Dynamic Gauss Newton Metropolis Algorithm
Abstract
GNM: The MCMC Jagger. A rocking awesome sampler. This python package is an affine invariant Markov chain Monte Carlo (MCMC) sampler based on the dynamic GaussNewtonMetropolis (GNM) algorithm. The GNM algorithm is specialized in sampling highly nonlinear posterior probability distribution functions of the form $e^{f(x)^2/2}$, and the package is an implementation of this algorithm. On top of the backoff strategy in the original GNM algorithm, there is the dynamic hyperparameter optimization feature added to the algorithm and included in the package to help increase performance of the backoff and therefore the sampling. Also, there are the Jacobian tester, error bars creator and many more features for the ease of use included in the code. The problem is introduced and a guide to installation is given in the introduction. Then how to use the python package is explained. The algorithm is given and finally there are some examples using exponential time series to show the performance of the algorithm and the backoff strategy.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:2001.03530
 Bibcode:
 2020arXiv200103530U
 Keywords:

 Statistics  Computation;
 Astrophysics  Earth and Planetary Astrophysics;
 Astrophysics  Solar and Stellar Astrophysics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 21 pages, 5 figures