Results for “bayesian MARS”

DOE OSTI2024

Generalized Bayesian MARS: Tools for Stochastic Computer Model Emulation

The multivariate adaptive regression spline (MARS) approach of Friedman and its Bayesian counterpart are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors limits the usefulness of MARS, and many popular alternatives, when dealing with stochastic computer models. Here, we propose a generalized Bayesian MARS (GBMARS) framework which admits the broad class of generalized hyperbolic distributions as the induced likelihood function. This allows us to develop tools for the emulation of stochastic simulators which are parsimonious, scalable, and interpretable and require minimal tuning, while providing powerful predictive and uncertainty quantification capabilities. GBMARS is capable of robust regression with t distributions, quantile regression with asymmetric Laplace distributions, and a general form of “Normal-Wald” regression in which the shape of the error distribution and the structure of the mean function are learned simultaneously. We demonstrate the effectiveness of GBMARS on various stochastic computer models, and we show that it compares favorably to several popular alternatives.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Discovering Active Subspaces for High-Dimensional Computer Models

Dimension reduction techniques have long been an important topic in statistics, and active subspaces (AS) have received much attention this past decade in the computer experiments literature. The most common approach towards estimating the AS is to use Monte Carlo with numerical gradient evaluation. While sensible in some settings, this approach has obvious drawbacks. Recent research has demonstrated that active subspace calculations can be obtained in closed form, conditional on a Gaussian process (GP) surrogate, which can be limiting in high-dimensional settings for computational reasons. In this paper, we produce the relevant calculations for a more general case when the model of interest is a linear combination of tensor products. These general equations can be applied to the GP, recovering previous results as a special case, or applied to the models constructed by other regression techniques including multivariate adaptive regression splines (MARS). Furthermore, using a MARS surrogate has many advantages including improved scaling, better estimation of active subspaces in high dimensions and the ability to handle a large number of prior distributions in closed form. In one real-world example, we obtain the active subspace of a radiation-transport code with 240 inputs and 9,372 model runs in under half an hour.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

An efficient Bayesian inversion of a geothermal prospect using a multivariate adaptive regression spline method

In this study, an efficient Bayesian framework equipped with a multivariate adaptive regression spline (MARS) technique is developed to alleviate computational burdens encountered in a conventional Bayesian inversion of a geothermal prospect. Fast MARS models are developed from training dataset generated by CPU-intensive hydrothermal models and used as surrogate of high-fidelity physical models in Markov Chain Monte Carlo (MCMC) sampling. This Bayesian inference with MARS-enabled MCMC method is used to reduce prior estimates of uncertainty in structural or characteristic hydrothermal flow parameters of the model to posterior distributions. A geothermal prospect near Superstition Mountain in Imperial County of California in USA is used to illustrate the proposed framework and demonstrate the computational efficiency of MARS-based Bayesian inversion. The developed MARS models are also used to efficiently drive calculation of Sobol’ total sensitivity indices. Furthermore, only top sensitive parameters are included in Bayesian inference to further improve the computational efficiency of inversion. Sensitivity analysis also confirms that water circulation through high permeable structures, rather than heat conduction through impermeable granite, is the primary heat transfer method. The presented framework is demonstrated an efficient tool to update knowledge of geothermal prospects by inversing field data. Although only thermal data is used in this study, other type of data, such as flow and transport observations, can be jointly used in this method for underground hydrocarbon reservoirs.

15 GEOTHERMAL ENERGY↗

DOE OSTI2021

An initial exploration of Bayesian model calibration for estimating the composition of rocks and soils on Mars

