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At least 631 records · Page 35

Using PyBioNetFit to leverage qualitative and quantitative data in biological model parameterization and uncertainty quantification

Data generated in studies of cellular regulatory systems are often qualitative. For example, measurements of signaling readouts in the presence and absence of mutations may reveal a rank ordering of responses across conditions but not the precise extents of mutation-induced differences. Qualitative data are often ignored by mathematical modelers or are considered in an ad hoc manner, as in the study of Kocieniewski and Lipniacki (2013) [Phys Biol 10: 035006], which was focused on the roles of MEK isoforms in ERK activation. In this earlier study, model parameter values were tuned manually to obtain consistency with a combination of qualitative and quantitative data. This approach is not reproducible, nor does it provide insights into parametric or prediction uncertainties. Here, starting from the same data and the same ordinary differential equation (ODE) model structure, we generate formalized statements of qualitative observations, making these observations more reusable, and we improve the model parameterization procedure by applying a systematic and automated approach enabled by the software package PyBioNetFit. We also demonstrate uncertainty quantification (UQ), which was absent in the original study. Our results show that PyBioNetFit enables qualitative data to be leveraged, together with quantitative data, in parameterization of systems biology models and facilitates UQ. These capabilities are important for reliable estimation of model parameters and model analyses in studies of cellular regulatory systems and reproducibility.

59 BASIC BIOLOGICAL SCIENCES↗

GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling

We present GIGA-Lens: a gradient-informed, GPU-accelerated Bayesian framework for modeling strong gravitational lensing systems, implemented in TensorFlow and JAX. The three components, optimization using multistart gradient descent, posterior covariance estimation with variational inference, and sampling via Hamiltonian Monte Carlo, all take advantage of gradient information through automatic differentiation and massive parallelization on graphics processing units (GPUs). We test our pipeline on a large set of simulated systems and demonstrate in detail its high level of performance. The average time to model a single system on four Nvidia A100 GPUs is 105 s. The robustness, speed, and scalability offered by this framework make it possible to model the large number of strong lenses found in current surveys and present a very promising prospect for the modeling of ${ \mathcal O }({10}^{5})$ lensing systems expected to be discovered in the era of the Vera C. Rubin Observatory, Euclid, and the Nancy Grace Roman Space Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

Calibrating Bayesian generative machine learning for Bayesiamplification

Recently, combinations of generative and Bayesian deep learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated distribution originating from limited training statistics. The interpretation of a distribution-wide uncertainty however remains ill-defined. We show a clear scheme for quantifying the calibration of Bayesian generative machine learning models. For a Continuous Normalizing Flow applied to a low-dimensional toy example, we evaluate the calibration of Bayesian uncertainties from either a mean-field Gaussian weight posterior, or Monte Carlo sampling network weights, to gauge their behaviour on unsteady distribution edges. Well calibrated uncertainties can then be used to roughly estimate the number of uncorrelated truth samples that are equivalent to the generated sample and clearly indicate data amplification for smooth features of the distribution.

97 MATHEMATICS AND COMPUTING↗

Neural message-passing for objective-based uncertainty quantification and optimal experimental design

Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.

97 MATHEMATICS AND COMPUTING↗

Chrono-Validation of Near-Real-Time Landslide Susceptibility Models via Plugin Statistical Simulations

