using Mamba
using Pandas

# Data
FP = open(raw"./data-salary.txt")
Data = read_csv(FP)
close(FP)
Data

# Model Definition
model = Model(
    y = Stochastic(1,
        (a, b, x, sigma) -> MvNormal(a + b*x, sigma),
        false
    ),
    b = Stochastic(() -> Normal(0, 100)),
    a = Stochastic(() -> Normal(0, 100)),
    sigma = Stochastic(() -> Rayleigh(100))
)

## Sampling Scheme
scheme = [NUTS(:a), NUTS(:b),Slice(:sigma,10)]
setsamplers!(model, scheme)

# Data Conversion
Dat = Dict{Symbol, Any}(
    :x => Array(Data[:X]),
    :y => Array(Data[:Y])
)

# Initial Values
inits = [
  Dict{Symbol, Any}(
    :y => Dat[:y],
    :a => rand(Normal(0, 1)),
    :b => rand(Normal(0, 1)),
    :sigma => rand(Rayleigh(1))
  ) for i in 1:4
]

## MCMC Simulations
sim = mcmc(model, Dat, inits, 4000, burnin=2000, thin=1, chains=4)
Mamba.describe(sim)

p = Mamba.plot(sim)
draw(p)

using Plots
gr()
Plots.plot(Dat[:x],Dat[:y],st=:scatter)