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At least 199 records · Page 11

Joint Bayesian Inference for Near-Surface Explosion Yield and Height-of-Burst

Forensic capabilities to understand chemical and nuclear explosions are greatly aided by an accurate estimate of explosive yield with uncertainty. The relationship between explosive size and geophysical observations of seismic, acoustic, and optical waves can be exploited to provide an estimate of yield. Any near-surface yield estimate is complicated by the surface interaction, so an estimate for the explosion height-of-burst is necessarily included in the relationship. Additionally, the relationship dictates a trade-off between estimates of yield and height-of-burst. Fortunately, the surface interaction for each type of observation is different, which breaks the trade-off, and the inclusion of height-of-burst with multiple data types improves yield estimation. We define simple parametric forward models to relate seismoäcoustoöptic observations from a data set of known explosive yields and height-of-bursts. The parameters of the models and a prediction for the yield and height-of-burst of a new event can then be estimated given new observations via Bayesian inference. We report posterior distribution estimates of the parametric models using a Markov chain Monte Carlo sampling technique. These models are then used to predict the yield and height-of-burst of SUGAR, a historical near-surface nuclear explosion, using its reported historical observations. The reported yield of 1.2 ktonne Trinitrotoluene (TNT)-equivalent (Department of Energy, 2015) is within the estimated posterior. Yield uncertainty can be estimated from the spread of the posterior, which is between 0.9 and 2.1 ktonne TNT-equivalent. The posterior for height-of-burst has a wider range between 10 m below and 8 m above ground that includes the true height-of-burst of 1 m.

58 GEOSCIENCES↗

Prior biosphere model impact on global terrestrial CO2 fluxes estimated from OCO-2 retrievals

This study assesses the impact of different state of the art global biospheric CO2 flux models, when applied as prior information, on inverse model “top-down” estimates of terrestrial CO2 fluxes obtained when assimilating Orbiting Carbon Observatory 2 (OCO-2) observations. This is done with a series of observing system simulation experiments (OSSEs) using synthetic CO2 column-average dry air mole fraction (XCO2) retrievals sampled at the OCO-2 satellite spatiotemporal frequency. The OSSEs utilized a 4-D variational (4D-Var) assimilation system with the GEOS-Chem global chemical transport model (CTM) to estimate CO2 net ecosystem exchange (NEE) fluxes using synthetic OCO-2 observations. The impact of biosphere models in inverse model estimates of NEE is quantified by conducting OSSEs using the NASA-CASA, CASA-GFED, SiB-4, and LPJ models as prior estimates and using NEE from the multi-model ensemble mean of the Multiscale Synthesis and Terrestrial Model Intercomparison Project as the “truth”. Results show that the assimilation of simulated XCO2 retrievals at OCO-2 observing modes over land results in posterior NEE estimates which generally reproduce “true” NEE globally and over terrestrial TransCom-3 regions that are well-sampled. However, we find larger spread among posterior NEE estimates, when using different prior NEE fluxes, in regions and seasons that have limited OCO-2 observational coverage and a large range in “bottom-up” NEE fluxes. Seasonally averaged posterior NEE estimates had standard deviations (SD) of ∼10 % to ∼50 % of the multi-model-mean NEE for different TransCom-3 land regions with significant NEE fluxes (regions/seasons with a NEE flux ≥0.5 PgC/yr). On a global average, the seasonally averaged residual impact of the prior model NEE assumption on the posterior NEE spread is ∼10 %–20 % of the posterior NEE mean. Additional OCO-2 OSSE simulations demonstrate that posterior NEE estimates are also sensitive to the assumed prior NEE flux uncertainty statistics, with spread in posterior NEE estimates similar to those when using variable prior model NEE fluxes. In fact, the sensitivity of posterior NEE estimates to prior error statistics was larger than prior flux values in some regions/times in the tropics and Southern Hemisphere where sufficient OCO-2 data were available and large differences between the prior and truth were evident. Overall, even with the availability of spatiotemporally dense OCO-2 data, noticeable residual differences (up to ∼20 %–30 % globally and 50 % regionally) in posterior NEE flux estimates remain that were caused by the choice of prior model flux values and the specification of prior flux uncertainties.

