Add PyMC3 sampler

I have started an attempt to add PyMC3 as a sampler option.

At the moment this can be used with the Uniform prior, for which I have added a new pymc3 method, and the GaussianLikelihood for which I have added a pymc3_likelihood method. I can convert the other prior classes to also have pymc3 methods too.

At the moment I've just got PyMC3 to run with the default NUTS sampler, but can change the _run_external_sampler method to take in other allowed sampler keyword args.

I've tested this with a linear regression example and it works!

examples/other_examples/linear_regression_pymc3.py

+#!/bin/python
+"""
+An example of how to use tupak to perform paramater estimation for
+non-gravitational wave data. In this case, fitting a linear function to
+data with background Gaussian noise
+
+"""
+from __future__ import division
+import tupak
+import numpy as np
+import matplotlib.pyplot as plt
+import inspect
+
+from tupak.core.likelihood import GaussianLikelihood
+
+# A few simple setup steps
+label = 'linear_regression_pymc3'
+outdir = 'outdir'
+tupak.utils.check_directory_exists_and_if_not_mkdir(outdir)
+
+# First, we define our "signal model", in this case a simple linear function
+def model(time, m, c):
+    return time * m + c
+
+# Now we define the injection parameters which we make simulated data with
+injection_parameters = dict(m=0.5, c=0.2)
+
+# For this example, we'll use standard Gaussian noise
+sigma = 1
+
+# These lines of code generate the fake data. Note the ** just unpacks the
+# contents of the injection_paramsters when calling the model function.
+sampling_frequency = 10
+time_duration = 10
+time = np.arange(0, time_duration, 1/sampling_frequency)
+N = len(time)
+data = model(time, **injection_parameters) + np.random.normal(0, sigma, N)
+
+# We quickly plot the data to check it looks sensible
+fig, ax = plt.subplots()
+ax.plot(time, data, 'o', label='data')
+ax.plot(time, model(time, **injection_parameters), '--r', label='signal')
+ax.set_xlabel('time')
+ax.set_ylabel('y')
+ax.legend()
+fig.savefig('{}/{}_data.png'.format(outdir, label))
+
+# Now lets instantiate a version of our GaussianLikelihood, giving it
+# the time, data and signal model
+likelihood = GaussianLikelihood(time, data, model, sigma=sigma)
+
+# From hereon, the syntax is exactly equivalent to other tupak examples
+# We make a prior
+priors = {}
+priors['m'] = tupak.core.prior.Uniform(0, 5, 'm')
+priors['c'] = tupak.core.prior.Uniform(-2, 2, 'c')
+
+# And run sampler
+result = tupak.run_sampler(
+    likelihood=likelihood, priors=priors, sampler='pymc3',
+    injection_parameters=injection_parameters, outdir=outdir,
+    draws=2000, label=label)
+result.plot_corner()