The Mars Curiosity rover carries an instrument, ChemCam, designed to measure the composition of surface rocks and soil using laser-induced breakdown spectroscopy (LIBS). The measured spectra from this instrument must be analyzed to identify the component elements in the target sample, as well as their relative proportions. This process, which we call disaggregation, is complicated by so-called matrix effects, which describe nonlinear changes in the relative heights of emission lines as an unknown function of composition due to atomic interactions within the LIBS plasma. In this work, we explore the use of the plasma physics code ATOMIC, developed at Los Alamos National Laboratory, for the disaggregation task. ATOMIC has recently been used to model LIBS spectra and can robustly reproduce matrix effects from first principles. The ability of ATOMIC to predict LIBS spectra presents an exciting opportunity to perform disaggregation in a manner not yet tried in the LIBS community, namely via Bayesian model calibration. However, using it directly to solve our inverse problem is computationally intractable due to the large parameter space and the computation time required to produce a single output. Therefore, we also explore the use of emulators as a fast solution for this analysis. We discuss a proof of concept Gaussian process emulator for disaggregating two-element compounds of sodium and copper. The training and test datasets were simulated with ATOMIC using a Latin hypercube design. After testing the performance of the emulator, we successfully recover the composition of 25 test spectra with Bayesian model calibration.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Bayesian Framework for Bioburden Density Estimation in Planetary Protection

To comply with the international planetary protection policy set forth by the Committee on Space Research and NASA Agency level requirements, spacecraft destined to biologically sensitive planetary bodies have to minimize terrestrial biological contamination. Analysis, testing and inspection are the standard forward verification activities that are used to demonstrate compliance with the biological contamination requirements. For testing of spacecraft surface areas, a swab or wipe sample is collected from surfaces prior to last access and subsequently processed in the lab using NASA Approved Planetary Protection Methods for Culture Based Assays. Raw data resulting from this assay is then statistically treated employing a mathematical paradigm stemming from the 1970’s Viking Lander Project to generate the bioburden density and total microbial bioburden present. This standard approach arbitrarily accounts for error and provides an upper conservative bound as it reports the maximum number of spores estimated to be present on flight hardware surfaces. A bioburden density estimate factors in the following variables: the observed bioburden count, representative volume processed, sampling efficiencies. Notably, to account for error in the approach, a 0 observed count is arbitrarily changed to a count of 1 for each hardware grouping. The data generated by spacecraft bioburden verification campaigns in the past have resulted in <80% of wipes and <90% of swabs containing a bioburden count of 0. As such, having a robust and well documented statistical approach for dealing with the probability of low incident rates is necessary to be able to estimate spacecraft bioburden. Being able to statistically describe the bioburden distribution and associated confidence level is a gamechanger for the development of bioburden allocations during mission design and will allow for tighter management of risk throughout spacecraft build. Thus, Empirical Bayes statistical approach was evaluated to estimate the microbial bioburden on spacecraft to mitigate the aforementioned mathematical concerns and provide a probabilistic bioburden distribution of the flight hardware surface. For application of this approach to performing bioburden calculations, a range of non-informative prior assumptions on hardware surfaces are explored for Bayesian analyses while informative priors using posterior distributions from prior assays are utilized for Empirical Bayes analyses. Several non-informative priors are currently under investigation to assess fitness including use of these priors to serve as a foundation to build off of NASA specification values or a basis of risk to account for unknowns during the integration and testing process. Informative priors under consideration are generated using sampled bioburden values from hardware originating within like processing environments (e.g. vendor cleaning process or similar assembly process), temporal spacecraft status events as a prediction for hardware cleanliness of future samples, and heritage system bioburden actuals to predict allocation for subsequent missions. Informative priors and probabilistic bioburden distributions are then validated using data sets from the Mars Exploration Rover, Mars Science Laboratory, and InSight missions. Using Empirical Bayes approach to generate a probabilistic bioburden distribution as demonstrated through mission use cases provides a valid approach for use in the end-to-end requirements verification process.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Multiclass Classification Using Bayesian Multivariate Adaptive Regression Splines

We present a new Bayesian model for the problem of multiclass classification. In this model, the probabilities of class membership of a given observation are determined by the mean of a latent Gaussian distribution. The mean functions of this latent distribution consist of combinations of highly flexible basis functions of the inputs: multivariate adaptive regression splines (MARS), first developed for multiple regression. We use reversible jump Markov chain Monte Carlo to make inference on the classification model, including the number of basis functions. We compare the probabilistic classification performance of our proposed approach to existing methods on simulated and benchmark data, and compare uncertainty estimates on simulated data. Our proposed method compares favorably with existing Bayesian and frequentist multiclass classification methods in out-of-sample probabilistic classification, and uncertainty estimation of these probabilistic classifications. We examine the fit of the proposed method to a data set of hurricane storm surge levels near Delaware Bay, US, and conclude that sea level rise is a key contributor to damage delivered by storm surge.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Application of machine learning and artificial intelligence to extend EFIT equilibrium reconstruction