The idea behind any validation scheme in landslide susceptibility studies is to test whether a model calibrated on a certain data can predict an unknown dataset of the same nature (landslide presences/absences and covariates). Almost the entirety of landslide susceptibility studies are validated by subsetting a single dataset into a training and test sets. This dataset usually corresponds either to event-specific or to historical inventories. Very rarely, a multi-temporal inventory is available and, in the few cases where this condition is met, the validation practices involve training a model on a specific landslide inventory, deriving a single predictive equation and validating it on a subsequent landslide inventory. This commonly leads landslide predictive studies, even those with a strong statistical rigor, to neglect the uncertainty estimation in their modeling scheme. In statistics, validation can also be performed via statistical simulations. This means that after fitting a given model, one can generate any number of predictive functions and test their predictive skills on any type and number of unknown datasets. In this work, we take a similar direction and we apply it to model and validate three separate co-seismic inventories, including an uncertainty estimation phase. We mapped these inventories within the same area in Indonesia, for three earthquakes occurred in 2012, 2017 and 2018. Specifically, we build three event-specific Bayesian Generalize Additive Models of the binomial family. From each model we then simulate 1000 predictive realizations over the remaining two inventories, by using a plug-in scheme where all the morphometric covariates are kept fixed and only the ground motion is replaced according to the prediction target. By doing so, we introduce a new analytical tool for near-real-time landslide predictive purposes, which is able to produce a probabilistic model which stands in between the definitions of susceptibility and hazard. In fact, our model is able to accurately estimate “where” and “when” - although not “how frequently” - landslide have occurred by featuring the multitemporal information of the trigger. In our findings, the simulations are quite similar to the fitted models; and the nine combinations we analyse produce excellent performance. This result confirms the assumption that “the past is the key to the future”, as we show that the relative contribution of each variable and their interactions in each probabilistic model remains practically the same across temporal replicates. This information is not trivial because it supports the routines implemented in global near-real-time applications.

Temporal validation↗

Quantifying modeling uncertainty in simplified beam models for building response prediction

The use of simple models for response prediction of building structures is preferred in earthquake engineering for risk evaluations at regional scales, as they make computational studies more feasible. The primary impediment in their gainful use presently is the lack of viable methods for quantifying (and reducing upon) the modeling errors/uncertainties they bear. This study presents a Bayesian calibration method wherein the modeling error is embedded into the parameters of the model. Here, the method is specifically described for coupled shear-flexural beam models here, but it can be applied to any parametric surrogate model. The major benefit the method offers is the ability to consider the modeling uncertainty in the forward prediction of any degree-of-freedom or composite response regardless of the data used in calibration. The method is extensively verified using two synthetic examples. In the first example, the beam model is calibrated to represent a similar beam model but with enforced modeling errors. In the second example, the beam model is used to represent the detailed finite element model of a 52-story building. Both examples show the capability of the proposed solution to provide realistic uncertainty estimation around the mean prediction.

47 OTHER INSTRUMENTATION↗

Survival of Juvenile Florida Scrub-Jays is Habitat Specific, Positively Correlated With Month and Negatively Correlated With Male Breeder Death

Juvenile survival in birds is difficult to estimate but this vital rate can be an important consideration for management decisions. We estimated juvenile survival of cooperatively breeding Florida Scrub-Jays (Aphelocoma coerulescens) in a landscape degraded by fire suppression and fragmentation using data from marked (n = 325) and unmarked juveniles (n = 1,306) with an integrated hierarchical Bayesian model. To assess the combined analyses, we also analyzed these datasets separately, with a Cormack-Jolly-Seber (CJS) model (marked) and young model (unmarked). Our data consisted of monthly censuses of territorial family groups from Florida Scrub-Jay populations in East Central Florida collected over a 22-yr period. Juvenile survival was estimated from July when young Florida Scrub-Jays begin developing independence to March when they become first year individuals and grouped according to the habitat quality class of their natal territory that were based on shrub height (with intermediate shrub heights being optimal and short and tall shrub heights being suboptimal) and the presence of sandy openings (the preferred open having many sandy openings; closed not having enough). Parameter estimates in the combined analysis were intermediate to the separate analyses. Notable differences among the separate analyses were that suboptimal habitat survival was lower in the unmarked analysis, the unmarked analysis showed a linear effect of time not seen in the marked analysis, and there was an effect of male breeder death in the marked but not unmarked analysis. The combined data analysis provided more inference than did either data set analyzed separately including juveniles in optimal-closed territories unexpectedly had higher survival than those in optimal-open, survival increased through time, and male breeder death had a negative effect on survival. This study suggests that optimal-closed habitat may play an important role in juvenile Florida Scrub-Jay survival perhaps by providing better cover from predators and warrants further investigation for management implications.

