Heligman-Pollard parameter estimator using Bayesian Melding with Incremental Mixture Importance Sampling

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Description

Runs all the necessary functions to estimate the eight Heligman-Pollard parameters in one step via Bayesian Melding with IMIS and optimization. In this order and with the proper arguments imputed the functions run are loop.optim, samp.postopt, like.resamp, final.resamp.

Usage

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hp.bm.imis(prior, nrisk, ndeath, K, d = 10, 
B = 400,  age = c(1e-05, 1, seq(5, 100, 5)), CI=95)

Arguments

prior

A matrix with dimensions 8000 x theta.dim containing the prior distribution for each Heligman-Pollard parameter

nrisk

A vector containing the total number of individuals at risk of death in each age group. Length should equal the length of age

ndeath

A vector containing the total number of deaths in each age group. Length should equal the length of age

K

The number of IMIS iterations

d

The number of optimizer iterations

B

The sample size at each importance sampling iteration

age

A vector of the ages at which the probabilities of death will be calculated

CI

Defines the width of the credible interval (Defaults to 95 percent). A summary table is printed with the median estimate and lower and upper confidence bounds. Setting CI=95 prints a table with the first column representing the 2.5th percentile for each parameter distribution, the second column represents the median value for each parameter distribution and the third column represents the 97.5th percentile for each parameter distribution.

Value

out

A summary table of the results with the median parameter values in the middle column, the lower bound results in the left column, and upper bound result in the right column

H.final

A B x theta.dim matrix containing the posterior distribution for each parameter

h.mu

The sets of parameters found in the optimizer step

h.sig

The covariance matrix for each set of parameters in h.mu

log.like

A vector of likelihoods for the prior plus resamples

log.like.0

A vector of the likelihoods for the prior

wts.0

A vector of importance weights for each set of parameters in the prior

d.keep

The number of optimizer runs where the likelihood exceeded the maximum likelihood of the prior

vwts

A vector containing the variance of the rescaled weights at each IMIS iteration

ewts

A vector containing the entropy of the rescaled weights at each IMIS iteration

mwts

A vector containing the maximum of the rescaled weights at each IMIS iteration

mwt.case

The maximum weight and associated case

nup

A vector containing the expected number of unique points at each IMIS iteration

frac.up

A vector containing the proportion of unique points in the final resample at each IMIS iteration

wts.k

A vector containing the importance weights for the final IMIS iteration

Note

Because there are multiple sampling steps sometimes with upper and lower bound restricitions, this function can take several minutes to run depending on the sample size, K

References

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

Poole, David and Adrian Raftery. 2000. "Inference for Deterministic Simulation Models: The Bayesian Melding Approach." Journal of the American Statistical Association 95:1244–1255.

Raftery, Adrian and Le Bao. 2009. "Estimating and Projecting Trends in HIV/AIDS Generalized Epidemics Using Incremental Mixture Importance Sampling." Technical Report 560, Department of Statistics, University of Washington.

See Also

loop.optim, samp.postopt, like.resamp, final.resamp

Examples

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##a prior##
## Not run: data(HPprior)
q0 <- HPprior
##number of deaths in each age group##
dx <- c(68, 47, 16, 10, 13, 29, 92, 151, 188, 179, 156, 155, 147, 150, 
122, 106, 88, 113, 63, 38, 32, 8)
##number at risk in each age group##
lx <- c(1974, 1906, 1860, 1844, 1834, 1823, 1793, 1700, 1549, 1361, 
1181, 1025, 870, 721, 571, 450, 344, 256, 142, 79, 41, 8)
result <- hp.bm.imis(prior=q0, K=10, nrisk=lx, ndeath=dx) 
## End(Not run)