Sajeev Philip↗

The eROSITA Final Equatorial-Depth Survey (eFEDS): The AGN catalog and its X-ray spectral properties

The eROSITA Final Equatorial Depth Survey (eFEDS), observed with eROSITA ahead of its planned 4-yr all-sky survey, is the largest contiguous-field X-ray survey at present. It yielded a large sample of X-ray sources with very rich multiband photometric and spectroscopic coverage. We present here the eFEDS active galactic nuclei (AGN) catalog and the eROSITA X-ray spectral properties of the eFEDS sources. Using a Bayesian method, we performed a systematic X-ray spectral analysis for all the eFEDS sources. We adopted multiple spectral models, including single-component power-law or hot-plasma models and double-component models of a power law plus soft excess. We investigated the capacity of eROSITA X-ray spectra for constraining AGN spectral shapes through a detailed analysis of the posterior parameter probability distribution functions. Hierarchical Bayesian modeling was used to recover the spectral parameter distribution of the sample. The source fluxes and luminosities were measured from the posterior of the spectral fitting. The eFEDS AGN catalog (22 079 sources) comprises ~80% of the eFEDS point sources. Despite a large number of faint sources, our spectral fitting provides reasonable measurements of spectral shapes and intrinsic luminosities for a majority of the sources. Because of sample selection bias, this AGN catalog is dominated by X-ray unobscured sources, with an obscured (logN H > 21.5) fraction of 8%; the power-law emission of the hot corona is also relatively soft, with a typical slope of 2.0. For type-I AGN, the X-ray emission is well correlated with the UV emission with the usual anticorrelation between the X-ray to UV spectral slope α OX and the UV luminosity. The X-ray spectral properties measured with various models are presented for all the eFEDS sources.

79 ASTRONOMY AND ASTROPHYSICS↗

A composite likelihood approach for inference under photometric redshift uncertainty

ABSTRACT Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.

(cosmology:) large-scale structure of Universe↗

Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory

We present the cosmological implications from final measurements of clustering using galaxies, quasars, and Lyα forests from the completed Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale structure. These experiments, composed of data from SDSS, SDSS-II, BOSS, and eBOSS, offer independent measurements of baryon acoustic oscillation (BAO) measurements of angular-diameter distances and Hubble distances relative to the sound horizon, r d , from eight different samples and six measurements of the growth rate parameter, fσ 8 , from redshift-space distortions (RSD). This composite sample is the most constraining of its kind and allows us to perform a comprehensive assessment of the cosmological model after two decades of dedicated spectroscopic observation. We show that the BAO data alone are able to rule out dark-energy-free models at more than eight standard deviations in an extension to the flat, ΛCDM model that allows for curvature. When combined with Planck Cosmic Microwave Background (CMB) measurements of temperature and polarization, under the same model, the BAO data provide nearly an order of magnitude improvement on curvature constraints relative to primary CMB constraints alone. Independent of distance measurements, the SDSS RSD data complement weak lensing measurements from the Dark Energy Survey (DES) in demonstrating a preference for a flat ΛCDM cosmological model when combined with Planck measurements. The combined BAO and RSD measurements indicate σ 8 =0.85±0.03, implying a growth rate that is consistent with predictions from Planck temperature and polarization data and with General Relativity. When combining the results of SDSS BAO and RSD, Planck, Pantheon Type Ia supernovae (SNe Ia), and DES weak lensing and clustering measurements, all multiple-parameter extensions remain consistent with a ΛCDM model. Regardless of cosmological model, the precision on each of the three parameters, Ω Λ , H 0 , and σ 8 , remains at roughly 1%, showing changes of less than 0.6% in the central values between models. In a model that allows for free curvature and a time-evolving equation of state for dark energy, the combined samples produce a constraint Ω K =-0.0022±0.0022. The dark energy constraints lead to w 0 =-0.909±0.081 and w a =$-0.49_{-0.30}^{+0.35}$, corresponding to an equation of state of w p =-1.018±0.032 at a pivot redshift z p =0.29 and a Dark Energy Task Force Figure of Merit of 94. The inverse distance ladder measurement under this model yields H 0 =68.18±0.79 km s -1 Mpc -1 , remaining in tension with several direct determination methods; the BAO data allow Hubble constant estimates that are robust against the assumption of the cosmological model. In addition, the BAO data allow estimates of H 0 that are independent of the CMB data, with similar central values and precision under a ΛCDM model. Our most constraining combination of data gives the upper limit on the sum of neutrino masses at Σm ν <0.115 eV (95% confidence). Finally, we consider the improvements in cosmology constraints over the last decade by comparing our results to a sample representative of the period 2000-2010. We compute the relative gain across the five dimensions spanned by w, Ω k , Σm ν , H 0 , and σ 8 and find that the SDSS BAO and RSD data reduce the total posterior volume by a factor of 40 relative to the previous generation. Finally, adding again the Planck, DES, and Pantheon SN Ia samples leads to an overall contraction in the five-dimensional posterior volume of 3 orders of magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗

