advanced-algorithmic-trading

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Finally we specify the Metropolis sampler to be used and then actually sample(..) the results.
These results are stored in the trace variable:
# Use PyMC3 to construct a model context
basic_model = pymc3.Model()
with basic_model:
# Define our prior belief about the fairness
# of the coin using a Beta distribution
theta = pymc3.Beta("theta", alpha=alpha, beta=beta)
# Define the Bernoulli likelihood function
y = pymc3.Binomial("y", n=n, p=theta, observed=z)
# Carry out the MCMC analysis using the Metropolis algorithm
# Use Maximum A Posteriori (MAP) optimisation as initial value for MCMC
start = pymc3.find_MAP()
# Use the Metropolis algorithm (as opposed to NUTS or HMC, etc.)
step = pymc3.Metropolis()
# Calculate the trace
trace = pymc3.sample(
iterations, step, start, random_seed=1, progressbar=True
)
Notice how the specification of the model via the PyMC3 API is akin to the actual mathematical
specification of the model with minimal "boilerplate" code. We will demonstrate the
power of this API in later chapters when we come to specify some more complex models.
Now that the model has been specified and sampled, we wish to plot the results. We create
a histogram from the trace (the list of all accepted samples) of the MCMC sampling using
50 bins. We then plot the analytic prior and posterior beta distributions using the SciPy
stats.beta.pdf(..) method. Finally, we add some labelling to the graph and display it:
# Plot the posterior histogram from MCMC analysis
bins=50
plt.hist(
trace["theta"], bins,
histtype="step", normed=True,
label="Posterior (MCMC)", color="red"
)
# Plot the analytic prior and posterior beta distributions
x = np.linspace(0, 1, 100)
plt.plot(
x, stats.beta.pdf(x, alpha, beta),
"--", label="Prior", color="blue"
)