Reference

KissABC

Module to perform approximate bayesian computation,

Simple Example: inferring the mean of a Normal distribution

using KissABC
using Distributions

prior=Normal(0,1)
data=randn(1000) .+ 1
sim(μ,other)=randn(1000) .+ μ
dist(x,y) = abs(mean(x) - mean(y))

plan=ABCplan(prior, sim, data, dist)
μ_post,Δ = ABCDE(plan, 1e-2)
@show mean(μ_post) ≈ 1.0

for more complicated code examples look at https://github.com/francescoalemanno/KissABC.jl/

ABCplan(prior, simulation, data, distance; params=())

Builds a type ABCplan which holds

Arguments:

• prior: a Distribution to use for sampling candidate parameters
• simulation: simulation function sim(prior_sample, constants) -> data that accepts a prior sample and the params constant and returns a simulated dataset
• data: target dataset which must be compared with simulated datasets
• distance: distance function dist(x,y) that return the distance (a scalar value) between x and y
• params: an optional set of constants to be passed as second argument to the simulation function

Factored{N} <: Distribution{Multivariate, MixedSupport}

a Distribution type that can be used to combine multiple UnivariateDistribution's and sample from them.

Example: it can be used as prior = Factored(Normal(0,1), Uniform(-1,1))

ABC(plan, α_target; nparticles = 100, parallel = false)

Classical ABC rejection algorithm.

Arguments:

• plan: a plan built using the function ABCplan.
• α_target: target acceptance rate for ABC rejection algorithm, nparticles/α will be sampled and only the best nparticles will be retained.
• nparticles: number of samples from the approximate posterior that will be returned
• parallel: when set to true multithreaded parallelism is enabled

ABCDE(plan, ϵ_target; nparticles=100, generations=500, α=0, parallel=false, verbose=true)

A sequential monte carlo algorithm inspired by differential evolution, very efficient (simpler version of B.M.Turner 2012, https://doi.org/10.1016/j.jmp.2012.06.004)

Arguments:

• plan: a plan built using the function ABCplan.
• ϵ_target: maximum acceptable distance between simulated datasets and the target dataset
• nparticles: number of samples from the approximate posterior that will be returned
• generations: total number of simulations per particle
• α: controls the ϵ for each simulation round as ϵ = m+α*(M-m) where m,M = extrema(distances)
• parallel: when set to true multithreaded parallelism is enabled
• verbose: when set to true verbosity is enabled

ABCSMCPR(plan, ϵ_target; nparticles = 100, maxsimpp = 1000.0, α = 0.3, c = 0.01, parallel = false, verbose = true)

Sequential Monte Carlo algorithm (Drovandi et al. 2011, https://doi.org/10.1111/j.1541-0420.2010.01410.x).

Arguments:

• plan: a plan built using the function ABCplan.
• ϵ_target: maximum acceptable distance between simulated datasets and the target dataset
• nparticles: number of samples from the approximate posterior that will be returned
• maxsimpp: average maximum number of simulations per particle
• α: proportion of particles to retain at every iteration of SMC, other particles are resampled
• c: probability that a sample will not be updated during one iteration of SMC
• parallel: when set to true multithreaded parallelism is enabled
• verbose: when set to true verbosity is enabled

sample_plan(plan::ABCplan, nparticles, parallel)

function to sample the prior distribution of both parameters and distances.

Arguments:

• plan: a plan built using the function ABCplan.
• nparticles: number of samples to draw.
• parallel: enable or disable threaded parallelism via true or false.

length(p::Factored) = begin

returns the number of distributions contained in p.

rand(rng::AbstractRNG, factoreddist::Factored)

function to sample one element from a Factored object

pdf(d::Factored, x) = begin

Function to evaluate the pdf of a Factored distribution object

compute_kernel_scales(prior::Distribution, V)

Function for ABCSMCPR whose purpose is to compute the characteristic scale of the perturbation kernel appropriate for prior given the Vector V of parameters

deperturb(prior::Distribution, sample, r1, r2, γ)

Function for ABCDE whose purpose is computing sample + γ (r1 - r2) + ϵ (the perturbation function of differential evolution) in a way suited to the prior.

Arguments:

• prior
• sample
• r1
• r2

kernel(prior::Distribution, c, scale)

Function for ABCSMCPR whose purpose is returning the appropriate Distribution to use as a perturbation kernel on sample c and characteristic scale

Arguments:

• prior: prior distribution
• c: sample acting as center of perturbation kernel
• scale: characteristic scale of perturbation kernel

kerneldensity(prior::Distribution, scales, s1, s2)

Function for ABCSMCPR whose purpose is returning the probability density of observing s2 under the kernel centered on s1 with scales given by scales and appropriate for prior.

perturb(prior::Distribution, scales, sample)

Function for ABCSMCPR whose purpose is perturbing sample according to the appropriate kernel for prior with characteristic scales.