Hands-On Machine Learning for Algorithmic Trading

Sampling-based stochastic inference

Sampling is about drawing samples, X=(x₁, ..., x_n), from a given distribution, p(x). Assuming the samples are independent, the law of large numbers ensures that for a growing number of samples, the fraction of a given instance, x_i, in the sample (for the discrete case) corresponds to its probability, p(x=x_i). In the continuous case, the analogous reasoning applies to a given region of the sample space. Hence, averages over samples can be used as unbiased estimators of the expected values of parameters of the distribution.

A practical challenge consists in ensuring independent sampling because the distribution is unknown. Dependent samples may still be unbiased, but tend to increase the variance of the estimate ...