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LBA_dHMC.jl
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LBA_dHMC.jl
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using Distributions,Parameters,DynamicHMC,LogDensityProblems,TransformVariables
using Random
import Distributions: pdf,logpdf,rand
export LBA,pdf,logpdf,rand
# See discussions at https://discourse.julialang.org/t/dynamichmc-reached-maximum-number-of-iterations/24721
############################################################################################
# Model functions
############################################################################################
mutable struct LBA{T1,T2,T3,T4} <: ContinuousUnivariateDistribution
ν::T1
A::T2
k::T3
τ::T4
σ::Float64
end
Base.broadcastable(x::LBA)=Ref(x)
LBA(;τ,A,k,ν,σ=1.0) = LBA(ν,A,k,τ,σ)
function selectWinner(dt)
if any(x->x >0,dt)
mi,mv = 0,Inf
for (i,t) in enumerate(dt)
if (t > 0) && (t < mv)
mi = i
mv = t
end
end
else
return 1,-1.0
end
return mi,mv
end
function sampleDriftRates(ν,σ)
noPositive=true
v = similar(ν)
while noPositive
v = [rand(Normal(d,σ)) for d in ν]
any(x->x>0,v) ? noPositive=false : nothing
end
return v
end
function rand(d::LBA)
@unpack τ,A,k,ν,σ = d
b=A+k
N = length(ν)
v = sampleDriftRates(ν,σ)
a = rand(Uniform(0,A),N)
dt = @. (b-a)/v
choice,mn = selectWinner(dt)
rt = τ .+ mn
return choice,rt
end
function rand(d::LBA,N::Int)
choice = fill(0,N)
rt = fill(0.0,N)
for i in 1:N
choice[i],rt[i]=rand(d)
end
return (choice=choice,rt=rt)
end
logpdf(d::LBA,choice,rt) = log(pdf(d,choice,rt))
function logpdf(d::LBA,data::T) where {T<:NamedTuple}
return sum(logpdf.(d,data...))
end
function logpdf(dist::LBA,data::Array{<:Tuple,1})
LL = 0.0
for d in data
LL += logpdf(dist,d...)
end
return LL
end
function pdf(d::LBA,c,rt)
@unpack τ,A,k,ν,σ = d
b=A+k; den = 1.0
rt < τ ? (return 1e-10) : nothing
for (i,v) in enumerate(ν)
if c == i
den *= dens(d,v,rt)
else
den *= (1-cummulative(d,v,rt))
end
end
pneg = pnegative(d)
den = den/(1-pneg)
den = max(den,1e-10)
isnan(den) ? (return 0.0) : (return den)
end
function dens(d::LBA,v,rt)
@unpack τ,A,k,ν,σ = d
dt = rt-τ; b=A+k
n1 = (b-A-dt*v)/(dt*σ)
n2 = (b-dt*v)/(dt*σ)
dens = (1/A)*(-v*cdf(Normal(0,1),n1) + σ*pdf(Normal(0,1),n1) +
v*cdf(Normal(0,1),n2) - σ*pdf(Normal(0,1),n2))
return dens
end
function cummulative(d::LBA,v,rt)
@unpack τ,A,k,ν,σ = d
dt = rt-τ; b=A+k
n1 = (b-A-dt*v)/(dt*σ)
n2 = (b-dt*v)/(dt*σ)
cm = 1 + ((b-A-dt*v)/A)*cdf(Normal(0,1),n1) -
((b-dt*v)/A)*cdf(Normal(0,1),n2) + ((dt*σ)/A)*pdf(Normal(0,1),n1) -
((dt*σ)/A)*pdf(Normal(0,1),n2)
return cm
end
function pnegative(d::LBA)
@unpack ν,σ=d
p=1.0
for v in ν
p*= cdf(Normal(0,1),-v/σ)
end
return p
end
############################################################################################
# DynamicHMC
############################################################################################
struct LBAProb{T}
data::T
N::Int
Nc::Int
end
function (problem::LBAProb)(θ)
@unpack data=problem
@unpack v,A,k,tau=θ
d=LBA(ν=v,A=A,k=k,τ=tau)
logpdf(d,data)+sum(logpdf.(TruncatedNormal(0,3,0,Inf),v)) +
logpdf(TruncatedNormal(.8,.4,0,Inf),A)+logpdf(TruncatedNormal(.2,.3,0,Inf),k)+
logpdf(TruncatedNormal(.4,.1,0,Inf),tau)
end
# Define problem with data and inits.
function sampleDHMC(data,N,Nc,nsamples)
p = LBAProb(data,N,Nc)
p((v=fill(.5,Nc),A=.8,k=.2,tau=.4))
# Write a function to return properly dimensioned transformation.
problem_transformation(p::LBAProb) =
as((v=as(Array,asℝ₊,Nc),A=asℝ₊,k=asℝ₊,tau=asℝ₊))
# Use Flux for the gradient.
P = TransformedLogDensity(problem_transformation(p), p)
#∇P = LogDensityRejectErrors(ADgradient(:ForwardDiff, P))
∇P = ADgradient(:ForwardDiff, P)
# FSample from the posterior.
n = dimension(problem_transformation(p))
chain, NUTS_tuned = NUTS_init_tune_mcmc(∇P, nsamples;
q = zeros(n), p = ones(n))
# Undo the transformation to obtain the posterior from the chain.
posterior = TransformVariables.transform.(Ref(problem_transformation(p)), get_position.(chain));
return (posterior, chain, NUTS_tuned)
end
############################################################################################
# Run Code
############################################################################################
#Random.seed!(5015)
dist = LBA(ν=[1.0,1.5,2.0],A=.8,k=.2,τ=.4)
N = 10
Nc = 3
for i in 1:100
data = rand(dist,N)
posterior , chain, NUTS_tuned= sampleDHMC(data,N,Nc,2000)
end
# Effective sample sizes (of untransformed draws)
@show ess = mapslices(effective_sample_size,
get_position_matrix(chain); dims = 1)
println()
# NUTS-specific statistics
@show NUTS_statistics(chain)
println()
@show NUTS_tuned