Search NASA⌕ Search

SEARCH · Search NASA

Results for “Posterior sample”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

Mixture density network estimation of continuous variable maximum likelihood using discrete training samples

Abstract Mixture density networks (MDNs) can be used to generate posterior density functions of model parameters $$\varvec{\theta }$$ θ given a set of observables $${\mathbf {x}}$$ x . In some applications, training data are available only for discrete values of a continuous parameter $$\varvec{\theta }$$ θ . In such situations, a number of performance-limiting issues arise which can result in biased estimates. We demonstrate the usage of MDNs for parameter estimation, discuss the origins of the biases, and propose a corrective method for each issue.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. In this work, this flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.

97 MATHEMATICS AND COMPUTING↗

Phosphorus speciation analysis of fatty-acid-based feedstocks and fast pyrolysis biocrudes via gel permeation chromatography inductively coupled plasma high-resolution mass spectrometry

Renewable feedstocks, such as lignocelulosic fast pyrolysis oils and both vegetable oil and animal fats, are becoming a viable alternative to petroleum for producing high-quality renewable transportation fuels. However, the presence of phosphorus-containing compounds, mainly from phospholipids, in these renewable feedstocks is known to poison and deactivate hydrotreating catalysts during fuel production. In this work, gel permeation chromatography (GPC) combined with inductively coupled plasma high-resolution mass spectrometry (ICP-HRMS) was used to analyze feedstocks including unprocessed soybean oil, animal fat, and pyrolysis oils from red oak and milorganite to identify phosphorus species. The results have shown the presence of a wide range of different phosphorous compounds among all the samples analysed in this work. The GPC-ICP-HRMS analyses of a vegetable oil and two animal fats have shown different fingerprints based on the molecular weight of each of the samples, highlighting the structural differences among their corresponding phosphorus-containing compounds. While the presence of low-molecular-weight species, such as phospholipids, was expected, several high-molecular-weight species (MW > 10 000 Da) have been found, suggesting that high-molecular-weight micelles or liposomes might have been formed due to the high concentration of phospholipids in these samples. Results obtained through the hydroxylation of a mix of phospholipids (asolectin) and its posterior GPC-ICP-HRMS agree with this hypothesis. With respect to the lignocellulosic catalytic fast pyrolysis oil samples, the GPC-ICP-HRMS results obtained suggest that either aggregation or polymerization reactions might have occurred during the pyrolysis process, yielding phosphorus-containing compounds with an approximate molecular weight above 91 000 kDa. In addition, an aggregation phenomenom has been observed for those phosphorus species present within the fast pyrolysis oils after being stored for 3 months, especially for those pyrolysis oils contaning pre-processed feedstocks, such as milorganite.

09 BIOMASS FUELS↗

Rigorous Data Fusion for Computationally Expensive Simulations

This manuscript comprises the final report for the 1-year, FY19 LDRD project "Rigorous Data Fusion for Computationally Expensive Simulations," wherein an alternative approach to Bayesian calibration was developed based a new sampling technique called VoroSpokes. Vorospokes is a novel quadrature and sampling framework defined with respect to Voronoi tessellations of bounded domains in $R^d$ developed within this project. In this work, we first establish local quadrature and sampling results on convex polytopes using randomly directed rays, or spokes, to approximate the quantities of interest for a specified target function. A theoretical justification for both procedures is provided along with empirical results demonstrating the unbiased convergence in the resulting estimates/samples. The local quadrature and sampling procedures are then extended to global procedures defined on more general domains by applying the local results to the cells of a Voronoi tessellation covering the domain in consideration. We then demonstrate how the proposed global sampling procedure can be used to define a natural framework for adaptively constructing Voronoi Piecewise Surrogate (VPS) approximations based on local error estimates. Finally, we show that the adaptive VPS procedure can be used to form a surrogate model approximation to a specified, potentially unnormalized, density function, and that the global sampling procedure can be used to efficiently draw independent samples from the surrogate density in parallel. The performance of the resulting VoroSpokes sampling framework is assessed on a collection of Bayesian inference problems and is shown to provide highly accurate posterior predictions which align with the results obtained using traditional methods such as Gibbs sampling and random-walk Markov Chain Monte Carlo (MCMC). Importantly, the proposed framework provides a foundation for performing Bayesian inference tasks which is entirely independent from the theory of Markov chains.

