energy_bfmi: Energy Bayesian Fraction of Missing Information (E-BFMI)

In tulpa: Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

Energy Bayesian Fraction of Missing Information (E-BFMI)

Description

Computes E-BFMI (Betancourt 2016) from the per-iteration Hamiltonian energies an HMC or NUTS sampler records: the variance of the energy transition between successive iterations over the variance of the marginal energy. Each chain is diffed separately, since a transition across a chain boundary compares unrelated trajectories, and the lowest chain value is reported: one badly exploring chain is enough to distrust a fit. Values below 0.3 indicate that momentum resampling moves the sampler too little between energy level sets.

Usage

energy_bfmi(energy, chain = NULL)

Arguments

energy	Numeric vector of per-iteration energies.
chain	Chain index of each entry of energy. NULL (default), or a vector of the wrong length, treats energy as one chain.

Value

A list with value (the lowest per-chain E-BFMI, NA when no chain has two finite, non-constant energies), per_chain, energy_centred (energies centred within each chain) and energy_diff (within-chain transitions), the last two pooled across chains for plotting.

Examples

set.seed(1)
energy <- c(cumsum(rnorm(200, sd = 0.3)), rnorm(200, sd = 1))
energy_bfmi(energy, chain = rep(1:2, each = 200))$per_chain

tulpa documentation built on Oct. 19, 2026, 5:09 p.m.