###### tags: `one-offs` `monte carlo`

# Competition between Monte Carlo Methods

**Overview**: In this note, I describe some old and rough thoughts about the differences between different Monte Carlo methods, and how they can be perceived.

## Discussion

At some point, I wrote that “It is not uncommon for papers which write about Monte Carlo methods to describe { MCMC, Importance Sampling, SMC, ... } as being in competition somehow.” I'm now not so sure about this; by now I probably think that it *is* basically uncommon, though it does happen.

Still, there is a bit to comment on here. I would not say that this perspective of competition is entirely misguided; e.g. in some scenarios, it can be useful to zoom in on a specific method for a specific task, rather than worrying about all possible solutions. However, doing this at too coarse a resolution is bound to gloss over the various developments in the past 15-20 years which highlight how these ideas can be fruitfully combined (e.g. Particle MCMC, SMC Samplers, Pseudo-Marginal MCMC, Annealed Importance Sampling, ...). I thus view any framing as an internal competition is a bit unfortunate, in that it would obscure the important aspect: that these techniques are all components of the same core toolbox.

Essentially, when one is using any of these tools, my sense is that it can be worthwhile to learn a bit about all of them, so as to avoid 'leaving money on the table', in some sense. At the very least, there is little to be gained from being too dismissive of the alternatives (which broadly holds true in computational disciplines at large). That is, I would advocate for focusing on identification of useful common ground between techniques, rather than getting bogged down in any form of 'competition'.

## Postscript

Even these days, it is not that rare to find people who have thought deeply about MCMC in various forms, but still haven't touched SMC, maybe under the perception that it is 'too different', or 'too difficult'. I personally hope that this perception changes; the tools and methods in both areas have substantial overlap, and most difference in difficulty seems to boil down to experience, rather than essential complexity.

I know people who would argue that SMC is essentially simpler than MCMC in many ways, and I can really see their point. Hopefully more people can start to believe this as well.