97 MATHEMATICS AND COMPUTING↗

Systems and methods for fast detection of elephant flows in network traffic

In a system for efficiently detecting large/elephant flows in a network, the rate at which the received packets are sampled is adjusted according to a top flow detection likelihood computed for a cache of flows identified in the arriving network traffic. After observing packets sampled from the network, Dirichlet-Categorical inference is employed to calculate a posterior distribution that captures uncertainty about the sizes of each flow, yielding a top flow detection likelihood. The posterior distribution is used to find the most likely subset of elephant flows. The technique rapidly converges to the optimal sampling rate at a speed O(1/n), where n is the number of packet samples received, and the only hyperparameter required is the targeted detection likelihood.

Gudibanda, Aditya↗

Effect of scanline orientation on ventricular flow propagation: assessment using high frame-rate color Doppler echocardiography

Color M-mode echocardiography has recently been utilized to describe diastolic flow propagation velocity (Vp) in the left ventricle. While increasing temporal resolution from 15 to 200 Hz, this M-mode technique requires the user to select a single scanline, potentially limiting quantification of Vp due to the complex three-dimensional inflow pattern. We previously performed computational fluid dynamics simulations to demonstrate the insignificance of the scanline orientation, however geometric complexity was limited. The purpose of this study was to utilize high frame-rate 2D color Doppler images to investigate the importance of scanline selection in patients for the quantification of Vp. 2D color Doppler images were digitally acquired at 50 frames/s in 6 subjects from the apical 4-chamber window (System 5, GE/Vingmed, Milwaukee, WI). Vp was determined for a set of scanlines positioned through 5 locations across the mitral annulus (from the anterior to posterior mitral annulus). An analysis of variance was performed to examine the differences in Vp as a function of scanline position. Vp was not effected by scanline position in sampled locations from the center of the mitral valve towards the posterior annulus. Although not statistically significant, there was a trend to slower propagation velocities on the anterior side of the valve (60.8 +/- 16.7 vs. 54.4 +/- 13.6 cm/s). This study clinically validates our previous numerical experiment showing that Vp is insensitive to small perturbations of the scanline through the mitral valve. However, further investigation is necessary to examine the impact of ventricular geometry in pathologies including dilated cardiomyopathy.

Non-NASA Center↗

BEYONDPLANCK II. CMB mapmaking through Gibbs sampling

We present a Gibbs sampling solution to the mapmaking problem for cosmic microwave background (CMB) measurements that builds on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps: noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods and it allows us, for the first time, to bring the destriping baseline length to a single sample. Here, we applied the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them in with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we are able to compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without the need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of the total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction. This methodology thus forms the conceptual basis for the mapmaking algorithm employed in the BEYONDPLANCK framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.

79 ASTRONOMY AND ASTROPHYSICS↗

Bayesian differential programming for robust systems identification under uncertainty

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

Science & Technology - Other Topics↗

SU-F-J-102: Lower Esophagus Margin Implications Based On Rapid Computational Algorithm for SBRT

