Skip to contents

Generate samples with a random walk

Source: R/rwmh_cube.R
rwmh_cube.Rd

Create new live points by evolving a current live point through a Metropolis-Hastings random walk, rejecting steps that fail to meet the likelihood criterion.

Usage

rwmh_cube(steps = 25, target_acceptance = 0.5)

Arguments

steps

Positive integer. Number of steps to take when generating a proposal point.

target_acceptance

Number between 1 / steps and 1.0. Target acceptance rate for proposed points.

Value

An object of class c("rwmh_cube", "ernest_lrps") that can be used with ernest_sampler() to specify the sampling behaviour.

Details

The random walk LRPS generates proposals by performing a fixed number of Metropolis-Hastings steps within the unit hypercube. Each step proposes a new location by adding a random perturbation to the current position, accepting or rejecting the step based on whether it satisfies the likelihood criterion. This process continues for the specified number of steps, with the final accepted position returned as the proposal.

Step-size Adaptation: The step size \(\epsilon\) is adapted between sampling rounds using update_lrps(). The adaptation uses a Newton-like method to target the desired acceptance rate \(\alpha_*\). Given the current acceptance rate \(\alpha_i\) and number of dimensions \(d\), the step size is updated with:

$$\epsilon_i * \exp(\frac{\alpha_i - \alpha^*}{d \cdot \alpha_*})$$

Given the previously-accepted sample \(X_{i-1}\) and the number of dimensions \(d\), proposed points are generated from:

$$X_{i-1} + S_d(0, \epsilon)$$

where \(S(0, \epsilon)\) is a point drawn uniformly from the $d$-dimensional ball centered on the origin with radius \(\epsilon\).

Control Parameters

  • steps: Start with 25. Increase to generate samples that more closely follow the posterior distribution; decrease for computational efficiency.

  • target_acceptance: Start with 0.4-0.6. Lower values encourage more global exploration of the posterior, higher values encourage explorations close to the starting point.

References

  • Skilling, J. (2006). Nested Sampling for General Bayesian Computation. Bayesian Analysis, 1(4), 833–859. doi:10.1214/06-BA127

  • Speagle, J. S. (2020). Dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences. Monthly Notices of the Royal Astronomical Society, 493, 3132–3158. doi:10.1093/mnras/staa278

See also

Other ernest_lrps: mini_balls(), multi_ellipsoid(), no_underrun(), slice_rectangle(), unif_cube(), unif_ellipsoid()

Examples

# Basic usage with default parameters
lrps <- rwmh_cube()

# A faster sampler for simple-to-traverse posterior surfaces
fast_lrps <- rwmh_cube(
  steps = 20,
  target_acceptance = 0.7
)