Likelihood-informed dimension reduction for nonlinear inverse problems

The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the prior to the posterior may, in many problems, be confined to a relatively low-dimensional subspace of the parameter space. We present a dimension reduction approach that defines and identifies such a subspace, called the 'likelihood-informed subspace' (LIS), by characterizing the relative influences of the prior and the likelihood over the support of the posterior distribution. This identification enables new and more efficient computational methods for Bayesian inference with nonlinear forward models and Gaussian priors. In particular, we approximate the posterior distribution as the product of a lower-dimensional posterior defined on the LIS and the prior distribution marginalized onto the complementary subspace. Markov chain Monte Carlo sampling can then proceed in lower dimensions, with significant gains in computational efficiency. We also introduce a Rao–Blackwellization strategy that de-randomizes Monte Carlo estimates of posterior expectations for additional variance reduction. We demonstrate the efficiency of our methods using two numerical examples: inference of permeability in a groundwater system governed by an elliptic PDE, and an atmospheric remote sensing problem based on Global Ozone Monitoring System (GOMOS) observations.

42 ENGINEERING↗

Hybrid nested sampling algorithm for Bayesian model selection applied to inverse subsurface flow problems

A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Approximate Bayesian computation for forward modeling in cosmology

Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to the posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.

79 ASTRONOMY AND ASTROPHYSICS↗

A Bayesian Approach for Statistical–Physical Bulk Parameterization of Rain Microphysics. Part I: Scheme Description

A novel framework is proposed for the bulk parameterization of rain microphysics: the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS). It is designed to facilitate direct constraint by observations using Bayesian inference. BOSS combines existing process-level microphysical knowledge with flexible process rate formulations and parameters constrained by observations within a Bayesian framework. Furthermore, using a raindrop size distribution (DSD) normalization method that relates DSD moments to one another via generalized power series, generalized multivariate power expressions are derived for the microphysical process rates as functions of a set of prognostic DSD moments. The scheme is flexible and can utilize any number and combination of prognostic moments and any number of terms in the process rate formulations. This means that both uncertainty in parameter values and structural uncertainty associated with the process rate formulations can be investigated systematically, which is not possible using traditional schemes. In this paper, BOSS is compared to two- and three-moment versions of a traditional bulk rain microphysics scheme (denoted as MORR). It is demonstrated that some process formulations in MORR are analytically equivalent to the generalized power expressions in BOSS using one or two terms, while others are not. BOSS is able to replicate the behavior of MORR in idealized one-dimensional rainshaft tests, but with a much more flexible and systematic design. Part II of this study describes the application of BOSS to derive rain microphysical process rates and posterior parameter distributions in Bayesian experiments using Markov chain Monte Carlo sampling constrained by synthetic observations.

58 GEOSCIENCES↗

MFNets: Multifidelity data-driven networks for Bayesian learning and prediction

This paper presents a multifidelity uncertainty quantification framework called MFNets. We seek to address three existing challenges that arise when experimental and simulation data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse heterogeneous data sources arising from simulations with different parameterizations, e.g simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multi-fidelity approaches to corrupted data. MFNets construct a network of latent variables (LVs) to facilitate the fusion of data from an ensemble of sources of varying credibility and cost. These LVs are posited as explanatory variables that provide the source of correlation in the observed data. Furthermore, MFNets provide a way to encode prior physical knowledge to enable efficient estimation of statistics and/or construction of surrogates via conditional independence relations on the LVs. We highlight the utility of our framework with a number of theoretical results which assess the quality of the posterior mean as a frequentist estimator and compare it to standard sampling approaches that use single fidelity, multilevel, and control variate Monte Carlo estimators. We also use the proposed framework to derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models -- to our knowledge the first such derivation. Finally, we demonstrate the ability to work with different uncertain parameters across different models.

