advanced-algorithmic-trading

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# Parameter values for prior and analytic posterior
n = 50
z = 10
alpha = 12
beta = 12
alpha_post = 22
beta_post = 52
# How many iterations of the Metropolis
# algorithm to carry out for MCMC
iterations = 100000
# 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
)
# 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(