Florida Scrub-Jay↗

Adaptive sampling for accelerating neutron diffraction-based strain mapping *

Abstract Neutron diffraction is a useful technique for mapping residual strains in dense metal objects. The technique works by placing an object in the path of a neutron beam, measuring the diffracted signals and inferring the local lattice strain values from the measurement. In order to map the strains across the entire object, the object is stepped one position at a time in the path of the neutron beam, typically in raster order, and at each position a strain value is estimated. Typical dwell times at neutron diffraction instruments result in an overall measurement that can take several hours to map an object that is several tens of centimeters in each dimension at a resolution of a few millimeters, during which the end users do not have an estimate of the global strain features and are at risk of incomplete information in case of instruments outages. In this paper, we propose an object adaptive sampling strategy to measure the significant points first. We start with a small initial uniform set of measurement points across the object to be mapped, compute the strain in those positions and use a machine learning technique to predict the next position to measure in the object. Specifically, we use a Bayesian optimization based on a Gaussian process regression method to infer the underlying strain field from a sparse set of measurements and predict the next most informative positions to measure based on estimates of the mean and variance in the strain fields estimated from the previously measured points. We demonstrate our real-time measure-infer-predict workflow on additively manufactured steel parts—demonstrating that we can get an accurate strain estimate even with 30%–40% of the typical number of measurements—leading the path to faster strain mapping with useful real-time feedback. We emphasize that the proposed method is general and can be used for fast mapping of other material properties such as phase fractions from time-consuming point-wise neutron measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Understanding capacity fade in organic redox-flow batteries by combining spectroscopy with statistical inference techniques

Organic redox-active molecules are attractive as redox-flow battery (RFB) reactants because of their low anticipated costs and widely tunable properties. Unfortunately, many lab-scale flow cells experience rapid material degradation (from chemical and electrochemical decay mechanisms) and capacity fade during cycling (>0.1%/day) hindering their commercial deployment. In this work, we combine ultraviolet-visible spectrophotometry and statistical inference techniques to elucidate the Michael attack decay mechanism for 4,5-dihydroxy-1,3-benzenedisulfonic acid (BQDS), a once-promising positive electrolyte reactant for aqueous organic redox-flow batteries. We use Bayesian inference and multivariate curve resolution on the spectroscopic data to derive uncertainty-quantified reaction orders and rates for Michael attack, estimate the spectra of intermediate species and establish a quantitative connection between molecular decay and capacity fade. Our work illustrates the promise of using statistical inference to elucidate chemical and electrochemical mechanisms of capacity fade in organic redox-flow battery together with uncertainty quantification, in flow cell-based electrochemical systems.

25 ENERGY STORAGE↗

Machine learning mathematical models for incidence estimation during pandemics

Accurate estimates of the incidence of infectious diseases are key for the control of epidemics. However, healthcare systems are often unable to test the population exhaustively, especially when asymptomatic and paucisymptomatic cases are widespread; this leads to significant and systematic under-reporting of the real incidence. Here, we propose a machine learning approach to estimate the incidence of a pandemic in real-time, using reported cases and the overall test rate. In particular, we use Bayesian symbolic regression to automatically learn the closed-form mathematical models that most parsimoniously describe incidence. We develop and validate our models using COVID-19 incidence values for nine different countries, confirming their ability to accurately predict daily incidence. Remarkably, despite the differences in epidemic trajectories and dynamics across countries, we find that a single model for all countries offers a more parsimonious description and is more predictive of actual incidence compared to separate models for each country. Our results show the potential to accurately model incidence in real-time using closed-form mathematical models, providing a valuable tool for public health decision-makers.

