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

Due to recent developments in concert hall design, there is an increasing interest in the analysis of sound energy decays consisting of multiple exponential decay rates. It has been considered challenging to estimate parameters associated with double-rate (slope) decay characteristics, and even more challenging when the coupled-volume systems contain more than two decay processes. To meet the need of characterizing energy decays of multiple decay processes, this work investigates coupled-volume systems using acoustic scale-models of three coupled rooms. Two Bayesian formulations are compared using the experimentally measured sound energy decay data. A fully parameterized Bayesian formulation has been found to be capable of characterization of multiple-slope decays beyond the single-slope and double-slope energy decays. Within the Bayesian framework using this fully parameterized formulation, an in-depth analysis of likelihood distributions over multiple-dimensional decay parameter space motivates the use of Bayesian information criterion, an efficient approach to solving Bayesian model selection problems that are suitable for estimating the number of exponential decays. The analysis methods are then applied to a geometric-acoustics simulation of a conceptual concert hall. Sound energy decays more complicated than single-slope and double-slope nature, such as triple-slope decays have been identified and characterized.

Bayesian characterization of multiple-slope sound energy decays in coupled-volume systems.

An image transformation method for translating a non-linear 2D geometrical transformation into two separable 1D geometrical transformations first determines the inverse of the 2D geometrical transformation to form an inverse 2D geometrical transformation. Then the method converts the inverse 2D geometrical transformation into an analytical inverted 2D geometrical transformation and separates the analytical inverse 2D geometrical transformation into first and second 1D geometrical transformations. The method then represents said inverse 2D geometrical transformation and first and second 1D geometrical transformations as tensor spline surfaces and then compares an evaluation of said first and second 1D geometrical transformations at each pixel with an evaluation of the analytical inverse 2D geometrical transformation at each pixel. If the error evaluation does not meet a predetermined level of performance then the separation and transformation steps are repeated. One-dimensional spatial transform processing it results in reduced calculation, efficient memory access, and ability to process data in a real-time environment. In-addition, since the method provides a compact representation of the spatial transforms, it can be scaled for a particular level of precision.

Method and system for processing a non-linear two dimensional spatial transformation

Room-acoustic energy decays often exhibit single-rate or multiple-rate characteristics in a wide variety of rooms/halls. Both the energy decay order and decay parameter estimation are of practical significance in architectural acoustics applications, representing two different levels of Bayesian probabilistic inference. This paper discusses a model-based sound energy decay analysis within a Bayesian framework utilizing the nested sampling algorithm. The nested sampling algorithm is specifically developed to evaluate the Bayesian evidence required for determining the energy decay order with decay parameter estimates as a secondary result. Taking the energy decay analysis in architectural acoustics as an example, this paper demonstrates that two different levels of inference, decay model-selection and decay parameter estimation, can be cohesively accomplished by the nested sampling algorithm.

/pdf/nested-sampling-applied-in-bayesian-room-acoustics-decay-58b4ggqobm.pdf

Nested sampling applied in Bayesian room-acoustics decay analysis.

Room-acoustic energy decay analysis of acoustically coupled-spaces within the Bayesian framework has proven valuable for architectural acoustics applications. This paper describes an efficient algorithm termed slice sampling Monte Carlo (SSMC) for room-acoustic decay parameter estimation within the Bayesian framework. This work combines the SSMC algorithm and a fast search algorithm in order to efficiently determine decay parameters, their uncertainties, and inter-relationships with a minimum amount of required user tuning and interaction. The large variations in the posterior probability density functions over multidimensional parameter spaces imply that an adaptive exploration algorithm such as SSMC can have advantages over the exiting importance sampling Monte Carlo and Metropolis–Hastings Markov Chain Monte Carlo algorithms. This paper discusses implementation of the SSMC algorithm, its initialization, and convergence using experimental data measured from acoustically coupled-spaces.

/pdf/efficient-estimation-of-decay-parameters-in-acoustically-58acjku99h.pdf

Efficient estimation of decay parameters in acoustically coupled-spaces using slice sampling.

Nested Sampling is a method introduced by Skilling as a bayesian sampling method for model selection and parameter estimation. We present a view of Nested Sampling as an approximate method for computing the Lebesgue Integral of a function. We then apply Nested Sampling to the problem of estimating the decay order and decay time as applied to the acoustics of coupled rooms.

Tomislav Jasa

Papers

Bayesian characterization of multiple-slope sound energy decays in coupled-volume systems.

Method and system for processing a non-linear two dimensional spatial transformation

Nested sampling applied in Bayesian room-acoustics decay analysis.

Efficient estimation of decay parameters in acoustically coupled-spaces using slice sampling.

Using Nested Sampling in the Analysis of Multi‐Rate Sound Energy Decay in Acoustically Coupled Rooms