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At least 1,369 records · Page 76

Exact Bayesian computation using H-functions

In the Bayesian Statistics, the use of conjugate prior distributions allows to obtain exact posterior quantities, avoiding the use of approximate methods. However, there are only a few conjugate structures available, which limits the use in practical problems. In this work we propose a general procedure to obtain the posterior distribution in an exact form in non-conjugate location parameter models with known (possibly, heteroskedastic) variance. The theory is based on special functions, specifically the H-function, which embraces most of the probability distributions. We express explicitly in a computable form all the Bayesian tools for posterior inferences, that is the posterior and the posterior predictive distributions and their moments, as well as the cumulative posterior distribution. As an illustration we consider a problem in astronomy of estimating the distance to the Large Magellanic Cloud, the largest galaxy now orbiting the Milky Way Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗

Real Time Effective Impedance Estimation for Power System State Estimation

Here, we introduce two tools-the Effective Impedance State Estimator (EISE), and the Real Time Effective Impedance Estimator (RTEIE). The EISE is novel in that it is an entirely data-driven state estimator, and does not require a network model. Thus, the EISE is well suited for applications in which an accurate network model is not available. Instead of using a network impedance model, the EISE uses an effective impedance network model that is learned online by the RTEIE. The RTEIE recursively estimates the effective impedance network model using phasor measurement unit (PMU) measurements. The mathematical reasoning for using an effective impedance model, rather than a full network impedance model, is given. The recursive estimation framework allows the RTEIE to take the entire history of phasor measurements into account to produce a model estimate, while still adjusting to changes in the network impedance due to external factors such as topology changes and temperature. The merits of the RTEIE and EISE are demonstrated by comparing the accuracy of the EISE with a conventional state estimator on a toy network.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Potential benefits of dosimetric VMAT tracking verified with 3D film measurements

Purpose: To evaluate three different plan adaptation strategies using 3D film-stack dose measurements of both focal boost and hypofractionated prostate VMAT treatments. The adaptation strategies (a couch shift, geometric tracking, and dosimetric tracking) were applied for three realistic intrafraction prostate motions. Methods: A focal boost (35 × 2.2 and 35 × 2.7 Gy) and a hypofractionated (5 × 7.25 Gy) prostate VMAT plan were created for a heterogeneous phantom that allows for internal prostate motion. For these plans geometric tracking and dosimetric tracking were evaluated by ionization chamber (IC) point dose measurements (zero-D) and measurements using a stack of EBT3 films (3D). The geometric tracking applied translations, rotations, and scaling of the MLC aperture in response to realistic prostate motions. The dosimetric tracking additionally corrected the monitor units to resolve variations due to difference in depth, tissue heterogeneity, and MLC-aperture. The tracking was based on the positions of four fiducial points only. The film measurements were compared to the gold standard (i.e., IC measurements) and the planned dose distribution. Additionally, the 3D measurements were converted to dose volume histograms, tumor control probability, and normal tissue complication probability parameters (DVH/TCP/NTCP) as a direct estimate of clinical relevance of the proposed tracking. Results: Compared to the planned dose distribution, measurements without prostate motion and tracking showed already a reduced homogeneity of the dose distribution. Adding prostate motion further blurs the DVHs for all treatment approaches. The clinical practice (no tracking) delivered the dose distribution inside the PTV but off target (CTV), resulting in boost dose errors up to 10%. The geometric and dosimetric tracking corrected the dose distribution’s position. Moreover, the dosimetric tracking could achieve the planned boost DVH, but not the DVH of the more homogeneously irradiated prostate. A drawback of both the geometric and dosimetric tracking was a reduced MLC blocking caused by the rotational component of the MLC aperture corrections. Because of the used CTV to PTV margins and the high doses in the considered fractionation schemes, the TCP differed less than 0.02 from the planned value for all targets and all correction methods. The rectal NTCP constraints, however, could not be realized using any of these methods. Conclusions: The geometric and dosimetric tracking use only a limited input, but they deposit the dose distribution with higher geometric accuracy than the clinical practice. The latter case has boost dose errors up to 10%. The increased accuracy has a modest impact [Δ(NT)CP < 0.02] because of the applied margins and the high dose levels used. To allow further margin reduction tracking methods are vital. The proposed methodology could further be improved by implementing a rotational correction using collimator rotations.

