SABC {EasyABC} | R Documentation |
Simulated Annealing approach to Approximate Bayesian Computation (SABC)
Description
Algorithms for the Simulated Annealing approach to Approximate Bayesian Computation (SABC).
Usage
SABC(r.model, r.prior, d.prior, n.sample, eps.init, iter.max,
v=ifelse(method=="informative",0.4,1.2), beta=0.8,
delta=0.1, resample=5*n.sample, verbose=n.sample,
method="noninformative", adaptjump=TRUE,
summarystats=FALSE, y=NULL, f.summarystats=NULL, ...)
Arguments
r.model |
Function that returns either a random sample from the likelihood or a scalar distance between such a sample and the data. The first argument must be the parameter vector. |
r.prior |
Function that returns a random sample from the prior. |
d.prior |
Function that returns the density of the prior distribution. |
n.sample |
Size of the ensemble. |
eps.init |
Initial tolerance or temperature. |
iter.max |
Total number of simulations from the likelihood. |
v |
Tuning parameter that governs the annealing speed. Defaults to 1.2, for the |
beta |
Tuning parameter that governs the mixing in parameter space. Defaults to 0.8. |
delta |
Tuning parameter for the resampling steps. Defaults to 0.1. |
resample |
Number of accepted particle updates after which a resampling step is performed. Defaults to 5* |
verbose |
Shows the iteration progress each |
adaptjump |
Whether to adapt covariance of jump distribution. Default is TRUE. |
method |
Argument to select algorithm. Accepts |
summarystats |
Whether summary statistics shall be calculated (semi-) automatically. Defaults to FALSE. |
y |
Data vector. Needs to be provided if either |
f.summarystats |
If |
... |
further arguments passed to |
Details
SABC defines a class of algorithms for particle ABC that are inspired by Simulated Annealing. Unlike other algorithms, this class is not based on importance sampling, and hence does not suffer from a loss of effective sample size due to re-sampling. The approach is presented in detail in Albert, Kuensch, and Scheidegger (2014; see references).
This package implements two versions of SABC algorithms, for the cases of a non-informative or an informative prior. These are described in detail in the paper. The algorithms can be selected using the method
argument: method=noninformative
or method=informative
.
In the informative case, the algorithm corrects for the bias caused by an over- or under-representation of the prior.
The argument adaptjump
allows a choice of whether to adapt the covariance of the jump distribution. Default is TRUE.
Furthermore, the package allows for three different ways of using the data.
If y
is not provided, the algorithm expects r.model
to return a scalar measuring the distance between a random sample from the likelihood and the data.
If y
is provided and summarystats = FALSE
, the algorithm expects r.model
to return a random sample from the likelihood and uses the relative sum of squares to measure the distances between y
and random likelihood samples.
If summarystats = TRUE
the algorithm calculates summary statistics semi-automatically, as described in detail in the paper by Fearnhead et al. (2012; see references).
The summary statistics are calculated by means of a linear regression applied to a sample from the prior and the image of f.summarystats
of an associated sample from the likelihood.
Value
Returns a list with the following components:
E |
Matrix with ensemble of samples. |
P |
Matrix with prior ensemble of samples. |
eps |
Value of tolerance (temperature) at final iteration. |
ESS |
Effective sample size, due to final bias correction ( |
Author(s)
Carlo Albert <carlo.albert@eawag.ch>, Andreas Scheidegger, Tobia Fasciati. Package initially compiled by Lukas M. Weber.
References
C. Albert, H. R. Kuensch and A. Scheidegger, Statistics and Computing 0960-3174 (2014), arXiv:1208.2157, A Simulated Annealing Approach to Approximate Bayes Computations.
P. Fearnhead and D. Prangle, J. R. Statist. Soc. B 74 (2012), Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation.
Examples
## Not run:
## Example for "noninformative" case
# Prior is uniform on [-10,10]
d.prior <- function(par)
dunif(par,-10,10)
r.prior <- function()
runif(1,-10,10)
# Model is the sum of two normal distributions. Return distance to observation 0:
f.dist <- function(par)
return( abs(rnorm( 1 , par , ifelse(runif(1)<0.5,1,0.1 ) )))
# Run algorithm ("noninformative" case)
res <- SABC(f.dist,r.prior,d.prior,n.sample=500,eps.init=2,iter.max=50000)
## End(Not run)
## Not run:
# Histogram of results
hist(res$E[,1],breaks=200)
## End(Not run)