anthonyebert / protoabc

R-package protoABC: Flexible approach to Approximate Bayesian Computation (ABC)

protoABC

The goal of protoABC is to provide a way to perform ABC (approximate Bayesian computation) inference as flexibly as possible. That is with arbitrarily complex simulation algorithms and distance functions.

The way we implement this is to consider the distance as the output of the simulation and leave the internal details to the user. Parameters in, distance out.

You need to supply a function which returns a positive number (the distance) with up to two arguments, the first is a vector of your parameters of interest, the second is a list of additional inputs to your function.

Installation

You can install protoABC from github with:

# install.packages("devtools")
devtools::install_github("AnthonyEbert/protoABC")

Example

The simplest example, a normal distribution. The summary statistic is the sample mean.

library(protoABC)

sample <- rnorm(1000, 3, 1.5)

inp <- list(
  sample_mean = mean(sample), 
  sample_sd   = sd(sample)
)

prior <- function(n){data.frame(mu = rnorm(n, 5))}

distance <- function(theta, inp){
  sim <- rnorm(1000, theta)
  output <- abs(mean(sim) - inp$sample_mean)
  return(output)
}

abc_post_1 <- abc_start(
  prior,
  distance,
  inp,
  method = "rejection",
  control = list(epsilon = 0.1)
)

summary(abc_post_1)
#>        mu       
#>  Min.   :2.833  
#>  1st Qu.:2.940  
#>  Median :2.992  
#>  Mean   :2.991  
#>  3rd Qu.:3.046  
#>  Max.   :3.154

The simplest example, a normal distribution. The summary statistics are the sample mean and the standard deviation.

prior <- function(n){
  data.frame(mu = runif(n, 2, 4), sd = rgamma(n, 1, 1))
}

prior_eval <- function(theta){
  prior_value <- dunif(theta["mu"], 2, 4) * dgamma(theta["sd"], 1, 1)
  
  return(prior_value)
}


distance <- function(theta, inp){
  
  sim <- rnorm(1000, theta["mu"], theta["sd"])
  
  output <- sqrt( (mean(sim) - inp$sample_mean)^2 + (sd(sim) - inp$sample_sd)^2)
  return(output)
}

abc_post_2 <- abc_start(
  prior,
  distance,
  inp,
  method = "RABC",
  control = list(n = 1000, prior_eval = prior_eval, pacc_final = 0.1), 
  output_control = list(print_output = FALSE)
)

## Summary

summary(abc_post_2)
#>        mu              sd       
#>  Min.   :2.835   Min.   :1.419  
#>  1st Qu.:2.946   1st Qu.:1.526  
#>  Median :2.985   Median :1.552  
#>  Mean   :2.983   Mean   :1.553  
#>  3rd Qu.:3.019   3rd Qu.:1.576  
#>  Max.   :3.128   Max.   :1.661