using Distributed, Gadfly
using Mamba

[ Info: Loading DataFrames support into Gadfly.jl

globe_toss = Dict{Symbol, Any}(
  :w => [6, 7, 5, 6, 6],
  :n => [9, 9, 9, 9, 9]
)
globe_toss[:N] = length(globe_toss[:w])

5

model = Model(
  w = Stochastic(1,
    (n, p, N) ->
      UnivariateDistribution[Binomial(n[i], p) for i in 1:N],
    false
  ),
  p = Stochastic(() -> Beta(1, 1))
);

inits = [
  Dict(:w => globe_toss[:w], :n => globe_toss[:n], :p => 0.5),
  Dict(:w => globe_toss[:w], :n => globe_toss[:n], :p => rand(Beta(1, 1)))
]

2-element Array{Dict{Symbol,Any},1}:
 Dict(:w=>[6, 7, 5, 6, 6],:p=>0.5,:n=>[9, 9, 9, 9, 9])
 Dict(:w=>[6, 7, 5, 6, 6],:p=>0.134808,:n=>[9, 9, 9, 9, 9])

scheme = [NUTS(:p)]
setsamplers!(model, scheme);

sim = mcmc(model, globe_toss, inits, 10000, burnin=2500, thin=1, chains=2)

MCMC Simulation of 10000 Iterations x 2 Chains...

Chain 1:   0% [0:25:43 of 0:25:45 remaining]
Chain 1:  10% [0:00:15 of 0:00:16 remaining]
Chain 1:  20% [0:00:07 of 0:00:09 remaining]
Chain 1:  30% [0:00:05 of 0:00:07 remaining]
Chain 1:  40% [0:00:03 of 0:00:06 remaining]
Chain 1:  50% [0:00:02 of 0:00:05 remaining]
Chain 1:  60% [0:00:02 of 0:00:04 remaining]
Chain 1:  70% [0:00:01 of 0:00:04 remaining]
Chain 1:  80% [0:00:01 of 0:00:03 remaining]
Chain 1:  90% [0:00:00 of 0:00:03 remaining]
Chain 1: 100% [0:00:00 of 0:00:03 remaining]

Chain 2:   0% [0:00:01 of 0:00:01 remaining]
Chain 2:  10% [0:00:01 of 0:00:01 remaining]
Chain 2:  20% [0:00:01 of 0:00:01 remaining]
Chain 2:  30% [0:00:01 of 0:00:01 remaining]
Chain 2:  40% [0:00:01 of 0:00:01 remaining]
Chain 2:  50% [0:00:01 of 0:00:01 remaining]
Chain 2:  60% [0:00:00 of 0:00:01 remaining]
Chain 2:  70% [0:00:00 of 0:00:01 remaining]
Chain 2:  80% [0:00:00 of 0:00:01 remaining]
Chain 2:  90% [0:00:00 of 0:00:01 remaining]
Chain 2: 100% [0:00:00 of 0:00:01 remaining]

Object of type "Mamba.ModelChains"

Iterations = 2501:10000
Thinning interval = 1
Chains = 1,2
Samples per chain = 7500

[0.57806; 0.57806; … ; 0.60297; 0.539374]

[0.606336; 0.606336; … ; 0.546535; 0.546535]

describe(sim)

Iterations = 2501:10000
Thinning interval = 1
Chains = 1,2
Samples per chain = 7500

Empirical Posterior Estimates:
     Mean       SD       Naive SE        MCSE      ESS
p 0.6589088 0.06839548 0.0005584468 0.00062540144 7500

Quantiles:
     2.5%     25.0%     50.0%     75.0%      97.5%
p 0.5160799 0.6135111 0.6627785 0.7068447 0.78476273