rejABC {poolABC}

Parameter estimation with Approximate Bayesian Computation using rejection sampling

Description

This function performs multivariate parameter estimation based on summary statistics using an Approximate Bayesian Computation (ABC) algorithm. The algorithm used here is the rejection sampling algorithm. The output of this function can be tailored towards a posterior local linear regression method correction.

Usage

rejABC(target, params, sumstats, tol, regression = FALSE)

Arguments

target

a vector with the target summary statistics. These are usually the set of observed summary statistics.

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.

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.

tol

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

regression

logical, indicating whether the user intends to perform a local linear regression correction after the rejection step. If set to FALSE (default) the output of this function will contain just the results of the rejection step. If set to TRUE, the output will contain more details required for the regression step.

Details

The rejection sampling algorithm generates random samples from the posterior distributions of the parameters of interest. Note that 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.

Value

a list with the results of the rejection sampling algorithm. The elements of the list depend of the logical value of regression.

s.target

a scaled vector of the observed summary statistics. This element only exists if regression is TRUE.

unadjusted

parameter estimates obtained with the rejection sampling.

ss

set of accepted summary statistics from the simulations.

s.sumstat

set of scaled accepted summary statistics from the simulations. This element only exists if regression is TRUE.

dst

euclidean distances in the region of interest.

Examples

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

# select a random simulation to act as target just to test the function
target <- sumstats[10 ,]

# Parameter estimation using rejection sampling
rejABC(target = target, params = params, sumstats = sumstats[-10, ], tol = 0.01)