faq.rst

Frequently Asked Questions

What is the acceptance rate of zeus?

Unlike most MCMC methods, zeus acceptance rate isn't varying during a run. As a matter of fact, its acceptance rate is identically 1, always. This is because of the Slice Sampler at its core.

Why should I use zeus instead of other MCMC samplers?

The first reason you should think of using zeus is due to the fact that it doesn't require any hand tuning at all. There is no need to adjust any hyperparameters or provide a proposal distribution.

Moreover, unlike other black-box MCMC methods zeus is more robust to the curse of dimensionality and handle challenging distributions better.

What are the walkers?

Walkers are the members of the ensemble. They are interacting parallel chains which collectively explore the posterior mass.

How many walkers should I use?

At least twice the number of parameters of your problem. A good rule of thump is to use between 2 and 4 times the number of parameters. If your distribution has multiple modes/peaks you may want to increase the number of walkers.

How should I initialize the positions of the walkers?

A good practice seems to be to initialize the walkers from a small ball close to the Maximum a Posteriori estimate. After a few autocorrelation times the walkers would have explored the rest of the usefull regions of the parameter space (i.e. the typical set), producing a great number of independent samples.

How long should I run zeus?

You don't have to run zeus for very long. If your goal is to produce 2D/1D contours and/or 1-sigma/2-sigma constraints for your parameters, running zeus for a few autocorrelation times (e.g. 10) is more than enough. You can also use the implemented callback functions (see Cookbook and API) to automate the termination of a run.

What can I do if the first few iterations take too long to complete?

This usually occurs when the walkers are initialised closed to each other. During the first 10-100 iterations zeus is tuning its proposal scale mu. During that time zeus may do more model evaluations than usual. Tuning of mu is faster if initialised from a large value. We thus recommend to set mu to an large value (e.g. mu=1e3) initially in the EnsembleSampler.

Is there any way to reduce the computational cost per iteration?

zeus's power originates in its flexibility. During each iteration, the walkers move along straight lines (i.e. slices) that cross the posterior mass. The construction of a slice involves two steps, an initial expanding/stepping-out and a subsequent shrinking procedure. One can decrease the computational cost per iteration by forcing zeus to conduct no expansions. This is achieved by setting light_mode=True in the EnsembleSampler at the cost of reduced flexibility. If the target distribution is close to normal/Gaussian one then this procedure can cut the cost to half.

What are the Moves and which one should I use?

zeus was originally built on the Differential and Gaussian moves. Starting from version 2.0.0, zeus supports a mixture of different moves/proposals. Moves are recipes that the walkers follow to cross the parameter space. The Differential Move remains the default choice but we also provide a suite of additional moves, such as the Global Move that can be used when sampling from challenging target distributions (e.g. highly dimensional multimodal distributions).

The move(s) you should use depends on the particular target distribution. The Differential Move seems to be a good choice for most distributions and 50-50 mixture of the Global Move and Local Move seem to perform very well in highly dimensional multimodal distributions when used after the burnin period is over.