, conf, greaterthan, x, conf.level = 0.95, max.shape1 = 100, step = 0.001)
mode |
scalar, the mode of the variable of interest. Must be a number between 0 and 1. |
conf |
level of confidence (expressed on a 0 to 1 scale) that the true value of the variable of interest is greater or less than argument |
greaterthan |
logical, if |
x |
scalar, value of the variable of interest (see above). |
conf.level |
magnitude of the returned confidence interval for the estimated beta distribution. Must be a single number between 0 and 1. |
max.shape1 |
scalar, maximum value of the shape1 parameter for the beta distribution. |
step |
scalar, step value for the shape1 parameter. See details. |
The beta distribution has two parameters: shape1 and shape2, corresponding to a and b in the original verion of BetaBuster. If r equals the number of times an event has occurred after n trials, shape1 = (r + 1) and shape2 = (n - r + 1).
A list containing the following:
shape1 |
the |
shape2 |
the |
mode |
the mode of the estimated beta distribution. |
mean |
the mean of the estimated beta distribution. |
median |
the median of the estimated beta distribution. |
lower |
the lower bound of the confidence interval of the estimated beta distribution. |
upper |
the upper bound of the confidence interval of the estimated beta distribution. |
variance |
the variance of the estimated beta distribution. |
Simon Firestone (Faculty of Veterinary and Agricultural Sciences, The University of Melbourne, Australia) with acknowledgements to Wes Johnson and Chun-Lung Su for the original standalone software.
Christensen R, Johnson W, Branscum A, Hanson TE (2010). Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians. Chapman and Hall, Boca Raton.
## EXAMPLE 1: ## If a scientist is asked for their best guess for the diagnostic sensitivity ## of a particular test and the answer is 0.90, and if they are also willing ## to assert that they are 80% certain that the sensitivity is greater than ## 0.75, what are the shape1 and shape2 parameters for a beta distribution ## satisfying these constraints? rval <- epi.betabuster(mode = 0.90, conf = 0.80, greaterthan = TRUE, x = 0.75, conf.level = 0.95, max.shape1 = 100, step = 0.001) rval$shape1; rval$shape2 ## The shape1 and shape2 parameters for the beta distribution that satisfy the ## constraints listed above are 9.875 and 1.986, respectively. ## This beta distribution reflects the probability distribution ## obtained if there were 9 successes, r: r <- rval$shape1 - 1; r ## from 10 trials, n: n <- rval$shape2 + rval$shape1 - 2; n dat <- data.frame(x = seq(from = 0, to = 1, by = 0.001), y = dbeta(x = seq(from = 0, to = 1,by = 0.001), shape1 = rval$shape1, shape2 = rval$shape2)) ## Density plot of the estimated beta distribution: ## Not run: library(ggplot2) ggplot(data = dat, aes(x = x, y = y)) + geom_line() + scale_x_continuous(name = "Test sensitivity") + scale_y_continuous(name = "Density") ## End(Not run)
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