97 MATHEMATICS AND COMPUTING↗

Lens Modeling of STRIDES Strongly Lensed Quasars Using Neural Posterior Estimation

Strongly lensed quasars can be used to constrain cosmological parameters through time-delay cosmography. Models of the lens masses are a necessary component of this analysis. To enable time-delay cosmography from a sample of $\mathcal{O}(10^3)$ lenses, which will soon become available from surveys like the Rubin Observatory’s Legacy Survey of Space and Time and the Euclid Wide Survey, we require fast and standardizable modeling techniques. To address this need, we apply neural posterior estimation (NPE) for modeling galaxy-scale strongly lensed quasars from the Strong Lensing Insights into the Dark Energy Survey (STRIDES) sample. NPE brings two advantages: speed and the ability to implicitly marginalize over nuisance parameters. We extend this method by employing sequential NPE to increase precision of mass model posteriors. We then fold individual lens models into a hierarchical Bayesian inference to recover the population distribution of lens mass parameters, accounting for out-of-distribution shift. After verifying our method using simulated analogs of the STRIDES lens sample, we apply our method to 14 Hubble Space Telescope single-filter observations. We find the population mean of the power-law elliptical mass distribution slope, γ lens , to be $\mathcal{M}_γ$ lens = 2.13 ± 0.06. Our result represents the first population-level constraint for these systems. This population-level inference from fully automated modeling is an important stepping stone toward cosmological inference with large samples of strongly lensed quasars.

79 ASTRONOMY AND ASTROPHYSICS↗

Bayesian calibration of terrestrial ecosystem models: A study of advanced Markov chain Monte Carlo methods

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this study, a Differential Evolution Adaptive Metropolis (DREAM) algorithm was used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The DREAM is a multi-chain method and uses differential evolution technique for chain movement, allowing it to be efficiently applied to high-dimensional problems, and can reliably estimate heavy-tailed and multimodal distributions that are difficult for single-chain schemes using a Gaussian proposal distribution. The results were evaluated against the popular Adaptive Metropolis (AM) scheme. DREAM indicated that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identified one mode. The calibration of DREAM resulted in a better model fit and predictive performance compared to the AM. DREAM provides means for a good exploration of the posterior distributions of model parameters. Lastly, it reduces the risk of false convergence to a local optimum and potentially improves the predictive performance of the calibrated model.

54 ENVIRONMENTAL SCIENCES↗

DAmodel: hierarchical Bayesian modelling of DA white dwarfs for spectrophotometric calibration

We use hierarchical Bayesian modelling to calibrate a network of 32 all-sky faint DA white dwarf (DA WD) spectrophotometric standards (⁠16.5 < V , 19.5⁠) alongside three CALSPEC standards, from 912 Å to 32 μm. The framework is the first of its kind to jointly infer photometric zero points and WD parameters (surface gravity log g⁠, effective temperature T eff ⁠, extinction A V ⁠, dust relation parameter R V ) by simultaneously modelling both photometric and spectroscopic data. We model panchromatic Hubble Space Telescope Wide Field Camera 3 (HST/WFC3) UVIS and IR photometry, HST/STIS UV spectroscopy, and ground-based optical spectroscopy to sub-per cent precision. Photometric residuals for the sample are the lowest yet yielding < 0.004 mag RMS on average from the UV to the NIR, achieved by jointly inferring time-dependent changes in system sensitivity and WFC3/IR count-rate nonlinearity. Our GPU-accelerated implementation enables efficient sampling via Hamiltonian Monte Carlo, critical for exploring the high-dimensional posterior space. The hierarchical nature of the model enables population analysis of intrinsic WD and dust parameters. Inferred spectral energy distributions from this model will be essential for calibrating the James Webb Space Telescope as well as next-generation surveys, including Vera Rubin Observatory’s Legacy Survey of Space and Time and the Nancy Grace Roman Space Telescope.

methods: statistical↗

Objective estimates based on experimental data and initial and final knowledge

An extension of the method of Jaynes, whereby least biased probability estimates are obtained, permits such estimates to be made which account for experimental data on hand as well as prior and posterior knowledge. These estimates can be made for both discrete and continuous sample spaces. The method allows a simple interpretation of Laplace's two rules: the principle of insufficient reason and the rule of succession. Several examples are analyzed by way of illustration.

