Calculate the parameters of a Beta distribution based on expert information

Share:

Description

The betaExpert function fits a (standard) Beta distribution to expert opinion. The expert provides information on a best-guess estimate (mode or mean), and an uncertainty range:

  • The parameter value is with 100*p% certainty greater than lower

  • The parameter value is with 100*p% certainty smaller than upper

  • The parameter value lies with 100*p% in between lower and upper

Usage

1
2
3
4
5
6
betaExpert(best, lower, upper, p = 0.95, method = "mode")

## S3 method for class 'betaExpert'
print(x, conf.level = .95, ...)
## S3 method for class 'betaExpert'
plot(x, y, ...)

Arguments

best

Best-guess estimate; see argument method

lower

Lower uncertainty limit

upper

Upper uncertainty limit

p

Expert's certainty level

method

Does best-guess estimate correspond to the mode or to the mean? Defaults to mode

x

Object of class betaExpert

y

Currently not implemented

conf.level

Confidence level used in printing quantiles of resulting Beta distribution

...

Other arguments to pass to function print and plot

Details

The methodology behind the betaExpert function is presented by Branscum et al. (2005) and implemented in the BetaBuster software, written by Chun-Lung Su.

The parameters of a standard Beta distribution are calculated based on a best-guess estimate and a 100(p)% uncertainty range, defined by a lower and/or upper limit. The betaExpert function uses minimization (optimize) to derive α and β from this best guess and lower and/or upper limit. The resulting distribution is a standard 2-parameter Beta distribution: Beta(α, β).

Value

A list of class "betaExpert":

alpha

Parameter α (shape1) of the Beta distribution

beta

Parameter β (shape2) of the Beta distribution

The print method for "betaExpert" additionally calculates the mean, median, mode, variance and range of the corresponding Beta distribution.

Author(s)

Brecht Devleesschauwer <brechtdv@gmail.com>

References

Branscum AJ, Gardner IA, Johnson WO (2005) Estimation of diagnostic-test sensitivity and specificity through Bayesian modeling. Prev Vet Med 68:145-163.

See Also

Package rriskDistributions, which provides a collection of functions for fitting distributions to given data or by known quantiles.

betaPERT, for modelling a generalized Beta distribution based on expert opinion

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
## Most likely value (mode) is 90%
## Expert states with 95% certainty that true value is larger than 70%
betaExpert(best = 0.90, lower = 0.70, p = 0.95)

## Most likely value (mode) is 0%
## Expert states with 95% certainty that true value is smaller than 40%
betaExpert(best = 0, upper = 0.40, p = 0.95)

## Most likely value (mode) is 80%
## Expert states with 90% certainty that true value lies in between 40% and 90%
betaExpert(best = 0.80, lower = 0.40, upper = 0.90, p = 0.90)

## Mean value is assumed to be 80%
## Expert states with 90% certainty that true value lies in between 40% and 90%
betaExpert(best = 0.80, lower = 0.40, upper = 0.90, p = 0.90, method = "mean")