Approximate Bayesian Computation (ABC)
is a simulation based method for Bayesian inference. It is commonly used in
evolutionary biology to estimate parameters of demographic models.
Coala makes it easy to conduct the simulations for an ABC analysis and works
well together with the abc
package for doing the estimation.
To demonstrate the principle, we will estimate the parameter of an
over-simplified toy model.
Let's assume that we have 50 genetic loci from 10 individuals from a panmictic
population. We will use the site frequency spectrum of the data as a set of
summary statistics to estimate the scaled mutation rate, theta
. Let's assume
we get the following frequency spectrum from the data:
sfs <- c(112, 57, 24, 34, 16, 29, 8, 10, 15)
We can now use coala to set the model up:
library(coala) model <- coal_model(10, 50) + feat_mutation(par_prior("theta", runif(1, 1, 5))) + sumstat_sfs()
Note that we used par_prior
to set a uniform prior between 1 and 5 for
theta
.
We can now easily simulate the model:
sim_data <- simulate(model, nsim = 2000, seed = 17)
For this toy model, we ran just 2000 simulations (to keep the time for
building this document within a reasonable range). A real analysis will need
many more, but you can reduce the simulation time by parallelizing them
with the cores
argument.
We need to prepare the simulation data for the abc
package. We can use
the create_abc_param
and create_abc_sumstat
functions for this purpose:
# Getting the parameters sim_param <- create_abc_param(sim_data, model) head(sim_param, n = 3) # Getting the summary statistics sim_sumstat <- create_abc_sumstat(sim_data, model) head(sim_sumstat, n = 3)
Now, we can estimate the posterior distribution of theta
:
suppressPackageStartupMessages(library(abc)) posterior <- abc(sfs, sim_param, sim_sumstat, 0.05, method = "rejection") hist(posterior, breaks = 20)
Due to the low number of simulations, this posterior should only be treated as a rough approximation. We have prepared a version using a million simulations instead. Generating it took significantly longer (about two hours on a modern laptop), but we get a smoother estimate of the posterior distribution:
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