Fajardo-Fontiveros, Oscar (ORCID:0000000207058972)↗

Uncertainty quantification for equations of state: copper as an example

Equations of state are essential for providing a fundamental description of materials properties in thermodynamic equilibrium and are used to provide closure relations for hydrodynamics simulations. Generally, equations of state rely on simple physics-based parameterized materials models to inform on the free energy of a material through out a given thermodynamic state space. Historically the parameters of these models have been tuned by hand to fit various experimental data. However, modern optimization and uncertainty quantification techniques allow us to quickly test thousands of parameter combinations and obtain meaningful uncertainty estimates on the parameters, opening opportunities for assessing systematic uncertainties in experiments, assessing model adequacy, and more. In this report, we use Bayesian inference to fit the solid (fcc) equation of state of copper. We focus on fitting five different experimental datasets, including the isobaric density, isobaric heat capacity, room temperature isotherm, principal isentrope, and principal Hugoniot. We fit all five data types simultaneously, and then explore the extent to which combinations of 2 subsets of the 5 datasets can constrain the EOS parameters, as compared to the fit to all 5. This information is useful for investigating the extent to which different datasets can con strain EOS models and thereby help guide experimental investigations in order to best constrain the EOS. We also discuss ways that the methodologies can be used to investigate systematic discrepancies between experiments, as well as how the methods can be used to assess model uncertainty. The framework we develop is general, in that it can be used with a variety of optimization or uncertainty quantification techniques and with a variety of data sources, including both experimental and ab-inito data.

97 MATHEMATICS AND COMPUTING↗

Decision-Tree Program

IND computer program introduces Bayesian and Markov/maximum-likelihood (MML) methods and more-sophisticated methods of searching in growing trees. Produces more-accurate class-probability estimates important in applications like diagnosis. Provides range of features and styles with convenience for casual user, fine-tuning for advanced user or for those interested in research. Consists of four basic kinds of routines: data-manipulation, tree-generation, tree-testing, and tree-display. Written in C language.

Buntine, Wray↗

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Tsaoussi, Lucia S.↗

Characterization and Valuation of the Uncertainty of Calibrated Parameters in Microsimulation Decision Models

We evaluated the implications of different approaches to characterize the uncertainty of calibrated parameters of microsimulation decision models (DMs) and quantified the value of such uncertainty in decision making. We calibrated the natural history model of CRC to simulated epidemiological data with different degrees of uncertainty and obtained the joint posterior distribution of the parameters using a Bayesian approach. We conducted a probabilistic sensitivity analysis (PSA) on all the model parameters with different characterizations of the uncertainty of the calibrated parameters. We estimated the value of uncertainty of the various characterizations with a value of information analysis. We conducted all analyses using high-performance computing resources running the Extreme-scale Model Exploration with Swift (EMEWS) framework. The posterior distribution had a high correlation among some parameters. The parameters of the Weibull hazard function for the age of onset of adenomas had the highest posterior correlation of -0.958. When comparing full posterior distributions and the maximum-a-posteriori estimate of the calibrated parameters, there is little difference in the spread of the distribution of the CEA outcomes with a similar expected value of perfect information (EVPI) of $\$$653 and $\$$685, respectively, at a willingness-to-pay (WTP) threshold of $\$$66,000 per quality-adjusted life year (QALY). Ignoring correlation on the calibrated parameters’ posterior distribution produced the broadest distribution of CEA outcomes and the highest EVPI of $\$$809 at the same WTP threshold. Different characterizations of the uncertainty of calibrated parameters affect the expected value of eliminating parametric uncertainty on the CEA. Ignoring inherent correlation among calibrated parameters on a PSA overestimates the value of uncertainty.

97 MATHEMATICS AND COMPUTING↗

Estimating coccidioidomycosis endemicity while accounting for imperfect detection using spatio - temporal occupancy modeling

Coccidioidomycosis, or Valley fever, is an infectious disease caused by inhaling Coccidioides fungal spores. Incidence has risen in recent years, and it is believed the endemic region for Coccidioides is expanding in response to climate change. While Valley fever case data can help us understand trends in disease risk, using case data as a proxy for Coccidioides endemicity is not ideal because case data suffers from imperfect detection, including false positives (e.g., travel-related cases reported outside of endemic area) and false negatives (e.g., misdiagnosis or underreporting). Here we proposed a Bayesian, spatio-temporal occupancy model to relate monthly, county-level presence/absence data on Valley fever cases to latent endemicity of Coccidioides, accounting for imperfect detection. We used our model to estimate endemicity in the western United States. We estimated high probability of endemicity in southern California, Arizona, and New Mexico, but also in regions without mandated reporting, including western Texas, eastern Colorado, and southeastern Washington. We also quantified spatio-temporal variability in detectability of Valley fever, given an area is endemic to Coccidioides. We estimated an inverse relationship between lagged 3- and 9-month precipitation and case detection, and a positive association with agriculture. This work can help inform public health surveillance needs and identify areas that would benefit from mandatory case reporting.