60 APPLIED LIFE SCIENCES↗

HO x radical chemistry in oxidation flow reactors with low-pressure mercury lamps systematically examined by modeling

Oxidation flow reactors (OFRs) using OH produced from low-pressure Hg lamps at 254 nm (OFR254) or both 185 and 254 nm (OFR185) are commonly used in atmospheric chemistry and other fields. OFR254 requires the addition of externally formed O 3 since OH is formed from O 3 photolysis, while OFR185 does not since O 2 can be photolyzed to produce O 3 , and OH can also be formed from H 2 O photolysis. In this study, we use a plug-flow kinetic model to investigate OFR properties under a very wide range of conditions applicable to both field and laboratory studies. We show that the radical chemistry in OFRs can be characterized as a function of UV light intensity, H 2 O concentration, and total external OH reactivity (OHR ext , e.g., from volatile organic compounds (VOCs), NO x , and SO 2 ). OH exposure is decreased by added external OH reactivity. OFR185 is especially sensitive to this effect at low UV intensity due to low primary OH production. OFR254 can be more resilient against OH suppression at high injected O 3 (e.g., 70 ppm), as a larger primary OH source from O 3 , as well as enhanced recycling of HO 2 to OH, make external perturbations to the radical chemistry less significant. However if the external OH reactivity in OFR254 is much larger than OH reactivity from injected O 3 , OH suppression can reach 2 orders of magnitude. For a typical input of 7 ppm O 3 (OHR O 3 = 10 s −1 ), 10-fold OH suppression is observed at OHR ext ~ 100 s −1 , which is similar or lower than used in many laboratory studies. The range of modeled OH suppression for literature experiments is consistent with the measured values except for those with isoprene. The finding on OH suppression may have important implications for the interpretation of past laboratory studies, as applying OH exp measurements acquired under different conditions could lead to over a 1-order-of-magnitude error in the estimated OH exp . The uncertainties of key model outputs due to uncertainty in all rate constants and absorption cross-sections in the model are within ±25 % for OH exposure and within ±60 % for other parameters. These uncertainties are small relative to the dynamic range of outputs. Uncertainty analysis shows that most of the uncertainty is contributed by photolysis rates of O 3 , O 2 , and H 2 O and reactions of OH and HO 2 with themselves or with some abundant species, i.e., O 3 and H 2 O 2 . OH exp calculated from direct integration and estimated from SO 2 decay in the model with laminar and measured residence time distributions (RTDs) are generally within a factor of 2 from the plug-flow OH exp . However, in the models with RTDs, OH exp estimated from SO 2 is systematically lower than directly integrated OH exp in the case of significant SO 2 consumption. We thus recommended using OH exp estimated from the decay of the species under study when possible, to obtain the most appropriate information on photochemical aging in the OFR. Using HO x -recycling vs. destructive external OH reactivity only leads to small changes in OH exp under most conditions. Changing the identity (rate constant) of external OH reactants can result in substantial changes in OH exp due to different reductions in OH suppression as the reactant is consumed. We also report two equations for estimating OH exposure in OFR254. We find that the equation estimating OH exp from measured O 3 consumption performs better than an alternative equation that does not use it, and thus recommend measuring both input and output O 3 concentrations in OFR254 experiments. This study contributes to establishing a firm and systematic understanding of the gas-phase HO x and O x chemistry in these reactors, and enables better experiment planning and interpretation as well as improved design of future reactors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Performance Prediction and Validation: Data, Frameworks, and Considerations

Improving the predictability and reliability of wind power generation and operations will reduce costs and potentially establish a framework to attract new capital into the distributed wind sector, a key cost reduction requirement highlighted in results from the distributed wind future market assessment conducted with dWind. Quantifying and refining the accuracy of project performance estimates will also directly address several of the key challenges identified by industry stakeholders in 2015 as part of the distributed wind resource assessment workshop and be cross-cutting for several other facets of the distributed wind portfolio. This presentation covers the efforts undertaken in 2016 to address these topics.