Recent progress in the application of machine learning (ML)/artificial intelligence (AI) algorithms to improve the Equilibrium Fitting (EFIT) code equilibrium reconstruction for fusion data analysis applications is presented. A device-independent portable core equilibrium solver capable of computing or reconstructing equilibrium for different tokamaks has been created to facilitate adaptation of ML/AI algorithms. A large EFIT database comprising of DIII-D magnetic, motional Stark effect, and kinetic reconstruction data has been generated for developments of EFIT model-order-reduction (MOR) surrogate models to reconstruct approximate equilibrium solutions. Furthermore, a neural-network MOR surrogate model has been successfully trained and tested using the magnetically reconstructed datasets with encouraging results. Other progress includes developments of a Gaussian process Bayesian framework that can adapt its many hyperparameters to improve processing of experimental input data and a 3D perturbed equilibrium database from toroidal full magnetohydrodynamic linear response modeling using the Magnetohydrodynamic Resistive Spectrum - Feedback (MARS-F) code for developments of 3D-MOR surrogate models.

Gaussian process↗

DOE OSTI2020

Predicting Biological Cleanliness: An Empirical Bayes Approach for Spacecraft Bioburden Accounting

To comply with the international planetary protection policy set forth by the Committee on Space Research and NASA Agency level requirements, spacecraft destined to biologically sensitive planetary bodies have to minimize terrestrial biological contamination. Analysis, testing and inspection are the standard forward verification activities that are used to demonstrate compliance with the biological contamination requirements. For testing of spacecraft surface areas, a swab or wipe sample is collected from surfaces prior to last access and subsequently processed in the lab using NASA Approved Planetary Protection Methods for Culture Based Assays. Raw data resulting from this assay is then statistically treated employing a mathematical paradigm stemming from the 1970’s Viking Lander Project to generate the bioburden density and total microbial bioburden present. This standard approach arbitrarily accounts for error and provides an upper conservative bound as it reports the maximum number of spores estimated to be present on flight hardware surfaces. A bioburden density estimate factors in the following variables: the observed bioburden count, representative volume processed, sampling efficiencies. Notably, to account for error in the approach, a 0 observed count is arbitrarily changed to a count of 1 for each hardware grouping. The data generated by spacecraft bioburden verification campaigns in the past have resulted in <80% of wipes and <90% of swabs containing a bioburden count of 0. As such, having a robust and well documented statistical approach for dealing with the probability of low incident rates is necessary to be able to estimate spacecraft bioburden. Being able to statistically describe the bioburden distribution and associated confidence level is a gamechanger for the development of bioburden allocations during mission design and will allow for tighter management of risk throughout spacecraft build. Thus, Empirical Bayes statistical approach was evaluated to estimate the microbial bioburden on spacecraft to mitigate the aforementioned mathematical concerns and provide a probabilistic bioburden distribution of the flight hardware surface. For application of this approach to performing bioburden calculations, a range of non-informative prior assumptions on hardware surfaces are explored for Bayesian analyses while informative priors using posterior distributions from prior assays are utilized for Empirical Bayes analyses. Several non-informative priors are currently under investigation to assess fitness including use of these priors to serve as a foundation to build off of NASA specification values or a basis of risk to account for unknowns during the integration and testing process. Informative priors under consideration are generated using sampled bioburden values from hardware originating within like processing environments (e.g. vendor cleaning process or similar assembly process), temporal spacecraft status events as a prediction for hardware cleanliness of future samples, and heritage system bioburden actuals to predict allocation for subsequent missions. Informative priors and probabilistic bioburden distributions are then validated using data sets from the Mars Exploration Rover, Mars Science Laboratory, and InSight missions. Using Empirical Bayes approach to generate a probabilistic bioburden distribution as demonstrated through mission use cases provides a valid approach for use in the end-to-end requirements verification process.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Recent Progress on the Stochastic Objective Decision Aide (SODA) Application

