Estimating Conditional Climate Distributions via Bayesian Transport Maps
Explore the source record for details and available documents.
Drennan, Daniel↗
SEARCH · Engineering Papers
Results for “Conditional distributions”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Bounds on galaxy stochasticity from halo occupation distribution modeling
The joint probability distribution of matter overdensity and galaxy counts in cells is a powerful probe of cosmology, and the extent to which variance in galaxy counts at fixed matter density deviates from Poisson shot noise is not fully understood. The lack of informed bounds on this stochasticity is currently the limiting factor in constraining cosmology with the galaxy–matter probability distribution function (PDF). We investigate stochasticity in the conditional distribution of galaxy counts along lines of sight with fixed matter density, and we present a halo occupation distribution (HOD)-based approach for obtaining plausible ranges for stochasticity parameters. To probe the high-dimensional space of possible galaxy–matter connections, we derive a set of HODs that conserve the galaxies’ linear bias and number density to produce RED M A G I C-like galaxy catalogs within the A BACUS S UMMIT suite of N -body simulations. We study the impact of individual HOD parameters and cosmology on stochasticity and perform a Monte Carlo search in HOD parameter space subject to the constraints on bias and density. In mock catalogs generated by the selected HODs, shot noise in galaxy counts spans both sub-Poisson and super-Poisson values, ranging from 80% to 133% of Poisson variance for cells with mean matter density. Nearly all of the derived HODs show a positive relationship between local matter density and stochasticity. For galaxy catalogs with higher stochasticity, modeling galaxy bias to second order is required for an accurate description of the conditional PDF of galaxy counts at fixed matter density. The presence of galaxy assembly bias also substantially extends the range of stochasticity in the super-Poisson direction. This HOD-based approach leverages degrees of freedom in the galaxy–halo connection to obtain informed bounds on nuisance model parameters and can be adapted to study other parametrizations of shot noise in galaxy counts, in particular to motivate prior ranges on stochasticity for cosmological analyses.
Britt, Dylan (ORCID:000000019905601X)↗
Cluster infall for mass calibration in the stage-IV era
The outskirts of galaxy clusters present a promising avenue for constraining cluster masses in a way that is robust to the impact of baryonic physics. We assess the accuracy to which the cluster infall regions can be used for cluster mass calibration. Building on previous work, we parametrize the velocity distribution 𝑃(𝑣r,𝑣tan|𝑟,𝑀) of dark matter halos on scales 𝑟 ≥ 5ℎ −1 Mpc as the product of the marginalized distribution 𝑃(𝑣 r |𝑟,𝑀) and the conditional distribution 𝑃(𝑣 tan |𝑣 r ,𝑟,𝑀), calibrating the radial and mass dependence of these distributions in numerical simulations. We then project our model along the line of sight to obtain accurate predictions for the distributions of line-of-sight velocities at a given projected radius and cluster mass 𝑃(𝑣 LOS |𝑅,𝑀), which we can observe with spectroscopic survey data. Furthermore, with our model, we forecast that spectra from the Dark Energy Spectroscopic Instrument can constrain cluster masses with subpercent-level precision, comparable to that of stage-IV weak lensing surveys.
79 ASTRONOMY AND ASTROPHYSICS↗
Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning
Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.
97 MATHEMATICS AND COMPUTING↗
A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions
Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.
97 MATHEMATICS AND COMPUTING↗
Reconciling Chord Length Distributions and Area Distributions for Fields of Fractal Cumulus Clouds
While the total cover of broken cloud fields can in principle be obtained from one-dimensional measurements, the cloud size distribution normally differs between two-dimensional (area) and one-dimensional retrieval (chord length) methods. In this study, we use output from high-resolution Large Eddy Simulations to generate a transfer function between the two. We retrieve chord lengths and areas for many clouds, and plot the one as a function of the other, and vice versa. We find that the cloud area distribution conditional on the chord length behaves like a gamma distribution with well-behaved parameters, with a mean μ=1.1L and a shape parameter β=L−0.645. Using this information, we are able to generate a transfer function that can adjust the chord length distribution so that it comes much closer to the cloud area distribution. Our transfer function improves the error in predicting the mean cloud size, and is performs without strong biases for smaller sample sizes. However, we find that the method is still has difficulties in accurately predicting the frequency of occurrence of the largest cloud sizes.