17 WIND ENERGY↗

Bayesian Parameter Estimation for Heavy-Duty Vehicles

Accurate vehicle parameters are valuable for design, modeling, and reporting. Estimating vehicle parameters can be a very time-consuming process requiring tightly-controlled experimentation. This work describes a method to estimate vehicle parameters such as mass, coefficient of drag/frontal area, and rolling resistance using data logged during standard vehicle operation. The method uses Monte Carlo to generate parameter sets which is fed to a variant of the road load equation. Modeled road load is then compared to measured load to evaluate the probability of the parameter set. Acceptance of a proposed parameter set is determined using the probability ratio to the current state, so that the chain history will give a distribution of parameter sets. Compared to a single value, a distribution of possible values provides information on the quality of estimates and the range of possible parameter values. The method is demonstrated by estimating dynamometer parameters. Results confirm the method's ability to estimate reasonable parameter sets, and indicates an opportunity to increase the certainty of estimates through careful selection or generation of the test drive cycle.

33 ADVANCED PROPULSION SYSTEMS↗

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↗

OSSOS. II. A SHARP TRANSITION IN THE ABSOLUTE MAGNITUDE DISTRIBUTION OF THE KUIPER BELT’S SCATTERING POPULATION

We measure the absolute magnitude, H, distribution, dN(H) ∝ 10{sup αH}, of the scattering Trans-Neptunian Objects (TNOs) as a proxy for their size-frequency distribution. We show that the H-distribution of the scattering TNOs is not consistent with a single-slope distribution, but must transition around H{sub g} ∼ 9 to either a knee with a shallow slope or to a divot, which is a differential drop followed by second exponential distribution. Our analysis is based on a sample of 22 scattering TNOs drawn from three different TNO surveys—the Canada–France Ecliptic Plane Survey, Alexandersen et al., and the Outer Solar System Origins Survey, all of which provide well-characterized detection thresholds—combined with a cosmogonic model for the formation of the scattering TNO population. Our measured absolute magnitude distribution result is independent of the choice of cosmogonic model. Based on our analysis, we estimate that the number of scattering TNOs is (2.4–8.3) × 10{sup 5} for H{sub r} < 12. A divot H-distribution is seen in a variety of formation scenarios and may explain several puzzles in Kuiper Belt science. We find that a divot H-distribution simultaneously explains the observed scattering TNO, Neptune Trojan, Plutino, and Centaur H-distributions while simultaneously predicting a large enough scattering TNO population to act as the sole supply of the Jupiter-Family Comets.

79 ASTRONOMY AND ASTROPHYSICS↗

Data synergy between leaf area index and clumping index Earth Observation products using photon recollision probability theory

Clumping index (CI) is a measure of foliage aggregation relative to a random distribution of leaves in space. The CI can help with estimating fractions of sunlit and shaded leaves for a given leaf area index (LAI) value. Both the CI and LAI can be obtained from global Earth Observation data from sensors such as the Moderate Resolution Imaging Spectrometer (MODIS). Here, the synergy between a MODIS-based CI and a MODIS LAI product is examined using the theory of spectral invariants, also referred to as photon recollision probability (‘p-theory’), along with raw LAI-2000/2200 Plant Canopy Analyzer data from 75 sites distributed across a range of plant functional types. The p-theory describes the probability (p-value) that a photon, having intercepted an element in the canopy, will recollide with another canopy element rather than escape the canopy. We show that empirically-based CI maps can be integrated with the MODIS LAI product. Our results indicate that it is feasible to derive approximate p-values for any location solely from Earth Observation data. This approximation is relevant for future applications of the photon recollision probability concept for global and local monitoring of vegetation using Earth Observation data.

