Probablistic Programming in Thirty Seconds

If you are already well-versed in probabalistic programming and just want to take a quick look at how Turing’s syntax works or otherwise just want a model to start with, we have provided a Bayesian coin-flipping model to play with.

This example can be run on however you have Julia installed (see Getting Started), but you will need to install the packages Turing, Distributions, MCMCChains, and StatsPlots if you have not done so already.

This is an excerpt from a more formal example introducing probabalistic programming which can be found in Jupyter notebook form here or as part of the documentation website here.

# Import libraries.
using Turing, StatsPlots, Random

# Set the true probability of heads in a coin.
p_true = 0.5

# Iterate from having seen 0 observations to 100 observations.
Ns = 0:100;

# Draw data from a Bernoulli distribution, i.e. draw heads or tails.
Random.seed!(12)
data = rand(Bernoulli(p_true), last(Ns))

# Declare our Turing model.
@model coinflip(y) = begin
    # Our prior belief about the probability of heads in a coin.
    p ~ Beta(1, 1)

    # The number of observations.
    N = length(y)
    for n in 1:N
        # Heads or tails of a coin are drawn from a Bernoulli distribution.
        y[n] ~ Bernoulli(p)
    end
end;

# Settings of the Hamiltonian Monte Carlo (HMC) sampler.
iterations = 1000
ϵ = 0.05
τ = 10

# Start sampling.
chain = sample(coinflip(data), HMC(iterations, ϵ, τ));

# Construct summary of the sampling process for the parameter p, i.e. the probability of heads in a coin.
psummary = Chains(chain[:p])
histogram(psummary)