singleABC {poolABC}

Parameter estimation with Approximate Bayesian Computation for a single target

Description

Perform multivariate parameter estimation based on summary statistics using an Approximate Bayesian Computation (ABC) algorithm. This function always uses a rejection sampling algorithm while a local linear regression algorithm might or might not be used.

Usage

singleABC(target, params, sumstats, limits, tol, method)

Arguments

target

a vector with the target summary statistics. These are usually computed from observed data or selected from a random simulation when performing cross-validation.

params

is a vector or matrix of simulated parameter values i.e. numbers from the simulations. Each row or vector entry should be a different simulation and each column of a matrix should be a different parameter. This is the dependent variable for the regression, if a regression step is performed.

sumstats

is a vector or matrix of simulated summary statistics. Each row or vector entry should be a different simulation and each column of a matrix should be a different statistic. These act as the independent variables if a regression step is performed.

limits

is a matrix with two columns and as many rows as there are parameters. Each row should contain the minimum value of the prior for a given parameter in the first column and the maximum value in the second column.

tol

is the tolerance rate, indicating the required proportion of points accepted nearest the target values.

method

either "rejection" or "regression" indicating whether a regression step should be performed during ABC parameter estimation.

Details

To use this function, the usual steps of ABC parameter estimation have to be performed. Briefly, data should have been simulated based on random draws from the prior distributions of the parameters of interest and a set of summary statistics should have been calculated from that data. The same set of summary statistics should have been calculated from the observed data to be used as the target input in this function. Parameter values are accepted if the Euclidean distance between the set of summary statistics computed from the simulated data and the set of summary statistics computed from the observed data is sufficiently small. The percentage of accepted simulations is determined by tol. This function performs a simple rejection by calling the rejABC() function.

When method is "regression", a local linear regression method is used to correct for the imperfect match between the summary statistics computed from the simulated data and the summary statistics computed from the observed data. The output of the rejABC() function is used as the input of the regABC() function to apply this correction. The parameter values accepted in the rejection step are weighted by a smooth function (kernel) of the distance between the simulated and observed summary statistics and corrected according to a linear transformation.

Value

the returned object is a list containing the following components:

unadjusted

parameter estimates obtained with the rejection sampling.

rej.prediction

point estimates of the posterior obtained with the rejection sampling.

adjusted

regression adjusted parameter values.

loc.prediction

point estimates of the regression adjusted posterior.

ss

set of accepted summary statistics from the simulations.

wt

regression weights.

Examples

# load the matrix with parameter values
data(params)
# load the matrix with simulated parameter values
data(sumstats)
# load the matrix with the prior limits
data(limits)

# select a random simulation to act as target just to test the function
target <- sumstats[10 ,]
# we should remove the random simulation from the sumstats and params matrices
sumstats <- sumstats[-10, ]; params <- params[-10, ]

# parameter estimation for a single target
singleABC(target = target, params = params, sumstats = sumstats, limits = limits,
tol = 0.01, method = "regression")