Quasi-Random Numbers with Halton Sequences

Just two quick plots.

For maximum simulated likelihood estimation and for some other cases, we need to integrate the likelihood function with respect to a distribution that reflects unobserved heterogeneity. When numeric integration is too difficult, then we can integrate by simulating the underlying distribution.

However, using random draws from the underlying distribution can be inefficient for integration, and there are several ways of speeding up the integration or of increasing the accuracy for the same amount of time.

One possibility is to use sequences that mimic random draws from the underlying distribution but have a better coverage of the underlying space, examples for low-discrepancy_sequences are Sobol and Halton sequences.