samppy 1.3.1

Hamiltonian sampling and analysis of sampled distributions

Package samppy implements Hamiltonian Markov-chain sampling and some additional analysis methods for multivariate probability distributions.

The probability distribution is represented only by an array of independent and identically distributed (i.i.d.) samples drawn from the distribution.

The package includes four modules:

• Module hamiltonian_sampler implements Hamiltonian Markov-Chain sampling. A HamiltonianSampler instance can generate random samples of a multivariate probability distribution, defined only by an non-normalized log-likelihood function, and the gradient of that function.

  The generated batch of sample vectors is stored in a 2D numpy array, either as rows or as columns.

  Class HamiltonianSampler defines a standard isotropic sampler. Class HamiltonianBoundedSampler is a subclass also allowing one- or two-sided interval limits for all vector elements.

• Module credibility includes functions to estimate jointly credible differences and/or correlations between pairs of elements in a random vector with a multivariate probability distribution, represented only by samples.

• A separate module credibility_pd has the same functionality, but operates on input data in Pandas DataFrame or Series format.

• Module sample_entropy includes a function to estimate the differential entropy of a multivariate probability distribution, represented only by samples. The entropy is estimated by the Kozachenko-Leonenko nearest-neighbor approximation (Singh and Poczos, 2016).

Usage

This package was developed mainly for use by other projects. It is distributed separately because it may be useful for other purposes.

The Hamiltonian sampler code was inspired by the LAHMC project by Jasha Sohlstein. The present implementation includes some safety features to facilitate its use. The present sampler does not include sampling within a general subspace manifold, but it allows bounded ranges for vector elements.

Requirements

The package requires recent versions of Numpy and Scipy. These are automatically installed. Pandas is not installed automatically, because the module requiring Pandas input will only be called from other program(s) that already use Pandas.

References

R M Neal (2011): MCMC using Hamiltonian dynamics. Ch. 5 in Brooks et al. (eds) Handbook of Markov Chain Monte Carlo. Chapman and Hall / CRC Press.

A. Leijon, G. E. Henter, and M. Dahlquist (2016): Bayesian analysis of phoneme confusion matrices. IEEE Transactions on Audio, Speech, and Language Processing 24(3):469–482. (Describes an application of credible-difference calculation.)

A. Leijon, P. von Gablenz, I. Holube, J. Taghia, and K. Smeds (2023). Bayesian analysis of ecological momentary assessment (EMA) data collected in adults before and after hearing rehabilitation. Frontiers in Digital Health, 5(1100705). download

F Perez-Cruz (2008): Estimation of Information Theoretic Measures for Continuous Random Variables. Advances in Neural Information Processing Systems 21 (NIPS 2008).

S Singh and B Poczos (2016): Analysis of k-nearest neighbor distances with application to entropy estimation. arXiv:1603.08578 [math.ST].