Idaho State University, in collaboration with Idaho National Laboratory, is engaged in development of a simple to use software application that utilizes stochastic techniques for the calculation of radiation doses associated with hypothetical radioactive material releases. This work is being performed through a grant from the U.S. Department of Energy (DOE) Nuclear Safety Research and Development (NSR and D) Program. Initial progress on the application was reported previously. Recent additions to the application are reported here. The Stochastic Objective Decision Aide (SODA) provides an easy to use software application to help decision makers support their judgment about the need or lack of need for safety structures, systems, and components. SODA is not intended to replace traditional design basis accident dose calculation methodology, nor is it intended to replace existing software used to perform formal dose consequence calculations. Rather, SODA is intended to supplement information obtained from existing codes to give a decision maker more information about an accident scenario. SODA also provides a simple method to perform parametric or sensitivity studies on individual input parameters. Non-reactor nuclear facilities operated under the approval authority of the US DOE use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge dose evaluation guidelines. Unmitigated events that sufficiently challenge dose evaluation guidelines merit the selection of safety structures, systems, or components (SSCs) to prevent or mitigate the hazard. Dose consequence calculations traditionally involve use of the 'five-factor' formula: ST = MAR.DR.ARF.RF.LPF where ST is the source term (Bq), MAR is the total available material-at-risk (Bq), DR is the damage ratio (no units), ARF is the airborne release fraction (no units), RF is the respirable fraction (no units), and LPF is the leak path factor (no units). Potential radiation doses are then calculated using: CED = χ/Q.BR.ST.DCF (2) where CED is the committed effective dose (Sv), χ/Q is the plume dispersion (s/m{sup 3}), BR is the breathing rate (m{sup 3}/s), ST is the source term (Bq), and DCF is the dose conversion factor (Sv/Bq). Conservative single value input parameters are typically used to represent ARF, RF, LPF and BR. The traditional methodology, while conservative, can lead to skewed conclusions in the balance between cost and risk reduction resulting in over engineered systems with greater design, construction and operating costs. Rather than using a bounding single point value for each parameter in the dose consequence calculation, SODA uses distributions for some or all of the parameters. Each input parameter distribution is stochastically sampled and the resulting dose consequence calculation is repeated many times to develop a dose consequence distribution. The resulting distribution provides more information for the decision maker to rely upon when determining the need for safety SSCs. The SODA application was developed using MATLAB and it incorporates the use of Monte Carlo techniques as well as a graphical user interface (GUI). The application includes user selection of the governing distribution for parameters such as the MAR, DR, ARF, RF, LPF,χ/Q, BR, and DCF. While MATLAB was used for the development work, the application is distributed as a self-contained executable program. Features of the application include pull down menus with available distributions for the various parameters. The user has the option to plot the input parameter distribution that results from the random sampling process. The resulting dose consequence distribution is automatically analyzed to determine its similarity to well know distributions. This was done using the Bayesian Information Criterion method. If the resulting distribution is sufficiently similar to a well-known distribution, the application provides information about the distributions such as the mean value and other parameters. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

The DESI PRObabilistic Value-added Bright Galaxy Survey (PROVABGS) Mock Challenge