54 ENVIRONMENTAL SCIENCES↗
Carbon monoxide over the Amazon Basin during the wet season
Measurements of the distribution of carbon monoxide in the lower atmosphere (150-5000 m) over the Amazon region of Brazil during the wet season, taken in conjunction with the 1987 NASA Global Tropospheric Experiment/Amazon Boundary Layer Experiment (ABLE 2B), are analyzed. About 100 hr of airborne, in situ CO measurements were obtained using a tunable diode laser system, providing insights into factors influencing the basin-scale distribution of CO in the Amazonian troposphere during wet season conditions. Distribution of CO over the altitudes 0.15-4.5 km was influenced by such factors as surface emissions from biological sources and long-range transport of pollutants from Northern Hemisphere sources. It is noted that the disruption of mixed layer growth and decay processes has a particularly important influence on CO concentration in the daytime lower troposphere and that the correlation of CO with O3 was positive under conditions influenced by Northern Hemisphere air and negative under all other conditions observed.
Harriss, R. C.↗
Range reference atmosphere models
A description is given of the methods used to establish the statistical parameters and models for wind and various thermodynamic quantities at an altitude of 0-70 km for nine geographical locations. It is noted that wind is modeled as a vector quantity using the bivariate normal probability function. With the five parameters of the bivariate normal distribution, the distribution for wind speed is derived as a generalized Rayleigh distribution. In addition, the frequency of wind direction is derived, and the conditional distribution of wind speed given the wind direction is derived. It is pointed out that these and other wind models are consistent with the rigorous mathematical properties of the bivariate normal probability theory. The thermodynamic quantities are consistent with the hydrostatic equation and the equation of state for the mean values. With these methods, many statistical relationships can be derived.
Smith, O. E.↗
Calculations of heavy ion charge state distributions for nonequilibrium conditions
Numerical calculations of the charge state distributions of test ions in a hot plasma under nonequilibrium conditions are presented. The mean ionic charges of heavy ions for finite residence times in an instantaneously heated plasma and for a non-Maxwellian electron distribution function are derived. The results are compared with measurements of the charge states of solar energetic particles, and it is found that neither of the two simple cases considered can explain the observations.
Luhn, A.↗
NASA GPM GV Science Requirements
An important scientific objective of the NASA portion of the GPM Mission is to generate quantitatively-based error characterization information along with the rainrate retrievals emanating from the GPM constellation of satellites. These data must serve four main purposes: (1) they must be of sufficient quality, uniformity, and timeliness to govern the observation weighting schemes used in the data assimilation modules of numerical weather prediction models; (2) they must extend over that portion of the globe accessible by the GPM core satellite to which the NASA GV program is focused - (approx.65 degree inclination); (3) they must have sufficient specificity to enable detection of physically-formulated microphysical and meteorological weaknesses in the standard physical level 2 rainrate algorithms to be used in the GPM Precipitation Processing System (PPS), i.e., algorithms which will have evolved from the TRMM standard physical level 2 algorithms; and (4) they must support the use of physical error modeling as a primary validation tool and as the eventual replacement of the conventional GV approach of statistically intercomparing surface rainrates fiom ground and satellite measurements. This approach to ground validation research represents a paradigm shift vis-&-vis the program developed for the TRMM mission, which conducted ground validation largely as a statistical intercomparison process between raingauge-derived or radar-derived rainrates and the TRMM satellite rainrate retrievals -- long after the original satellite retrievals were archived. This approach has been able to quantify averaged rainrate differences between the satellite algorithms and the ground instruments, but has not been able to explain causes of algorithm failures or produce error information directly compatible with the cost functions of data assimilation schemes. These schemes require periodic and near-realtime bias uncertainty (i.e., global space-time distributed conditional accuracy of the retrieved rainrates) and local error covariance structure (i.e., global space-time distributed error correlation information for the local 4-dimensional space-time domain -- or in simpler terms, the matrix form of precision error). This can only be accomplished by establishing a network of high quality-heavily instrumented supersites selectively distributed at a few oceanic, continental, and coastal sites. Economics and pragmatics dictate that the network must be made up of a relatively small number of sites (6-8) created through international cooperation. This presentation will address some of the details of the methodology behind the error characterization approach, some proposed solutions for expanding site-developed error properties to regional scales, a data processing and communications concept that would enable rapid implementation of algorithm improvement by the algorithm developers, and the likely available options for developing the supersite network.
