advanced-algorithmic-trading

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plt.plot(
x, stats.beta.pdf(x, alpha_post, beta_post),
label=’Posterior (Analytic)’, color="green"
)
# Update the graph labels
plt.legend(title="Parameters", loc="best")
plt.xlabel("$\\theta$, Fairness")
plt.ylabel("Density")
plt.show()
When the code is executed the following output is given:
Applied logodds-transform to theta and added transformed theta_logodds to
model.
[----- 14% ] 14288 of 100000 complete in 0.5 sec
[---------- 28% ] 28857 of 100000 complete in 1.0 sec
[---------------- 43% ] 43444 of 100000 complete in 1.5 sec
[-----------------58%-- ] 58052 of 100000 complete in 2.0 sec
[-----------------72%------- ] 72651 of 100000 complete in 2.5 sec
[-----------------87%------------- ] 87226 of 100000 complete in 3.0 sec
[-----------------100%-----------------] 100000 of 100000 complete in 3.4 sec
Clearly, the sampling time will depend upon the speed of your computer.
output of the analysis is given in Figure 4.2:
The graphical
Figure 4.2: Comparison of the analytic and MCMC-sampled posterior belief distributions of the
fairness θ, overlaid with the prior belief
In this particular case of a single-parameter model, with 100,000 samples, the convergence
of the Metropolis algorithm is extremely good. The histogram closely follows the analytically
calculated posterior distribution, as we would expect. In a relatively simple model such as this