We present dynesty, a public, open-source, Python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using Dynamic Nested Sampling. By adaptively allocating samples based on posterior structure, Dynamic Nested Sampling has the benefits of Markov Chain Monte Carlo algorithms that focus exclusively on posterior estimation while retaining Nested Sampling's ability to estimate evidences and sample from complex, multi-modal distributions. We provide an overview of Nested Sampling, its extension to Dynamic Nested Sampling, the algorithmic challenges involved, and the various approaches taken to solve them. We then examine dynesty's performance on a variety of toy problems along with several astronomical applications. We find in particular problems dynesty can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature. More detailed statistical results related to Nested Sampling are also included in the Appendix.

dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences

Spectroscopy of exoplanetary atmospheres has become a well established method for the characterisation of extrasolar planets. We here present a novel inverse retrieval code for exoplanetary atmospheres. T-REx (Tau Retrieval for Exoplanets) is a line-by-line radiative transfer fully
Bayesian retrieval framework. T-REx includes the following features: 1) the optimised use of molecular line-lists from the ExoMol project; 2) an unbiased atmospheric composition prior selection, through custom built pattern recognition software; 3) the use of two independent algorithms to fully sample the Bayesian likelihood space: nested sampling as well as a more classical Markov Chain Monte Carlo approach; 4) iterative Bayesian parameter and model selection using the full Bayesian Evidence as well as the Savage-Dickey Ratio for nested models, and 5) the ability to
fully map very large parameter spaces through optimal code parallelisation and scalability to cluster computing. In this publication we outline the T-REx framework and demonstrate, using a theoretical hot-Jupiter transmission spectrum, the parameter retrieval and model selection. We investigate the impact of Signal-to-Noise and spectral resolution on the retrievability of individual
model parameters, both in terms of error bars on the temperature and molecular mixing ratios as well as its effect on the model's global Bayesian evidence.

https://iopscience.iop.org/article/10.1088/0004-637X/802/2/107/pdf

Tau-rex i: a next generation retrieval code for exoplanetary atmospheres

A distortion corrected panoramic vision system and method provides a visually correct composite image acquired through wide angle optics and projected onto a viewing surface. The system uses image acquisition devices to capture a scene up to 360° or 4π steradians broad. An image processor corrects for luminance or chrominance non-uniformity and applies a spatial transform to each image frame. The spatial transform is convolved by concatenating the viewing transform, acquisition geometry and optical distortion transform, and display geometry and optical transform. The distortion corrections are applied separately for red, green, and blue components to eliminate lateral color aberrations of the optics. A display system is then used to display the resulting composite image on a display device which is then projected through the projection optics and onto a viewing surface. The resulting image is visibly distortion free and matches the characteristics of the viewing surface.

Panoramic vision system and method

This paper develops a general trans-dimensional Bayesian methodology for geoacoustic inversion. Trans-dimensional inverse problems are a generalization of fixed-dimensional inversion that includes the number and type of model parameters as unknowns in the problem. By extending the inversion state space to multiple subspaces of different dimensions, the posterior probability density quantifies the state of knowledge regarding inversion parameters, including effects due to limited knowledge about appropriate parametrization of the environment and error processes. The inversion is implemented here using a reversible-jump Markov chain Monte Carlo algorithm and the seabed is parametrized using a partition model. Unknown data errors are addressed by including a data-error model. Jumps between dimensions are implemented with a birth–death methodology that allows transitions between dimensions by adding or removing interfaces while maintaining detailed balance in the Markov chain. Trans-dimensional inversion results in an inherently parsimonious solution while partition modeling provides a naturally self-regularizing algorithm based on data information content, not on subjective regularization functions. Together, this results in environmental estimates that quantify appropriate seabed structure as supported by the data, allowing sharp discontinuities while approximating smooth transitions where needed. This approach applies generally to geoacoustic inversion and is illustrated here with seabed reflection-coefficient data.

/pdf/trans-dimensional-geoacoustic-inversion-24h2cppums.pdf

Trans-dimensional geoacoustic inversion

Spectroscopy of exoplanetary atmospheres has become a well established method for the characterisation of extrasolar planets. We here present a novel inverse retrieval code for exoplanetary atmospheres. TauRex (Tau Retrieval for Exoplanets) is a line-by-line radiative transfer fully Bayesian retrieval framework. TauRex includes the following features: 1) the optimised use of molecular line-lists from the Exomol project; 2) an unbiased atmospheric composition prior selection, through custom built pattern recognition software; 3) the use of two independent algorithms to fully sample the Bayesian likelihood space: nested sampling as well as a more classical Markov Chain Monte Carlo approach; 4) iterative Bayesian parameter and model selection using the full Bayesian Evidence as well as the Savage-Dickey Ratio for nested models, and 5) the ability to fully map very large parameter spaces through optimal code parallelisation and scalability to cluster computing. In this publication we outline the TauRex framework and demonstrate, using a theoretical hot-Jupiter transmission spectrum, the parameter retrieval and model selection. We investigate the impact of Signal-to-Noise and spectral resolution on the retrievability of individual model parameters, both in terms of error bars on the temperature and molecular mixing ratios as well as its effect on the model's global Bayesian evidence.

Tau-REx I: A next generation retrieval code for exoplanetary atmospheres

This paper discusses an efficient method for evaluating multiple decay times within the Bayesian framework. Previous works [N. Xiang and P. M. Goggans, J. Acoust. Soc. Am. 110, 1415–1424 (2001); 113, 2685–2697 (2003); N. Xiang, P. M. Goggans, T. Jasa, and M. Kleiner, 117, 3707–3715 (2005)] have applied the Bayesian inference to cope with demanding tasks in estimating multiple decay times from Schroeder decay functions measured or calculated in acoustically coupled spaces. Since then a number of recent works call for efficient estimation methods within the Bayesian framework. An efficient analysis is of practical significance for better understanding and modeling the sound energy decay process in acoustically coupled spaces or even in single spaces for reverberation time estimation. This paper will first formulate the Bayesian posterior probability distribution function (PPDF) in a matrix form to reduce the dimensionality as applied to the decay time evaluation. Based on existence of only global extremes o...

Evaluation of decay times in coupled spaces : An efficient search algorithm within the Bayesian framework

In accordance with the specific embodiment of the present invention, a tuner alternates between receiving a first video signal and a second video signal, such that every other frame of a specific signal is received. This is accomplished by writing to an IF1 and IF2 control register, during a vertical blanking interval. Subsequently, the video images are displayed in full motion video by interpolating the alternating frames of data not received by the tuner.

Method and system for providing a video signal

Bayesian inference comprises of parameter estimation and model selection/comparison. A common approach to solving both of these problems has been to use statistical sampling techniques that are inherently non‐Bayesian. This paper presents new Bayesian sampling method that solves both problems by changing the focus of Bayesian inference to the model selection problem first. In the papers [N. Xiang and P. M. Goggins, J. Acoust. Soc. Am. 110, 1415–1424 (2001); 113, 2685–2697 (2003)], the authors developed a model for the decay times and decay modes of acoustically coupled rooms in terms of measured Schroeder’s decay functions. This paper shows how the Bayesian sampling method can be used to evaluate the ‘‘Bayesian evidence’’ term used in model selection as well as determining the decay times along with error estimates.

Tomislav Jasa

Papers

Evaluation of decay times in coupled spaces : An efficient search algorithm within the Bayesian framework

Method and system for providing a video signal

Bayesian sampling with applications to energy decay analysis in acoustically coupled spaces