regABC {poolABC}

Parameter estimation with Approximate Bayesian Computation using local linear regression

Description

This function performs multivariate parameter estimation based on summary statistics using an Approximate Bayesian Computation (ABC) algorithm. The algorithm used here is the local linear regression algorithm.

Usage

regABC(rej, parameter, tol = 1, simple = FALSE)

Arguments

rej

is a list with the results of the rejection sampling algorithm. The output of the rejABC() function is the ideal input here.

parameter

is a parameter vector (long vector of numbers from the simulations). Each vector entry should correspond to a different simulation. This is the dependent variable for the regression.

tol

is the tolerance rate, indicating the required proportion of points accepted nearest the target values. Note that the default value here is 1 because all points accepted in the rejection step should be used for the regression.

simple

logical, if TRUE a simplified output with only the essential information will be produced. If FALSE (default) the output will contain more information.

Details

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 for parameter inference. A previous rejection sampling step should also have been performed, where parameter values were 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 was sufficiently small. Then, the output of the rejection step is used as the input for this function and 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 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. This function calls the function stats::lm() to accomplish this.

Value

a list with the results from the regression correction

adjusted

regression adjusted parameter values.

unadjusted

parameter estimates obtained with the rejection sampling.

wt

regression weights.

ss

set of accepted summary statistics from the simulations.

predmean

estimates of the posterior mean for each parameter.

fv

fitted value from the regression.

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
rej <- rejABC(target = target, params = params, sumstats = sumstats[-10, ],
tol = 0.01, regression = TRUE)

# parameter estimation using local linear regression
# note that you should select a parameter from the unadjusted matrix
regABC(rej = rej, parameter = rej$unadjusted[, 1])