# declarative: DIY Markov Chains.

[ library, math, mit ] [ Propose Tags ]

This package presents a simple combinator language for Markov transition operators that are useful in MCMC.

Any transition operators sharing the same stationary distribution and obeying the Markov and reversibility properties can be combined in a couple of ways, such that the resulting operator preserves the stationary distribution and desirable properties amenable for MCMC.

We can deterministically concatenate operators end-to-end, or sample from a collection of them according to some probability distribution. See Geyer, 2005 for details.

A useful strategy is to hedge one's 'sampling risk' by occasionally interleaving a computationally-expensive transition (such as a gradient-based algorithm like Hamiltonian Monte Carlo or NUTS) with cheap Metropolis transitions.

transition = frequency [
(9, metropolis 1.0)
, (1, hamiltonian 0.05 20)
]

Alternatively: sample consecutively using the same algorithm, but over a range of different proposal distributions.

transition = concatAllT [
slice 0.5
, slice 1.0
, slice 2.0
]

Or just mix and match and see what happens!

transition =
sampleT
(sampleT (metropolis 0.5) (slice 0.1))
(sampleT (hamiltonian 0.01 20) (metropolis 2.0))

Check the test suite for example usage.

Versions [faq] 0.1.0.0, 0.1.0.1, 0.2.1, 0.2.2, 0.2.3, 0.3.3, 0.3.4, 0.4.0, 0.5.0, 0.5.1, 0.5.2, 0.5.3, 0.5.4 base (>=4 && <6), hasty-hamiltonian (>=1.1.1), kan-extensions (==5.*), lens (==4.*), mcmc-types (>=1.0.1), mighty-metropolis (>=1.0.1), mwc-probability (>=1.0.1), pipes (==4.*), primitive (>=0.6 && <1.0), speedy-slice (>=0.1.2), transformers (>=0.5 && <1.0) [details] MIT Jared Tobin jared@jtobin.ca Math http://github.com/jtobin/declarative head: git clone http://github.com/jtobin/declarative.git by JaredTobin at 2016-12-21T21:15:22Z LTSHaskell:0.5.2, NixOS:0.5.4, Stackage:0.5.4 6603 total (8 in the last 30 days) (no votes yet) [estimated by Bayesian average] λ λ λ Docs not available All reported builds failed as of 2016-12-22

## Modules

• Numeric
• Numeric.MCMC
• Numeric.MCMC.Anneal