54 ENVIRONMENTAL SCIENCES↗

Statistical estimates of the binary properties of rotational variables

ABSTRACT We present a model to estimate the average primary masses, companion mass ranges, the inclination limit for recognizing a rotational variable, and the primary mass spreads for populations of binary stars. The model fits a population’s binary mass function distribution and allows for a probability that some mass functions are incorrectly estimated. Using tests with synthetic data, we assess the model’s sensitivity to each parameter, finding that we are most sensitive to the average primary mass and the minimum companion mass, with less sensitivity to the inclination limit and little to no sensitivity to the primary mass spread. We apply the model to five populations of binary spotted rotational variables identified in ASAS-SN, computing their binary mass functions using RV data from APOGEE. Their average primary mass estimates are consistent with our expectations based on their CMD locations ($\sim 0.75 \, {\rm M}_{\odot }$ for lower main sequence primaries and $\sim 0.9$–$1.2 \, {\rm M}_{\odot }$ for RS CVn and sub-subgiants). Their companion mass range estimates allow companion masses down to $M_2/M_1\simeq 0.1$, although the main sequence population may have a higher minimum mass fraction ($\sim 0.4$). We see weak evidence of an inclination limit $\gtrsim 50^{\circ }$ for the main sequence and sub-subgiant groups and no evidence of an inclination limit in the other groups. No groups show strong evidence for a preferred primary mass spread. We conclude by demonstrating that the approach will provide significantly better estimates of the primary mass and the minimum mass ratio and reasonable sensitivity to the inclination limit with 10 times as many systems.

Phillips, Anya (ORCID:000900051914974X)↗

Characteristic energy range of electron scattering due to plasmaspheric hiss

In this paper, we investigate the characteristic energy range of electron flux decay due to the interaction with plasmaspheric hiss in the Earth's inner magnetosphere. The Van Allen Probes have measured the energetic electron flux decay profiles in the Earth's outer radiation belt during a quiet period following the geomagnetic storm that occurred on 7 November 2015. The observed energy of significant electron decay increases with decreasing L shell and is well correlated with the energy band corresponding to the first adiabatic invariant μ = 4–200 MeV/G. The electron diffusion coefficients due to hiss scattering are calculated at L = 2–6, and the modeled energy band of effective pitch angle scattering is also well correlated with the constant μ lines and is consistent with the observed energy range of electron decay. Using the previously developed statistical plasmaspheric hiss model during modestly disturbed periods, we perform a 2-D Fokker-Planck simulation of the electron phase space density evolution at L = 3.5 and demonstrate that plasmaspheric hiss causes the significant decay of 100 keV–1 MeV electrons with the largest decay rate occurring at around 340 keV, forming anisotropic pitch angle distributions at lower energies and more flattened distributions at higher energies. Finally, our study provides reasonable estimates of the electron populations that can be most significantly affected by plasmaspheric hiss and the consequent electron decay profiles.

79 ASTRONOMY AND ASTROPHYSICS↗

Winter connectivity and leapfrog migration in a migratory passerine

Abstract Technological advances in migratory tracking tools have revealed a remarkable diversity in migratory patterns. One such pattern is leapfrog migration, where individuals that breed further north migrate to locations further south. Here, we analyzed migration patterns in the Painted Bunting ( Passerina ciris ) using a genetic‐based approach. We started by mapping patterns of genetic variation across geographic space (called a genoscape) using 386 individuals from 25 populations across the breeding range. We then genotyped an additional 230 samples from 31 migration stopover locations and 178 samples from 16 wintering locations to map patterns of migratory connectivity. Our analyses of genetic variation across the breeding range show the existence of four genetically distinct groups within the species: Eastern, Southwestern, Louisiana, and Central groups. Subsequent assignment of migrating and wintering birds to genetic groups illustrated that birds from the Central group migrated during the fall via western Mexico or southern Texas, spent the winter from northeastern Mexico to Panama, and migrated north via the Gulf Coast of Mexico. While Louisiana birds overlapped with Central birds on their spring migratory routes along the Gulf Coast, we found that Louisiana birds had a more restricted wintering distribution in the Yucatan Peninsula and Central America. Further estimation of the straight‐line distance from the predicted breeding location to the wintering location revealed that individuals sampled at lower winter latitudes traveled to greater distances (i.e., the predicted breeding area was further north; p > .001), confirming that these species exhibit a leapfrog migration pattern. Overall, these results demonstrate the utility of a genoscape‐based approach for identifying range‐wide patterns of migratory connectivity such as leapfrog migration with a high degree of clarity.

