idm: Imprecise Dirichlet Model

In imprecise101: Introduction to Imprecise Probabilities

Imprecise Dirichlet Model

Description

This function computes lower and upper posterior probabilities under an imprecise Dirichlet model when prior information is not available.

This function searches for the lower and upper bounds of a given level of the highest posterior density interval under the imprecise Dirichlet prior.

Usage

idm(nj, s = 1, N, tj = NA_real_, k, cA = 1)

hpd(
  alpha = 3,
  beta = 5,
  p = 0.95,
  tolerance = 1e-04,
  maxiter = 100,
  verbose = FALSE
)

Arguments

nj	number of observations in the j th category
s	learning parameter
N	total number of drawings
tj	mean probability associated with the j th category
k	number of elements in the sample space
cA	the number of elements in the event A
alpha	shape1 parameter of beta distribution
beta	shape2 parameter of beta distribution
p	level of credible interval
tolerance	level of error allowed
maxiter	maximum number of iterations
verbose	logical option suppressing messages

Value

idm returns a list of lower and upper probabilities.

p.lower	Minimum of imprecise probabilities
p.upper	Maximum of imprecise probabilities
v.lower	Variance of lower bound
v.upper	Variance of upper bound
s.lower	Standard deviation of lower bound
s.upper	Standard deviation of upper bound
p	Precise probabilty
p.delta	Degree of imprecision

hpd gives a list of scalar values corresponding to the lower and upper bounds of highest posterior probability density region.

References

Walley, P. (1996), Inferences from Multinomial Data: Learning About a Bag of Marbles. Journal of the Royal Statistical Society: Series B (Methodological), 58: 3-34. https://doi.org/10.1111/j.2517-6161.1996.tb02065.x

Examples

idm(nj=1, N=6, s=2, k=4)
x <- hpd(alpha=3, beta=5, p=0.95) # c(0.0031, 0.6587) when s=2
# round(x,4); x*(1-x)^5

imprecise101 documentation built on Feb. 16, 2023, 6:08 p.m.