Smith, E.↗
Probabilistic neural networks for fluid flow surrogate modeling and data recovery
We consider the use of probabilistic neural networks for fluid flow surrogate modeling and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (i) the shallow-water equations, (ii) a two-dimensional cylinder flow, (iii) the wake of a NACA0012 airfoil with a Gurney flap, and (iv) the NOAA sea surface temperature data set. Furthermore, the present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow surrogate model but also systematically quantifies the uncertainty therein to assist with model interpretability.
42 ENGINEERING↗
A Simple Stochastic Model for Generating Broken Cloud Optical Depth and Top Height Fields
A simple and fast algorithm for generating two correlated stochastic twodimensional (2D) cloud fields is described. The algorithm is illustrated with two broken cumulus cloud fields: cloud optical depth and cloud top height retrieved from Moderate Resolution Imaging Spectrometer (MODIS). Only two 2D fields are required as an input. The algorithm output is statistical realizations of these two fields with approximately the same correlation and joint distribution functions as the original ones. The major assumption of the algorithm is statistical isotropy of the fields. In contrast to fractals and the Fourier filtering methods frequently used for stochastic cloud modeling, the proposed method is based on spectral models of homogeneous random fields. For keeping the same probability density function as the (first) original field, the method of inverse distribution function is used. When the spatial distribution of the first field has been generated, a realization of the correlated second field is simulated using a conditional distribution matrix. This paper is served as a theoretical justification to the publicly available software that has been recently released by the authors and can be freely downloaded from http://i3rc.gsfc.nasa.gov/Public codes clouds.htm. Though 2D rather than full 3D, stochastic realizations of two correlated cloud fields that mimic statistics of given fields have proved to be very useful to study 3D radiative transfer features of broken cumulus clouds for better understanding of shortwave radiation and interpretation of the remote sensing retrievals.
Prigarin, Sergei M.↗
The distribution of [α/Fe] in the Milky Way disc
ABSTRACT Using a sample of red giant stars from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) Data Release 16, we infer the conditional distribution $p([\alpha /{\rm Fe}]\, |\, [{\rm Fe}/{\rm H}])$ in the Milky Way disk for the α-elements Mg, O, Si, S, and Ca. In each bin of [Fe/H] and Galactocentric radius R, we model p([α/Fe]) as a sum of two Gaussians, representing ‘low-α’ and ‘high-α’ populations with scale heights $z_1=0.45\, {\rm kpc}$ and $z_2=0.95\, {\rm kpc}$, respectively. By accounting for age-dependent and z-dependent selection effects in APOGEE, we infer the [α/Fe] distributions that would be found for a fair sample of long-lived stars covering all z. Near the Solar circle, this distribution is bimodal at sub-solar [Fe/H], with the low-α and high-α peaks clearly separated by a minimum at intermediate [α/Fe]. In agreement with previous results, we find that the high-α population is more prominent at smaller R, lower [Fe/H], and larger |z|, and that the sequence separation is smaller for Si and Ca than for Mg, O, and S. We find significant intrinsic scatter in [α/Fe] at fixed [Fe/H] for both the low-α and high-α populations, typically ∼0.04-dex. The means, dispersions, and relative amplitudes of this two-Gaussian description, and the dependence of these parameters on R, [Fe/H], and α-element, provide a quantitative target for chemical evolution models and a test for hydrodynamic simulations of disk galaxy formation. We argue that explaining the observed bimodality will probably require one or more sharp transitions in the disk’s gas accretion, star formation, or outflow history in addition to radial mixing of stellar populations.