Purpose: To quantify inter-fraction esophagus-variation. Methods: Computed tomography and daily on-treatment 0.3-T MRI data sets for 7 patients were analyzed using a novel Matlab-based (Mathworks, Natick, MA) rapid computational method. Rigid registration was performed from the cricoid to the gastro-esophageal junction. CT and MR-based contours were compared at slice intervals of 3mm. Variation was quantified by “expansion,” defined as additional length in any radial direction from CT contour to MR contour. Expansion computations were performed with 360° of freedom in each axial slice. We partitioned expansions into left anterior, right anterior, right posterior, and left posterior quadrants (LA, RA, RP, and LP, respectively). Sample means were compared by analysis of variance (ANOVA) and Fisher’s Protected Least Significant Difference test. Results: Fifteen fractions and 1121 axial slices from 7 patients undergoing SBRT for primary lung cancer (3) and metastatic lung disease (4) were analyzed, generating 41,970 measurements. Mean LA, RA, RP, and LP expansions were 4.30±0.05 mm, 3.71±0.05mm, 3.17±0.07, and 3.98±0.06mm, respectively. 50.13% of all axial slices showed variation > 5 mm in one or more directions. Variation was greatest in lower esophagus with mean LA, RA, RP, and LP expansion (5.98±0.09 mm, 4.59±0.09 mm, 4.04±0.16 mm, and 5.41±0.16 mm, respectively). The difference was significant compared to mid and upper esophagus (p<.0001). The 95th percentiles of expansion for LA, RA, RP, LP were 13.36 mm, 9.97 mm, 11.29 mm, and 12.19 mm, respectively. Conclusion: Analysis of on-treatment MR imaging of the lower esophagus during thoracic SBRT suggests margin expansions of 13.36 mm LA, 9.97 mm RA, 11.29 mm RP, 12.19 mm LP would account for 95% of measurements. Our novel algorithm for rapid assessment of margin expansion for critical structures with 360° of freedom in each axial slice enables continuously adaptive patient-specific margins which may reduce overlap with high-dose regions.

60 APPLIED LIFE SCIENCES↗

A fast particle-based approach for calibrating a 3-D model of the Antarctic ice sheet

We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases. Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea level rise in 2300 increases from 6.5 m to 13.1 m when we increase the number of calibrated parameters from three to 11. With previous calibration methods, it would be challenging to go beyond five parameters. Here, this work provides an important next step toward improving the uncertainty quantification of complex, computationally intensive and decision-relevant models.

54 ENVIRONMENTAL SCIENCES↗

PROVABGS: The Probabilistic Stellar Mass Function of the BGS One-percent Survey

We present the probabilistic stellar mass function (pSMF) of galaxies in the DESI Bright Galaxy Survey (BGS), observed during the One-percent Survey. The One-percent Survey was one of DESI's survey validation programs conducted from 2021 April to May, before the start of the main survey. It used the same target selection and similar observing strategy as the main survey and successfully observed the spectra and redshifts of 143,017 galaxies in the r < 19.5 magnitude-limited BGS Bright sample and 95,499 galaxies in the fainter surface-brightness- and color-selected BGS Faint sample over z < 0.6. We derive pSMFs from posteriors of stellar mass, M*, inferred from DESI photometry and spectroscopy using the Hahn et al. PRObabilistic Value-Added BGS (PROVABGS) Bayesian spectral energy distribution modeling framework. We use a hierarchical population inference framework that statistically and rigorously propagates the M* uncertainties. Furthermore, we include correction weights that account for the selection effects and incompleteness of the BGS observations. We present the redshift evolution of the pSMF in BGS, as well as the pSMFs of star-forming and quiescent galaxies classified using average specific star formation rates from PROVABGS. Overall, the pSMFs show good agreement with previous stellar mass function measurements in the literature. Our pSMFs showcase the potential and statistical power of BGS, which in its main survey will observe >100 × more galaxies. Moreover, we present the statistical framework for subsequent population statistics measurements using BGS, which will characterize the global galaxy population and scaling relations at low redshifts with unprecedented precision.

