Binary Metropolised Gibbs (BMG)

Implementation of the binary-state Metropolised Gibbs sampler described by Schafer [81][82] in which components are drawn sequentially from full conditional marginal distributions and accepted together in a single Metropolis-Hastings step. The sampler simulates autocorrelated draws from a distribution that can be specified up to a constant of proportionality.

Model-Based Constructor

BMG(params::ElementOrVector{Symbol}; args...)

Construct a Sampler object for BMG sampling. Parameters are assumed to have binary numerical values (0 or 1).

Arguments

  • params : stochastic node(s) to be updated with the sampler.
  • args... : additional keyword arguments to be passed to the BMGVariate constructor.

Value

Returns a Sampler{BMGTune} type object.

Example

See the Pollution and other Examples.

Stand-Alone Function

sample!(v::BMGVariate)

Draw one sample from a target distribution using the BMG sampler. Parameters are assumed to have binary numerical values (0 or 1).

Arguments

  • v : current state of parameters to be simulated.

Value

Returns v updated with simulated values and associated tuning parameters.

Example

################################################################################
## Linear Regression
##   y ~ MvNormal(X * (beta0 .* gamma), 1)
##   gamma ~ DiscreteUniform(0, 1)
################################################################################

using Mamba

## Data
n, p = 25, 10
X = randn(n, p)
beta0 = randn(p)
gamma0 = rand(0:1, p)
y = X * (beta0 .* gamma0) + randn(n)

## Log-transformed Posterior(gamma) + Constant
logf = function(gamma::DenseVector)
  logpdf(MvNormal(X * (beta0 .* gamma), 1.0), y)
end

## MCMC Simulation with Binary Metropolised Gibbs
t = 10000
sim = Chains(t, p, names = map(i -> "gamma[$i]", 1:p))
gamma = BMGVariate(zeros(p), logf)
for i in 1:t
  sample!(gamma)
  sim[i, :, 1] = gamma
end
describe(sim)

BMGVariate Type

Declaration

typealias BMGVariate SamplerVariate{BMGTune}

Fields

  • value::Vector{Float64} : simulated values.
  • tune::BMGTune : tuning parameters for the sampling algorithm.

Constructor

BMGVariate(x::AbstractVector{T<:Real}, logf::Function; k::Integer=1)

Construct a BMGVariate object that stores simulated values and tuning parameters for BMG sampling.

Arguments

  • x : initial values.
  • logf : function that takes a single DenseVector argument of parameter values at which to compute the log-transformed density (up to a normalizing constant).
  • k : number of parameters to select at random for simultaneous updating in each call of the sampler.

Value

Returns a BMGVariate type object with fields set to the supplied x and tuning parameter values.

BMGTune Type

Declaration

type BMGTune <: SamplerTune

Fields

  • logf::Nullable{Function} : function supplied to the constructor to compute the log-transformed density, or null if not supplied.
  • k::Int : number of parameters to select at random for simultaneous updating in each call of the sampler.