Eoin - 3 months ago 31

Python Question

I am working to learn pyMC 3 and having some trouble. Since there are limited tutorials for pyMC3 I am working from Bayesian Methods for Hackers. I'm trying to port the pyMC 2 code to pyMC 3 in the Bayesian A/B testing example, with no success. From what I can see the model isn't taking into account the observations at all.

I've had to make a few changes from the example, as pyMC 3 is quite different, so what should look like this:

import pymc as pm

`# The parameters are the bounds of the Uniform.`

p = pm.Uniform('p', lower=0, upper=1)

# set constants

p_true = 0.05 # remember, this is unknown.

N = 1500

# sample N Bernoulli random variables from Ber(0.05).

# each random variable has a 0.05 chance of being a 1.

# this is the data-generation step

occurrences = pm.rbernoulli(p_true, N)

print occurrences # Remember: Python treats True == 1, and False == 0

print occurrences.sum()

# Occurrences.mean is equal to n/N.

print "What is the observed frequency in Group A? %.4f" % occurrences.mean()

print "Does this equal the true frequency? %s" % (occurrences.mean() == p_true)

# include the observations, which are Bernoulli

obs = pm.Bernoulli("obs", p, value=occurrences, observed=True)

# To be explained in chapter 3

mcmc = pm.MCMC([p, obs])

mcmc.sample(18000, 1000)

figsize(12.5, 4)

plt.title("Posterior distribution of $p_A$, the true effectiveness of site A")

plt.vlines(p_true, 0, 90, linestyle="--", label="true $p_A$ (unknown)")

plt.hist(mcmc.trace("p")[:], bins=25, histtype="stepfilled", normed=True)

plt.legend()

instead looks like:

`import pymc as pm`

import random

import numpy as np

import matplotlib.pyplot as plt

with pm.Model() as model:

# Prior is uniform: all cases are equally likely

p = pm.Uniform('p', lower=0, upper=1)

# set constants

p_true = 0.05 # remember, this is unknown.

N = 1500

# sample N Bernoulli random variables from Ber(0.05).

# each random variable has a 0.05 chance of being a 1.

# this is the data-generation step

occurrences = [] # pm.rbernoulli(p_true, N)

for i in xrange(N):

occurrences.append((random.uniform(0.0, 1.0) <= p_true))

occurrences = np.array(occurrences)

obs = pm.Bernoulli('obs', p_true, observed=occurrences)

start = pm.find_MAP()

step = pm.Metropolis()

trace = pm.sample(18000, step, start)

pm.traceplot(trace);

plt.show()

Apologies for the lengthy post but in my adaptation there have been a number of small changes, e.g. manually generating the observations because pm.rbernoulli no longer exists. I'm also not sure if I should be finding the start prior to running the trace. How should I change my implementation to correctly run?

Answer

You were indeed close. However, this line:

```
obs = pm.Bernoulli('obs', p_true, observed=occurrences)
```

is wrong as you are just setting a constant value for p (p_true == 0.05). Thus, your random variable p defined above to have a uniform prior is not constrained by the likelihood and your plot shows that you are just sampling from the prior. If you replace p_true with p in your code it should work. Here is the fixed version:

```
import pymc as pm
import random
import numpy as np
import matplotlib.pyplot as plt
with pm.Model() as model:
# Prior is uniform: all cases are equally likely
p = pm.Uniform('p', lower=0, upper=1)
# set constants
p_true = 0.05 # remember, this is unknown.
N = 1500
# sample N Bernoulli random variables from Ber(0.05).
# each random variable has a 0.05 chance of being a 1.
# this is the data-generation step
occurrences = [] # pm.rbernoulli(p_true, N)
for i in xrange(N):
occurrences.append((random.uniform(0.0, 1.0) <= p_true))
occurrences = np.array(occurrences)
obs = pm.Bernoulli('obs', p, observed=occurrences)
start = pm.find_MAP()
step = pm.Metropolis()
trace = pm.sample(18000, step, start)
pm.traceplot(trace);
```