59 BASIC BIOLOGICAL SCIENCES↗

Scalable statistical inference of photometric redshift via data subsampling

Handling big data has largely been a major bottleneck in traditional statistical models. Consequently, when accurate point prediction is the primary target, machine learning models are often preferred over their statistical counterparts for bigger problems. But full probabilistic statistical models often outperform other models in quantifying uncertainties associated with model predictions. We develop a data-driven statistical modeling framework that combines the uncertainties from an ensemble of statistical models learned on smaller subsets of data carefully chosen to account for imbalances in the input space. We demonstrate this method on a photometric redshift estimation problem in cosmology, which seeks to infer a distribution of the redshift—the stretching effect in observing the light of far-away galaxies—given multivariate color information observed for an object in the sky. Our proposed method performs balanced partitioning, graph-based data subsampling across the partitions, and training of an ensemble of Gaussian process models.

data subsampling↗

Collisions of Dark Matter Axion Stars with Astrophysical Sources

If QCD axions form a large fraction of the total mass of dark matter, then axion stars could be very abundant in galaxies. As a result, collisions with each other, and with other astrophysical bodies, can occur. We calculate the rate and analyze the consequences of three classes of collisions, those occurring between a dilute axion star and: another dilute axion star, an ordinary star, or a neutron star. In all cases we attempt to quantify the most important astrophysical uncertainties, we also pay particular attention to scenarios in which collisions lead to collapse of otherwise stable axion stars, and possible subsequent decay through number changing interactions. Collisions between two axion stars can occur with a high total rate, but the low relative velocity required for collapse to occur leads to a very low total rate of collapses. On the other hand, collisions between an axion star and an ordinary star have a large rate, Γ$_{⊙}$ ∼ 3000 collisions/year/galaxy, and for sufficiently heavy axion stars, it is plausible that most or all such collisions lead to collapse. We identify in this case a parameter space which has a stable region and a region in which collision triggers collapse, which depend on the axion number (N ) in the axion star, and a ratio of mass to radius cubed characterizing the ordinary star (M$_{s}$ /R$_{s}^{3}$ ). Finally, we revisit the calculation of collision rates between axion stars and neutron stars, improving on previous estimates by taking cylindrical symmetry of the neutron star distribution into account. Collapse and subsequent decay through collision processes, if occurring with a significant rate, can affect dark matter phenomenology and the axion star mass distribution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Micromechanics of Fracture Propagation During Multistage Stress Relaxation and Creep in Brittle Rocks

Time-dependent rock deformation caused by the initiation and growth of fractures leads to the weakening of the rock mass. Understanding the fracturing mechanisms involved in the time-dependent behavior in brittle rocks is very important and to achieve this goal, a systematic series of three types of experiments was performed on double-flawed prismatic Barre granite specimens under unconfined compression. The first series aimed to identify the failure mechanism in the short-term failure mode under monotonic loading, the, second series involved multistage relaxation (constant strain) experiments to analyze the damage at different strain levels, and the third series explored the fracture propagation under multistage creep (constant load) experiments. The spatial and temporal evolution of cracking mechanisms were evaluated using the acoustic emission (AE) and two-dimensional digital image correlation (2D-DIC) techniques to observe the whole crack growth process as well as the accumulated inelastic strain at the specified region of interest. Results suggest that in the case of multistage creep experiments, the time to failure was less compared to the multistage relaxation, when loaded above the crack damage threshold (CD) estimated from the monotonic testing. Furthermore, the frequency magnitude distribution of the AE events generated in the three loading conditions followed the Gutenberg Richter model. A relatively lower b-value was obtained for the creep experiments, indicative of high energy AE events and faster crack growth. In addition, the AE and DIC results also revealed high evolution of tensile cracks at-different stages of creep and relaxation compared to shear and mixed-mode cracks.