Rosenbaum, B. M.↗

A Bayesian Framework for Reliability Analysis of Spacecraft Deployments

Deployable subsystems are essential to mission success of most spacecraft. These subsystems enable critical functions including power, communications and thermal control. The loss of any of these functions will generally result in loss of the mission. These subsystems and their components often consist of unique designs and applications for which various standardized data sources are not applicable for estimating reliability and for assessing risks. In this study, a two stage sequential Bayesian framework for reliability estimation of spacecraft deployment was developed for this purpose. This process was then applied to the James Webb Space Telescope (JWST) Sunshield subsystem, a unique design intended for thermal control of the Optical Telescope Element. Initially, detailed studies of NASA deployment history, "heritage information", were conducted, extending over 45 years of spacecraft launches. This information was then coupled to a non-informative prior and a binomial likelihood function to create a posterior distribution for deployments of various subsystems uSing Monte Carlo Markov Chain sampling. Select distributions were then coupled to a subsequent analysis, using test data and anomaly occurrences on successive ground test deployments of scale model test articles of JWST hardware, to update the NASA heritage data. This allowed for a realistic prediction for the reliability of the complex Sunshield deployment, with credibility limits, within this two stage Bayesian framework.

Evans, John W.↗

Sequential Monte Carlo for Cut-Bayesian Posterior Computation

We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We prove finite sample concentration bounds for estimators derived from the proposed method along with a linear tempering extension and apply these results to a realistic setting where a computer model is misspecified. We then illustrate the SMC method for inference in a modular chemical reactor example that includes submodels for reaction kinetics, turbulence, mass transfer, and diffusion. The samples obtained are commensurate with a direct-sampling approach that consists of running multiple Markov chains, with computational efficiency gains using the SMC method. Overall, the SMC method presented yields a novel, rigorous approach to computing with cut-Bayesian posterior distributions.

97 MATHEMATICS AND COMPUTING↗

Conservative Estimation of Tail Probabilities from Limited Sample Data

Several sparse-sample uncertainty quantification (UQ) methods are compared for conservative but not overly conservative estimation of small tail probabilities involving responses that lay beyond specified thresholds in the tails of probability distributions. Sixteen very differently shaped distributions (or probability density functions, PDFs) and tail probability magnitudes ranging from 10 -5 to 10 -1 are considered in order for the study to be relevant to a wide range of risk analysis and quantification of margins and uncertainty (QMU) problems. The emphasis of the study is on limited data regimes ranging from N = 2 to 20 samples, reflective of most experimental and some expensive computational situations. Relatively simple sparse-sample UQ methods tested for this regime involve statistical tolerance interval "Equivalent Normal and related "Ensemble of Normals" and "Superdistribution (SD) approaches. (The independently derived SD is effectively equivalent to the Bayesian posterior predictive distribution given the assumptions of the derivation.) The performance of the methods was generally improved for N ≥ 5 samples with a generalized Jackknife resampling technique, which determines a tail probability estimate by averaging estimates from smaller sub-samples. Several quantitative metrics for method conservatism and accuracy of tail probability estimation are used to assess and rank the methods' performance over many random trials for each test PDF and probability magnitude. A variant of Bootstrap resampling was also tried, but did not significantly improve tail probability estimates in most cases. Detailed results are presented from over 100-million tests over the above factors that provide useful granular information on which methods or combination of methods perform best in various areas of the factor space.

97 MATHEMATICS AND COMPUTING↗

TensorBNN: Bayesian inference for neural networks using TensorFlow

We report that TensorBNN is a new package based on TensorFlow that implements Bayesian inference for modern neural network models. The posterior density of neural network model parameters is represented as a point cloud sampled using Hamiltonian Monte Carlo. The TensorBNN package leverages TensorFlow's architecture and its ability to use modern graphics processing units in both the training and prediction stages.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