advanced-algorithmic-trading

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we do not need to compute 100,000 samples. Far fewer would be more than sufficient. However,
it does emphasise the convergence properties of the Metropolis algorithm.
We can also consider a concept known as the trace, which is the vector of samples produced
by the MCMC sampling procedure. We can use the helpful traceplot method to plot both a
kernel density estimate (KDE) of the histogram displayed above, as well as the trace itself.
The trace plot is extremely useful for assessing convergence of an MCMC algorithm and
whether we need to exclude a period of initial samples (known as the burn in). To output the
trace we simply call traceplot with the trace variable:
# Show the trace plot
pymc3.traceplot(trace)
plt.show()
The full trace plot is given in Figure 4.3:
Figure 4.3: Trace plot of the MCMC sampling procedure for the fairness parameter θ
As you can see, the KDE estimate of the posterior belief in the fairness reflects both our prior
belief of θ = 0.5 and our data with a sample fairness of θ = 0.2. In addition we can see that the
MCMC sampling procedure has "converged to the distribution" since the sampling series looks
stationary.
For completeness, here is the full listing:
import matplotlib.pyplot as plt
import numpy as np
import pymc3
import scipy.stats as stats
plt.style.use("ggplot")