Binary MCMC Model Composition (BMC3)¶
Implementation of the binary-state MCMC Model Composition of Madigan and York [55] in which proposed updates are always state changes. Liu [52] shows this sampler is more efficient than Gibbs sampling for a binary vector. Schafer [79][80] proposes a method for block updates of binary vectors using this sampler. The sampler simulates autocorrelated draws from a distribution that can be specified up to a constant of proportionality.
Model-Based Constructors¶
-
BMC3
(params::ElementOrVector{Symbol}; k::Integer=1)¶ -
BMC3
(params::ElementOrVector{Symbol}, indexset::Vector{Vector{Int}}) Construct a
Sampler
object for BMC3 sampling. Parameters are assumed to have binary numerical values (0 or 1).Arguments
params
: stochastic node(s) to be updated with the sampler.k
: number of parameters to select at random for simultaneous updating in each call of the sampler.indexset
: candidate set of indices of the parameters whose states are to be changed simultaneously.
Value
Returns aSampler{BMC3Tune}
type object.
Stand-Alone Functions¶
-
bmc3!
(v::BMMGVariate, logf::Function; k::Integer=1)¶ -
bmc3!
(v::BMMGVariate, indexset::Vector{Vector{Int}}, logf::Function) Simulate one draw from a target distribution using the BMC3 sampler. Parameters are assumed to have binary numerical values (0 or 1).
Arguments
v
: current state of parameters to be simulated.logf
: function that takes a singleDenseVector
argument of parameter values at which to compute the log-transformed density (up to a normalizing constant).k
: number of parameters, such thatk <= length(v)
, to select at random for simultaneous updating in each call of the sampler.indexset
: candidate set of indices of the parameters whose states are to be changed simultaneously.
Value
Returnsv
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 MCMC Model Composition t = 10000 sim = Chains(t, p, names = map(i -> "gamma[$i]", 1:p)) gamma = BMC3Variate(zeros(p)) for i in 1:t bmc3!(gamma, logf) sim[i, :, 1] = gamma end describe(sim) p = plot(sim, [:trace, :mixeddensity]) draw(p, filename = "bmc3plot")
BMC3Variate Type¶
Declaration¶
typealias BMC3Variate SamplerVariate{BMC3Tune}
Fields¶
value::Vector{Float64}
: simulated values.tune::BMC3Tune
: tuning parameters for the sampling algorithm.
Constructors¶
-
BMC3Variate
(x::AbstractVector{T<:Real})¶ -
BMC3Variate
(x::AbstractVector{T<:Real}, tune::BMC3Tune) Construct a
BMC3Variate
object that stores simulated values and tuning parameters for BMC3 sampling.Arguments
x
: simulated values.tune
: tuning parameters for the sampling algorithm. If not supplied, parameters are set to their defaults.
Value
Returns aBMC3Variate
type object with fields set to the values supplied to argumentsx
andtune
.