79 ASTRONOMY AND ASTROPHYSICS↗
A generative modeling approach to reconstructing 21 cm tomographic data
Abstract Analyses of the cosmic 21 cm signal are hampered by astrophysical foregrounds that are far stronger than the signal itself. These foregrounds, typically confined to a wedge-shaped region in Fourier space, often necessitate the removal of a vast majority of modes, thereby degrading the quality of the data anisotropically. To address this challenge, we introduce a novel deep generative model based on stochastic interpolants to reconstruct the 21 cm data lost to wedge filtering. Our method leverages the non-Gaussian nature of the 21 cm signal to effectively map wedge-filtered 3D lightcones to samples from the conditional distribution of wedge-recovered lightcones. We demonstrate how our method is able to restore spatial information effectively, considering both varying cosmological initial conditions and astrophysics. Furthermore, we discuss a number of future avenues where this approach could be applied in analyses of the 21 cm signal, potentially offering new opportunities to improve our understanding of the Universe during the epochs of cosmic dawn and reionization. Code, pre-trained models, and scripts for making plots in this paper can be found here .
Sabti, Nashwan (ORCID:000000027924546X)↗
Power conditioning equipment for a thermoelectric outer planet spacecraft, volume 1, book 1
Equipment was designed to receive power from a radioisotope thermoelectric generator source, condition, distribute, and control this power for the spacecraft loads. The TOPS mission, aimed at a representative tour of the outer planets, would operate for an estimated 12 year period. Unique design characteristics required for the power conditioning equipment results from the long mission time and the need for autonomous on-board operations due to large communications distances and the associated time delays of ground initiated actions. The salient features of the selected power subsystem configuration are: (1) The PCE regulates the power from the radioisotope thermoelectric generator power source at 30 vdc by means of a quad-redundant shunt regulator; (2) 30 vdc power is used by certain loads, but is more generally inverted and distributed as square-wave ac power; (3) a protected bus is used to assure that power is always available to the control computer subsystem to permit corrective action to be initiated in response to fault conditions; and (4) various levels of redundancy are employed to provide high subsystem reliability.
Andrews, R. E.↗
Astigmatic electron beam propagation
An astigmatic electron beam with an ellipticity ratio of approximately 2:1 was examined using the Enhanced Modified Faraday Cup (EMFC) diagnostic to measure its properties and show how the power density distribution varies near the beam waist. Results show that the beam has two power density peaks, one on either side of the beam crossover point, resulting from different focal distances of the major and minor axes of the elliptical beam shape. Quantification of the beam properties was used to establish a depth-of-field where the beam diameter and peak power densities are relatively constant. For the 1 kW beam studied here, the depth-of-field measured approximately ±5 mm from the beam crossover point, illustrating how electron beam diagnostics can be used to identify process control limits for repeatable and reliable welds under non-ideal electron beam power density distribution conditions.
36 MATERIALS SCIENCE↗
A modified Susceptible-Infected-Recovered model for observed under-reported incidence data
Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.
60 APPLIED LIFE SCIENCES↗
Continuing Development of the Nuclear Data Processing Code AMPX [Poster]
The ENDF/B-VIII.1 evaluation library has seen a great growth in the thermal neutron scattering sub-library. The SCALE code system has traditionally approached CE transport by assuming that the CE library on disk represented the fully expanded cumulative probability distributions, conditional on exiting angle and marginal on exiting energy. While this is a complete description of the data, it comes at the potential cost of large amounts of on-disk storage. This approach was strained by several TSL files in ENDF/B-VIII.1, such as graphite, which contained data for a large number of Bragg edges. In the fully expanded probability distributions, this was found to be a disproportionately large fraction of the SCALE CE library.
GNDS↗