The PRObabilistic Value-added Bright Galaxy Survey (PROVABGS) catalog will provide measurements of galaxy properties, such as stellar mass ($M*$), star formation rate (SFR), stellar metallicity (Z), and stellar age ($t_{age}$), for >10 million galaxies of the Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Survey. Full posterior distributions of the galaxy properties will be inferred using state-of-the-art Bayesian spectral energy distribution (SED) modeling of DESI spectroscopy and Legacy Surveys photometry. In this work, we present the SED model, the neural emulator for the model, and the Bayesian inference framework of PROVABGS. Furthermore, we apply the PROVABGS SED modeling on realistic synthetic DESI spectra and photometry, constructed using the L-Galaxies semi-analytic model. We compare the inferred galaxy properties to the true values of the simulation using a hierarchical Bayesian framework to quantify accuracy and precision. Overall, we accurately infer the true $M*$, SFR, Z, and $t_{age}$ of the simulated galaxies. However, the priors on galaxy properties induced by the SED model have a significant impact on the posteriors, which we characterize in detail. This work also demonstrates that a joint analysis of spectra and photometry significantly improves the constraints on galaxy properties over photometry alone and is necessary to mitigate the impact of the priors. With the methodology presented and validated in this work, PROVABGS will maximize information extracted from DESI observations and extend current galaxy studies to new regimes and unlock cutting-edge probabilistic analyses. https://github.com/changhoonhahn/provabgs/

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

The Dark Energy Survey supernova program: a reanalysis of cosmology results and evidence for evolving dark energy with an updated Type Ia supernova calibration

We present improved cosmological constraints from a re-analysis of the Dark Energy Survey (DES) 5-year sample of Type Ia supernovae (DES-SN5YR). This re-analysis includes an improved photometric cross-calibration, recent white dwarf observations to cross-calibrate between DES and low-redshift surveys, retraining the salt3 light-curve model and fixing a numerical approximation in the host-galaxy colour law. Our fully recalibrated sample, which we call DES-Dovekie, comprises ~1600 likely Type Ia SNe from DES and ~200 low-redshift SNe from other surveys. With DES-Dovekie, we obtain Ω m = 0.330 ± 0.015 in flat Lambda-cold dark matter (⁠ΛCDM) which changes Ω m by –0.022 compared to DES-SN5YR. Combining DES-Dovekie with cosmic microwave background data from Planck, Atacama Cosmology Telescope, and South Pole Telescope and the DESI DR2 measurements in a flat CDM cosmology, we find ω 0 = –0.803 ± 0.054 and ω a = –0.72 ± 0.21⁠. Our results hold a significance of 3.2σ, reduced from 4.2σ for DES-SN5YR, to reject the null hypothesis that the data are compatible with the cosmological constant. This significance is equivalent to a Bayesian model preference odds of approximately 5:1 in favour of the flat ω 0 ω a CDM model. Using generally accepted thresholds for model preference, our updated data exhibits only a weak preference for evolving dark energy.

dark energy↗

DOE OSTI2024

Evaluating cosmological biases using photometric redshifts for Type Ia Supernova cosmology with the Dark Energy Survey Supernova Program

Cosmological analyses with Type Ia Supernovae (SNe Ia) have traditionally been reliant on spectroscopy for both classifying the type of supernova and obtaining reliable redshifts to measure the distance–redshift relation. While obtaining a host-galaxy spectroscopic redshift for most SNe is feasible for small-area transient surveys, it will be too resource intensive for upcoming large-area surveys such as the Vera Rubin Observatory Legacy Survey of Space and Time, which will observe on the order of millions of SNe. Here, we use data from the Dark Energy Survey (DES) to address this problem with photometric redshifts (photo-z) inferred directly from the SN light curve in combination with Gaussian and full p(z) priors from host-galaxy photo-z estimates. Using the DES 5-yr photometrically classified SN sample, we consider several photo-z algorithms as host-galaxy photo-z priors, including the Self-Organizing Map redshifts (SOMPZ), Bayesian Photometric Redshifts (BPZ), and Directional-Neighbourhood Fitting (DNF) redshift estimates employed in the DES 3 × 2 point analyses. With detailed catalogue-level simulations of the DES 5-yr sample, we find that the simulated w can be recovered within ±0.02 when using SN+SOMPZ or DNF prior photo-z, smaller than the average statistical uncertainty for these samples of 0.03. With data, we obtain biases in w consistent with simulations within ~1σ for three of the five photo-z variants. We further evaluate how photo-z systematics interplay with photometric classification and find classification introduces a subdominant systematic component. This work lays the foundation for next-generation fully photometric SNe Ia cosmological analyses.

(cosmology:) dark energy↗