idm {imprecise101}

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