60 APPLIED LIFE SCIENCES↗

Hierarchical Estimation For Planetary Protection

The software uses Bayes' theorem to describe the probability of an event based on prior knowledge of conditions that might be related to the event. The purpose of Bayesian analysis is to determine posterior probabilities based on prior probabilities where new information can be used in the decision-making process as additional data is gathered. The software will be used in Probabilistic Risk Assessments (PRAs) related to the Europa Clipper mission, which is one of NASA’s top priorities. Ultimately, the mission entails sending the Europa Clipper spacecraft to Jupiter’s Europa moon to orbit the planet and collect data for research and development. Europa is the smallest of the four Galilean moons orbiting Jupiter and is believed by researchers to be the most promising place to look for present-day environments suitable for life. Europa is thought to have an iron core, a rocky mantle, and a salt-water ocean covered by an ice-layered surface.

Gribok, Andrei [Idaho National Laboratory (INL), I↗

A Bayesian Approach for Statistical–Physical Bulk Parameterization of Rain Microphysics. Part II: Idealized Markov Chain Monte Carlo Experiments

Observationally informed development of a new framework for bulk rain microphysics, the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS; described in Part I of this study), is demonstrated. This scheme’s development is motivated by large uncertainties in cloud and weather simulations associated with approximations and assumptions in existing microphysics schemes. Here, a proof-of-concept study is introduced using a Markov chain Monte Carlo sampling algorithm with BOSS to probabilistically estimate microphysical process rates and parameters directly from a set of synthetically generated rain observations. The framework utilized is an idealized steady-state one-dimensional column rainshaft model with specified column-top rain properties and a fixed thermodynamical profile. Different configurations of BOSS—flexibility being a key feature of this approach—are constrained via synthetic observations generated from a traditional three-moment bulk microphysics scheme. The ability to retrieve correct parameter values when the true parameter values are known is illustrated. For cases when there is no set of true parameter values, the accuracy of configurations of BOSS that have different levels of complexity is compared. It is found that addition of the sixth moment as a prognostic variable improves prediction of the third moment (proportional to bulk rain mass) and rain rate. In contrast, increasing process rate formulation complexity by adding more power terms has little benefit—a result that is explained using further-idealized experiments. BOSS rainshaft simulations are shown to well estimate the true process rates from constraint by bulk rain observations, with the further benefit of rigorously quantified uncertainty of these estimates.

58 GEOSCIENCES↗

DIGS: deep inference of galaxy spectra with neural posterior estimation

Abstract With the advent of billion-galaxy surveys with complex data, the need of the hour is to efficiently model galaxy spectral energy distributions (SEDs) with robust uncertainty quantification. The combination of simulation-based inference (SBI) and amortized neural posterior estimation (NPE) has been successfully used to analyse simulated and real galaxy photometry both precisely and efficiently. In this work, we utilise this combination and build on existing literature to analyse simulated noisy galaxy spectra. Here, we demonstrate a proof-of-concept study of spectra that is (a) an efficient analysis of galaxy SEDs and inference of galaxy parameters with physically interpretable uncertainties; and (b) amortized calculations of posterior distributions of said galaxy parameters at the modest cost of a few galaxy fits with Markov chain Monte Carlo (MCMC) methods. We utilise the SED generator and inference framework Prospector to generate simulated spectra, and train a dataset of 2 × 10 6 spectra (corresponding to a five-parameter SED model) with NPE. We show that SBI—with its combination of fast and amortized posterior estimations—is capable of inferring accurate galaxy stellar masses and metallicities. Our uncertainty constraints are comparable to or moderately weaker than traditional inverse-modelling with Bayesian MCMC methods (e.g. 0.17 and 0.26 dex in stellar mass and metallicity for a given galaxy, respectively). We also find that our inference framework conducts rapid SED inference (0.9–1.2 × 10 5 galaxy spectra via SBI/NPE at the cost of 1 MCMC-based fit). With this work, we set the stage for further work that focuses of SED fitting of galaxy spectra with SBI, in the era of JWST galaxy survey programs and the wide-field Roman Space Telescope spectroscopic surveys.

spectroscopy↗