adaptive-rejection-sampler

Adaptive rejection sampling works by constructing adaptive upper and lower bounds, or envelopes, around a log-concave probability density function to efficiently generate random samples. The envelopes are refined iteratively as more samples are drawn, improving efficiency.

To implement adaptive rejection sampling in R, follow detailed algorithm steps and pseudocode to construct envelopes, verify log-concavity, and handle domain boundaries. Proper implementation ensures robust sampling for Monte Carlo simulations and Bayesian inference.

You need adaptive rejection sampling for Monte Carlo methods when generating random samples from complex, custom log-concave probability distributions where standard sampling techniques are inefficient or fail. It is particularly useful for Bayesian inference requiring custom densities.

To verify log-concavity for a target probability distribution, check whether the logarithm of the density function is concave. The skill provides specific guidance on correctly checking this log-concavity requirement, which is mandatory for the algorithm to work.

Handle unbounded, lower-bounded, upper-bounded, and fully bounded domains by applying specific domain and boundary handling strategies provided during implementation. These strategies ensure the adaptive envelopes correctly bound the target distribution.

Common pitfalls and performance considerations for rejection sampling algorithms include failing to verify log-concavity, improperly handling domain boundaries, and inefficient envelope construction. The skill details these issues to ensure a correct and performant implementation.