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Weights

Weights determine relative probabilities in equilibrium workflows. Algorithms only need differences in log weight, so the representation can stay flexible.

The same callable concept also covers Bayesian targets:

  • Bayesian inference: logweight(theta) = logposterior(theta) = loglikelihood(theta) + logprior(theta)
  • Statistical mechanics: logweight(x) = -beta * E(x)

In the sampler API this callable is stored as the algorithm ensemble, with logweight(alg) as an equivalent accessor.

For canonical targets,

\[\pi(x) = \frac{e^{-\beta E(x)}}{Z(\beta)},\]

so

\[\log \pi(x) = -\beta E(x) - \log Z(\beta),\]

and local acceptance decisions depend on

\[\Delta \log \pi = -\beta\,\Delta E.\]

1) Canonical ensemble: BoltzmannEnsemble

For energy $E$, the log weight is $-\beta E$.

using Random
using MonteCarloX

rng = MersenneTwister(1)
alg = Metropolis(rng; β=0.5)  # internally uses BoltzmannEnsemble(0.5)

Use this for standard fixed-temperature sampling.

2) Tabulated weights: BinnedObject

Use when the weight is not known analytically, or when adapting it online (multicanonical or Wang-Landau).

using MonteCarloX

lw = BinnedObject(-20:2:20, 0.0)
lw[0]   = 1.5
value   = lw(0)
lw_zero = zero(lw)

BinnedObject supports discrete and continuous bin definitions, including multidimensional bin tuples.

How to choose

  • Known canonical target: BoltzmannEnsemble
  • Exploratory generalized-ensemble run: BinnedObject + Multicanonical or WangLandau

API reference

MonteCarloX.BinnedObject — Type
BinnedObject(domain::AbstractRange, init)

Construct a binned log weight object for the given domain and initial value. The type of domain determines the specific binned log weight type:

Examples

# Discrete 1D
bo1d = BinnedObject(0:10, 0.0)
# Discrete ND
bo2d = BinnedObject((0:5, 0:5), 0.0)
# Continuous 1D
bo1d_cont = BinnedObject(0.0:0.5:5.0, 0.0)
# Continuous ND
bo2d_cont = BinnedObject((0.0:0.5:5.0, 0.0:0.5:5.0), 0.0)
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MonteCarloX.get_centers — Function
get_centers(bo::BinnedObject, dim::Int=1)

Return bin centers along dimension dim. For discrete bins this returns the bin support values.

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Base.zero — Method
zero(lw::BinnedObject)

Return a new BinnedObject of the same bins as lw but with all values set to zero.

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