initial work on incorporating Stan.jl

src/MCMC/testStan.jl

+######### Stan program example  ###########
+
+# module Tmp
+const σw0 = 1.0
+const σw = 1
+const σv = 1.0
+const theta0 = [0.5, 25, 8]
+s2piσv = log(sqrt(2*pi) * σv)
+ProjDir = pwd()
+
+function f_sample(x::Vector, t::Int64)
+    c = 8*cos(1.2*(t-1))
+    @inbounds for i = 1:length(x)
+        x[i] =  0.5*x[i] + 25*x[i]./(1+x[i]^2) + c + σw*randn()
+    end
+    return x
+end
+f_sample(x::Float64, t::Int64) = 0.5*x + 25*x/(1+x^2) + 8*cos(1.2*(t-1)) + σw*randn()
+
+
+
+T = 100
+M = 1
+x = Array(Float64,T)
+y = Array(Float64,T)
+x0 = 0
+
+x[1] = σw*randn()
+y[1] = σv*randn()
+for t = 1:T-1
+    x[t+1] = f_sample(x[t],t)
+    y[t+1] = 0.05x[t+1]^2  + σv*randn()
+end # t
+
+
+
+
+using Stan, Mamba
+
+
+odemodel ="
+data {
+  int<lower=1> T;
+  real y[T];
+}
+
+parameters {
+  real theta[3];
+  real sigma[2];
+  real x[T];
+}
+
+model {
+  sigma[1] ~ cauchy(1,1);
+  sigma[2] ~ cauchy(1,1);
+  theta[1] ~ cauchy(0.5,0.5);
+  theta[2] ~ cauchy(25,25);
+  theta[3] ~ cauchy(8,8);
+  x[1] ~ normal(0,1);
+  y[1] ~ normal(0.05*x[1]*x[1], sigma);
+  for (t in 1:(T-1)){
+   x[t+1] ~ normal(theta[1]*x[t] + theta[2]*x[t]/(1+x[t]*x[t]) + theta[3]*cos(1.2*(t-1)),sigma[1]);
+   y[t+1] ~ normal(0.05*x[t+1]*x[t+1], sigma[2]);
+  }
+}
+"
+
+odedict =
+  Dict(
+    "T" => T,
+    "y" => y)
+
+stanmodel = Stanmodel(name="ode", model=odemodel, nchains=4, update=10000)
+@time sim1 = stan(stanmodel, [odedict], ProjDir, diagnostics=false, CmdStanDir=CMDSTAN_HOME)
+
+## Subset Sampler Output to variables suitable for describe().
+monitor = ["lp__", "accept_stat__"]
+sim = sim1[1:size(sim1, 1), monitor, 1:size(sim1, 3)]
+
+describe(sim)
+println()
+
+p = plot(sim, [:trace, :mean, :density, :autocor], legend=true)
+draw(p, ncol=4, filename="$(stanmodel.name)-infoplot", fmt=:pdf)
+
+
+
+## Subset Sampler Output to variables suitable for describe().
+monitor = ["theta.1","theta.2","theta.3"]
+sim = sim1[1:size(sim1, 1), monitor, 1:size(sim1, 3)]
+
+describe(sim)
+println()
+
+p = plot(sim, [:trace, :mean, :density, :autocor], legend=true)
+draw(p, ncol=4, filename="$(stanmodel.name)-thetaplot", fmt=:pdf)
+
+
+
+## Subset Sampler Output to variables suitable for describe().
+monitor = ["sigma.1", "sigma.2"]
+sim = sim1[:, monitor, :]
+describe(sim)
+println()
+
+p = plot(sim, [:trace, :mean, :density, :autocor], legend=true)
+draw(p, nrow=4, ncol=4, filename="$(stanmodel.name)-sigmaplot", fmt=:pdf)
+
+