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8 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. Here, we also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Tolerance bounds for log gamma regression models

The present procedure for finding lower confidence bounds for the quantiles of Weibull populations, on the basis of the solution of a quadratic equation, is more accurate than current Monte Carlo tables and extends to any location-scale family. It is shown that this method is accurate for all members of the log gamma(K) family, where K = 1/2 to infinity, and works well for censored data, while also extending to regression data. An even more accurate procedure involving an approximation to the Lawless (1982) conditional procedure, with numerical integrations whose tables are independent of the data, is also presented. These methods are applied to the case of failure strengths of ceramic specimens from each of three billets of Si3N4, which have undergone flexural strength testing.

Jones, R. A.↗
NASA NTRS1984

A validation methodology for fault-tolerant clock synchronization

A validation method for the synchronization subsystem of a fault-tolerant computer system is presented. The high reliability requirement of flight crucial systems precludes the use of most traditional validation methods. The method presented utilizes formal design proof to uncover design and coding errors and experimentation to validate the assumptions of the design proof. The experimental method is described and illustrated by validating an experimental implementation of the Software Implemented Fault Tolerance (SIFT) clock synchronization algorithm. The design proof of the algorithm defines the maximum skew between any two nonfaulty clocks in the system in terms of theoretical upper bounds on certain system parameters. The quantile to which each parameter must be estimated is determined by a combinatorial analysis of the system reliability. The parameters are measured by direct and indirect means, and upper bounds are estimated. A nonparametric method based on an asymptotic property of the tail of a distribution is used to estimate the upper bound of a critical system parameter. Although the proof process is very costly, it is extremely valuable when validating the crucial synchronization subsystem.

Johnson, S. C.↗
DOE OSTI2021

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be ${12.39}_{-0.98}^{+1.30}$ km and ${2.072}_{-0.066}^{+0.067}$ M ⊙ respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is ${\mathrm{log}}_{10}(T\,[{\rm{K}}])={5.99}_{-0.06}^{+0.05}$ for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Furthermore, our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters (within the prior support) and can thus be computed from the posterior samples.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2021

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be-+12.390.981.30km and-+2.0720.0660.067Me respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is=-+TlogK5.99100.060.05([])for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters(within the prior support)and can thus be computed from the posterior samples.

Millisecond pulsars↗
NASA NTRSDate not supplied

Improving the Representation of Land Surface Processes Using the Data Assimilation Research Testbed (DART)

The land surface is a critical part of the earth system as processes related to water, carbon, energy and nitrogen cycling have important implications for climate forcing, air quality, water availability and seasonal atmospheric forecasting. Despite advances in land surface modeling, land surface model performance is often limited because of errors related to initial and boundary conditions, model structure, and parameters. Data assimilation (DA) techniques combined with an expanding network of earth system observations present an opportunity to reduce these errors and improve simulations. Here, we emphasize the implementation of tools and approaches to overcome challenges related to land DA to constrain carbon and water cycling. In particular, we discuss the implementation of adaptive inflation to modify ensemble spread in response to time-varying networks of gridded observations. We also discuss methods to generate ensemble spread through boundary condition (meteorology) forcing that can be applied to site-level applications. Next, we describe the application of vertical localization upon surface soil moisture observations, and forward operators specifically designed for the assimilation of snow and solar-induced fluorescence observations. Finally, we discuss the potential benefit of a quantile conserving filter used to update bounded quantities (state or parameter values).

Brett Raczka↗
NASA NTRS2019

A NICER view of PSR J0030+0541: Millisecond Pulsar Parameter Estimation

We report on Bayesian parameter estimation of the mass and equatorial radius of the millisecond pulsar PSRJ0030+0451, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray spectral timing event data. We perform relativistic ray-tracing of thermal emission from hot regions of the pulsar’s surface. We assume two distinct hot regions based on two clear pulsed components in the phase-folded pulse-profile data; we explore a number of forms (morphologies and topologies) for each hot region, inferring their parameters in addition to the stellar mass and radius. For the family of models considered, the evidence (prior predictive probability of the data) strongly favors a model that permits both hot regions to be located in the same rotational hemisphere. Models wherein both hot regions are assumed to be simply connected circular single-temperature spots, in particular those where the spots are assumed to be reflection-symmetric with respect to the stellar origin, are strongly disfavored. For the inferred configuration, one hot region subtends an angular extent of only a few degrees (in spherical coordinates with origin at the stellar center) and we are insensitive to other structural details; the second hot region is far more azimuthally extended in the form of a narrow arc, thus requiring a larger number of parameters to describe. The inferred mass M and equatorial radius Req are, respectively, -1.34+ M 0.16 0.15 and-12.71+ km 1.19 1.14 , while the compactness = -GM R c 0.156+ eq 2 0.010 0.008 is more tightly constrained; the credible interval bounds reported here are approximately the 16% and 84% quantiles in marginal posterior mass.

T E Riley↗
DOE OSTI2020

Characterization of Partially Observed Epidemics - Application to COVID-19

This report documents a statistical method for the "real-time" characterization of partially observed epidemics. Observations consist of daily counts of symptomatic patients, diagnosed with the disease. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information for the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and is predicated on a model for the distribution of the incubation period. The model parameters are estimated as distributions using a Markov Chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. The method is applied to the COVID-19 pandemic of 2020, using data at the country, provincial (e.g., states) and regional (e.g. county) levels. The epidemiological model includes a stochastic component due to uncertainties in the incubation period. This model-form uncertainty is accommodated by a pseudo-marginal Metropolis-Hastings MCMC sampler, which produces posterior distributions that reflect this uncertainty. We approximate the discrepancy between the data and the epidemiological model using Gaussian and negative binomial error models; the latter was motivated by the over-dispersed count data. For small daily counts we find the performance of the calibrated models to be similar for the two error models. For large daily counts the negative-binomial approximation is numerically unstable unlike the Gaussian error model. Application of the model at the country level (for the United States, Germany, Italy, etc.) generally provided accurate forecasts, as the data consisted of large counts which suppressed the day-to-day variations in the observations. Further, the bulk of the data is sourced over the duration before the relaxation of the curbs on population mixing, and is not confounded by any discernible country-wide second wave of infections. At the state-level, where reporting was poor or which evinced few infections (e.g., New Mexico), the variance in the data posed some, though not insurmountable, difficulties, and forecasts were able to capture the data with large uncertainty bounds. The method was found to be sufficiently sensitive to discern the flattening of the infection and epidemic curve due to shelter-in-place orders after around 90% quantile for the incubation distribution (about 10 days for COVID-19). The proposed model was also used at a regional level to compare the forecasts for the central and north-west regions of New Mexico. Modeling the data for these regions illustrated different disease spread dynamics captured by the model. While in the central region the daily counts peaked in the late April, in the north-west region the ramp-up continued for approximately three more weeks.

59 BASIC BIOLOGICAL SCIENCES↗