58 GEOSCIENCES↗

Nuclear Forensics Analysis with Missing and Uncertain Data

We have applied a new imputation-based method for analyzing incomplete data, called Monte Carlo Bayesian Database Generation (MCBDG), to the Spent Fuel Isotopic Composition (SFCOMPO) database. About 60% of the entries are absent for SFCOMPO. The method estimates missing values of a property from a probability distribution created from the existing data for the property, and then generates multiple instances of the completed database for training a machine learning algorithm. Uncertainty in the data is represented by an empirical or an assumed error distribution. The method makes few assumptions about the underlying data, and compares favorably against results obtained by replacing missing information with constant values.

97 MATHEMATICS AND COMPUTING↗

Empirical evidence that mean soil contaminant concentration is not a conservative indicator of external exposure to wildlife

Adequate information on external exposure is often a limiting factor in ecological risk assessments because of a lack of exposure data for free-ranging animals as they interact with a heterogeneous distribution of contaminants. Instead, most wildlife exposure data are estimated from model simulations. However, empirical exposure data are rarely available to verify model results, or to test fundamental assumptions inherent in exposure assessments. We used novel, GPS-coupled radiation dosimeters on reindeer (Rangifer tarandus) to quantify their external exposure for five months in a Chernobyl fallout affected mountainous area of Norway. The exposure data were then used to test a fundamental assumption in screening-level risk assessments: Mean soil contaminant concentrations can be used to conservatively estimate chronic external exposures to representative animals. External exposure and GPS coordinates were obtained hourly and compared to model simulations of exposure based on airborne surveys of 137 Cs soil contamination. Our objectives were to determine 1) if modelled dose estimates based on mean 137 Cs soil concentrations were conservative, and 2) if modelled dose estimates could be improved by adjusting for spatial–temporal heterogeneity of contaminants using 137 Cs concentrations within reindeers’ GPS-defined home ranges and core areas. We found that external exposure modelled from mean soil contaminant concentrations underestimated exposure by 70% compared to empirical measurements from GPS-dosimeter collars worn on individual animals. Using area-weighted mean contaminant levels within the animals’ home range improved the model estimates, but still underestimated the field dosimeter data by 53%. The best estimate of external exposure was obtained when high-use areas within their home range, along with spatial heterogeneity of the contaminant, was accounted for by using area-weighted mean soil contaminant levels within GPS-derived core areas. Accounting for temporal use of core areas within animals’ home range provided a 24% improvement. Here, a comparison of our analyses to similar work performed on Chernobyl wolves found the two studies concur that risk assessors should be cautious in relying on the paradigm of using averaged soil contaminant levels to provide conservative estimates of external exposure to representative individuals. Results of modelled external exposure based on mean soil contaminant concentrations could misguide assessors and cause inappropriate management decisions.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Shedding light on the economic costs of long-duration power outages: A review of resilience assessment methods and strategies

Here this paper provides a literature review of methods and modeling techniques to estimate the cost of power system outages, along with the value of outage mitigation or system resilience. Regulators, policymakers, and infrastructure owners have a growing need to understand the methods for estimating the benefits of resilience improvements of electric infrastructure against natural and man-made disasters. There is a broad literature that estimates the cost of short-duration outages and a small but developing literature on estimating the cost of long-duration outages. This article reviews the models used to estimate the cost of outages and discusses their relative strengths. Additionally, this paper identifies key questions from stakeholders regarding resilience investment and maps them to the relevant models that would help answer them. We include recommendations for future work to include recent advances in regional economic modeling that can estimate region and demographic-specific costs and the distributional consequences of potential resilience projects.

24 POWER TRANSMISSION AND DISTRIBUTION↗