Mysteries in Forward Event Chain Monte Carlo

A Blog Entry on Bayesian Computation by an Applied Mathematician

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FECMC is a generalization of BPS in that it reduces to BPS (in the limit) when the orthogonal components are fully refreshed.¹

However, an interesting phenomenon is that the scaling limit seems to be entirely different from the BPS case, when orthogonal switches are employed as recommended in (Michel et al., 2020).

The frequency of orthogonal switches seems to be crucial. As an edge case, without refreshing the orthogonal components, the scaling limit seems to lose ergodicity:

1 Animations

Below we’ll list the animations of the trajectories of FECMC (1) with its orthogonal components fully refreshed, (2) switched, and (3) no orthogonal refresh.

(1) FECMC with its orthogonal components fully refresed

(2) FECMC with its orthogonal components switched

(3) FECMC with no orthogonal refresh

2 The Dynamics of FECMC with no refresh

The deterministic dynamics seems to be determined by the initial value.

Here we add two more examples with different initial values:

References

Michel, M., Durmus, A., and Sénécal, S. (2020). Forward event-chain monte carlo: Fast sampling by randomness control in irreversible markov chains. Journal of Computational and Graphical Statistics, 29(4), 689–702.

Footnotes

1. FECMC with full orthogonal refresh is \(d\to\infty\) asymptotically equivalent to BPS, allegedly.