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 x.
greaterthan
logical, if TRUE you are making the statement that you are conf confident that the true value of the variable of interest is greater than x. If FALSE you are making the statement that you are conf confident that the true value of the variable of interest is less than x.
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.
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).
the shape1 parameter for the estimated beta distribution.
shape2
the shape2 parameter for the estimated beta distribution.
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.
Author(s)
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.
References
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.
Examples
## 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$shape1 - 2; n
## Density plot of the estimated beta distribution:
plot(seq(from = 0, to = 1, by = 0.001),
dbeta(x = seq(from = 0, to = 1,by = 0.001), shape1 = rval$shape1,
shape2 = rval$shape2), type = "l", xlab = "Test sensitivity",
ylab = "Density")