79 ASTRONOMY AND ASTROPHYSICS↗

Invertible neural networks for E3SM land model calibration and simulation

We apply an invertible neural network (INN) for E3SM land model calibration and simulation with eight parameters at the Missouri Ozark AmeriFlux forest site. INN provides bijective (two-way) mappings between inputs and outputs, thus it can solve probabilistic inverse problems and forward approximations simultaneously. We demonstrate INN's inverse and forward capability in both synthetic and real-data applications. Results indicate that INN produces accurate parameter posterior distributions similar to Markov Chain Monte Carlo sampling and it generates model outputs close to the forward model simulations. Additionally, both the inverse and forward evaluations in INN are computationally efficient which allows for rapid integration of observations for parameter estimation and fast model predictions.

Lu, Dan↗

Deep Active Learning for Solvability Prediction in Power Systems

Traditional methods for solvability region analysis can only have inner approximations with inconclusive conservatism and handle limited types of power flow models. In this letter, we propose a deep active learning framework for solvability prediction in power systems. Compared with passive learning where the training is performed after all instances are labeled, active learning selects most informative instances to be labeled and therefore significantly reduces the size of the labeled dataset for training. In the active learning framework, the acquisition functions, which correspond to different sampling strategies, are defined in terms of the on-the-fly posterior probability from the classifier. First, the IEEE 39-bus system is employed to validate the proposed framework, where a two-dimensional case is illustrated to visualize the effectiveness of the sampling method followed by the high-dimensional numerical experiments. Then, the Northeast Power Coordinating Council (NPCC) 140-bus system is used to validate the performance on large-scale power systems.

42 ENGINEERING↗

A technique for extracting blood samples from mice in fire toxicity tests

The extraction of adequate blood samples from moribund and dead mice has been a problem because of the small quantity of blood in each animal and the short time available between the animals' death and coagulation of the blood. These difficulties are particularly critical in fire toxicity tests because removal of the test animals while observing proper safety precautions for personnel is time-consuming. Techniques for extracting blood samples from mice were evaluated, and a technique was developed to obtain up to 0.8 ml of blood from a single mouse after death. The technique involves rapid exposure and cutting of the posterior vena cava and accumulation of blood in the peritoneal space. Blood samples of 0.5 ml or more from individual mice have been consistently obtained as much as 16 minutes after apparent death. Results of carboxyhemoglobin analyses of blood appeared reproducible and consistent with carbon monoxide concentrations in the exposure chamber.

Bucci, T. J.↗

The redshift distribution of cosmological samples: a forward modeling approach

Determining the redshift distribution n ( z ) of galaxy samples is essential for several cosmological probes including weak lensing. For imaging surveys, this is usually done using photometric redshifts estimated on an object-by-object basis. We present a new approach for directly measuring the global n ( z ) of cosmological galaxy samples, including uncertainties, using forward modeling. Our method relies on image simulations produced using \textsc(UFig) (Ultra Fast Image Generator) and on ABC (Approximate Bayesian Computation) within the MCCL (Monte-Carlo Control Loops) framework. The galaxy population is modeled using parametric forms for the luminosity functions, spectral energy distributions, sizes and radial profiles of both blue and red galaxies. We apply exactly the same analysis to the real data and to the simulated images, which also include instrumental and observational effects. By adjusting the parameters of the simulations, we derive a set of acceptable models that are statistically consistent with the data. We then apply the same cuts to the simulations that were used to construct the target galaxy sample in the real data. The redshifts of the galaxies in the resulting simulated samples yield a set of n ( z ) distributions for the acceptable models. We demonstrate the method by determining n ( z ) for a cosmic shear like galaxy sample from the 4-band Subaru Suprime-Cam data in the COSMOS field. We also complement this imaging data with a spectroscopic calibration sample from the VVDS survey. We compare our resulting posterior n ( z ) distributions to the one derived from photometric redshifts estimated using 36 photometric bands in COSMOS and find good agreement. This offers good prospects for applying our approach to current and future large imaging surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Stan : A Probabilistic Programming Language

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.

97 MATHEMATICS AND COMPUTING↗

A Scalable Gradient Free Method for Bayesian Experimental Design with Implicit Models

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Zhang, Jiaxin↗