"""
A model for coal mining disasters data with a changepoint

switchpoint ~ U(0, 110)
early_mean ~ Exp(1.)
late_mean ~ Exp(1.)
disasters[t] ~ Po(early_mean if t <= switchpoint, late_mean otherwise)

"""

from pymc3 import *

from numpy import arange, array

__all__ = ['disasters_data', 'switchpoint', 'early_mean', 'late_mean', 'rate',
           'disasters']

# Time series of recorded coal mining disasters in the UK from 1851 to 1962
disasters_data = array([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,
                        3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,
                        2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,
                        1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,
                        0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,
                        3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,
                        0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])
years = len(disasters_data)

with Model() as model:

    # Prior for distribution of switchpoint location
    switchpoint = DiscreteUniform('switchpoint', lower=0, upper=years)
    # Priors for pre- and post-switch mean number of disasters
    early_mean = Exponential('early_mean', lam=1.)
    late_mean = Exponential('late_mean', lam=1.)

    # Allocate appropriate Poisson rates to years before and after current
    # switchpoint location
    idx = arange(years)
    rate = switch(switchpoint >= idx, early_mean, late_mean)

    # Data likelihood
    disasters = Poisson('disasters', rate, observed=disasters_data)


def run(n=1000):
    if n == "short":
        n = 50
    with model:

        # Initial values for stochastic nodes
        start = {'early_mean': 2., 'late_mean': 3.}

        tr = sample(n, tune=500, start=start)

        traceplot(tr, varnames=[early_mean, late_mean],
                  priors=[Exponential.dist(1)] * 2)

        if n != 50:
            summary(tr)

if __name__ == '__main__':
    run()
