Heligman-Pollard parameter prior formation for use with Bayesian Melding using IMIS

Description

Forms a prior distribution (drawn from a uniform distribution) for each of the eight Heligman-Pollard parameters. First, using optim(), mle estimates of the parameters are fitted to the deaths and persons at risk supplied by the user. Once these estimates (returned as mle) and their standard errors (se) are obtained, 8000 (See documentation for prior.form) draws from a uniform distribution with bounds mle[i] +/- senum*se are taken to form a prior distribution for each parameter.

Usage

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pri.mle(nrisk, ndeath, age = c(0, 1, seq(5, 100, 5)), 
lo = c(1e-08, 1e-07, 1e-07, 1e-07, 1e-07, 15, 1e-07, 1), 
hi = c(1, 1, 1, 0.5, 15, 55, 0.1, 1.5), senum = 15, 
theta.test = c(0.06008, 0.31087, 0.34431, 0.00698, 1.98569,
26.71071, 0.00022, 1.088), opt.meth = "Nelder-Mead")

Arguments

nrisk

The number of persons at risk of death in each age group

ndeath

The number of deaths in each age group

age

A vector containing the ages at which probabilities of death are calculated

lo

If opt.meth="L-BFGS", this vector contains the lower bounds in lower argument of optim() )

hi

If opt.meth="L-BFGS", this vector contains the upper bounds in upper argument of optim() )

senum

The number of standard errors on each side of the mle estimate. This argument controls how wide or narrow the uniform distribution is from which the prior distribution will be drawn.

theta.test

Start values for optim. The defaults encompass the Brass standard (Rogers and McKnown 1989).

opt.meth

The same as method in opim().

Details

Priors drawn with this function can be used with the function hp.bm.imis or other functions from the HPbayes package.

Value

q0

A matrix containing the prior distibution with each column corresponding to one of the Heligman-Pollard parameters

mle

A vector containing the mle estimates. These define the center of each uniform from which the prior was drawn

se.out

A vector containing the standard error for each element of mle

pri.lo

The lower bounds on the uniform distributions from which the prior for each parameter is drawn

pri.hi

The upper bounds on the uniform distributions from which the prior for each parameter is drawn

References

Heligman, Larry and John H. Pollard. 1980 "The Age Pattern of Mortality." Journal of the Institute of Actuaries 107:49–80.

See Also

hp.bm.imis, optim

Examples

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data(HPprior) ##loads a vector of persons at risk (lx) and deaths (dx)
prior <- pri.mle(nrisk=lx, ndeath=dx)
summary(prior$q0)