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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Inverse sequential procedures for the monitoring of time series

When one or more new values are added to a developing time series, they change its descriptive parameters (mean, variance, trend, coherence). A 'change index (CI)' is developed as a quantitative indicator that the changed parameters remain compatible with the existing 'base' data. CI formulate are derived, in terms of normalized likelihood ratios, for small samples from Poisson, Gaussian, and Chi-Square distributions, and for regression coefficients measuring linear or exponential trends. A substantial parameter change creates a rapid or abrupt CI decrease which persists when the length of the bases is changed. Except for a special Gaussian case, the CI has no simple explicit regions for tests of hypotheses. However, its design ensures that the series sampled need not conform strictly to the distribution form assumed for the parameter estimates. The use of the CI is illustrated with both constructed and observed data samples, processed with a Fortran code 'Sequitor'.

Radok, Uwe↗
NASA NTRS1979

Parameter estimation in X-ray astronomy using maximum likelihood

Methods of estimation of parameter values and confidence regions by maximum likelihood and Fisher efficient scores starting from Poisson probabilities are developed for the nonlinear spectral functions commonly encountered in X-ray astronomy. It is argued that these methods offer significant advantages over the commonly used alternatives called minimum chi-squared because they rely on less pervasive statistical approximations and so may be expected to remain valid for data of poorer quality. Extensive numerical simulations of the maximum likelihood method are reported which verify that the best-fit parameter value and confidence region calculations are correct over a wide range of input spectra.

Wachter, K.↗
DOE OSTI2022

A Compound Poisson Generator Approach to Point-source Inference in Astrophysics

Abstract The identification and description of point sources is one of the oldest problems in astronomy, yet even today the correct statistical treatment for point sources remains one of the field’s hardest problems. For dim or crowded sources, likelihood-based inference methods are required to estimate the uncertainty on the characteristics of the source population. In this work, a new parametric likelihood is constructed for this problem using compound Poisson generator (CPG) functionals that incorporate instrumental effects from first principles. We demonstrate that the CPG approach exhibits a number of advantages over non-Poissonian template fitting (NPTF)—an existing method—in a series of test scenarios in the context of X-ray astronomy. These demonstrations show that the effect of the point-spread function, effective area, and choice of point-source spatial distribution cannot, generally, be factorized as they are in NPTF, while the new CPG construction is validated in these scenarios. Separately, an examination of the diffuse-flux emission limit is used to show that most simple choices of priors on the standard parameterization of the population model can result in unexpected biases: when a model comprising both a point-source population and diffuse component is applied to this limit, nearly all observed flux will be assigned to either the population or to the diffuse component. A new parameterization is presented for these priors that properly estimates the uncertainties in this limit. In this choice of priors, CPG correctly identifies that the fraction of flux assigned to the population model cannot be constrained by the data.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1983

Estimating time and time-lag in time-of-flight velocimetry

Estimating time and time-lag in time-of-flight velocimeters is investigated. Statistics of a filtered Poisson point process is given. A Maximum Likelihood Estimator is compared with suboptimum estimators in terms of robustness. For a dominating background combined spatial and temporal processing can improve the robustness compared with purely temporal processing. Schemes for the spatial filters are given.

Lading, L.↗
DOE OSTI2022

A Hybrid Method for Tensor Decompositions that Leverages Stochastic and Deterministic Optimization

In this paper, we propose a hybrid method that uses stochastic and deterministic search to compute the maximum likelihood estimator of a low-rank count tensor with Poisson loss via state-of-theart local methods. Our approach is inspired by Simulated Annealing for global optimization and allows for fine-grain parameter tuning as well as adaptive updates to algorithm parameters. We present numerical results that indicate our hybrid approach can compute better approximations to the maximum likelihood estimator with less computation than the state-of-the-art methods by themselves.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2009

Error-Rate Bounds for Coded PPM on a Poisson Channel

Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.

Moision, Bruce↗
NASA NTRS2008

Mitigating Photon Jitter in Optical PPM Communication

A theoretical analysis of photon-arrival jitter in an optical pulse-position-modulation (PPM) communication channel has been performed, and now constitutes the basis of a methodology for designing receivers to compensate so that errors attributable to photon-arrival jitter would be minimized or nearly minimized. Photon-arrival jitter is an uncertainty in the estimated time of arrival of a photon relative to the boundaries of a PPM time slot. Photon-arrival jitter is attributable to two main causes: (1) receiver synchronization error [error in the receiver operation of partitioning time into PPM slots] and (2) random delay between the time of arrival of a photon at a detector and the generation, by the detector circuitry, of a pulse in response to the photon. For channels with sufficiently long time slots, photon-arrival jitter is negligible. However, as durations of PPM time slots are reduced in efforts to increase throughputs of optical PPM communication channels, photon-arrival jitter becomes a significant source of error, leading to significant degradation of performance if not taken into account in design. For the purpose of the analysis, a receiver was assumed to operate in a photon- starved regime, in which photon counts follow a Poisson distribution. The analysis included derivation of exact equations for symbol likelihoods in the presence of photon-arrival jitter. These equations describe what is well known in the art as a matched filter for a channel containing Gaussian noise. These equations would yield an optimum receiver if they could be implemented in practice. Because the exact equations may be too complex to implement in practice, approximations that would yield suboptimal receivers were also derived.

Moision, Bruce↗
NASA NTRS1998

Optimum Receiver Structure for PPM Signals with Avalanche Photodiode Statistics

The maximum likelihood decision statistic for detection of pulse-position modulated signals with an avalanche photodiode is derived, using the more accurate Webb density rather than Poisson or Gaussian approximations for the distribution of avalanche photodiode output electrons. It is shown that for Webb-distributed output electtrons, the maximum likelihood rule is to choose the PPM word corresponding to the slot with the maximum electron count.

avalanche photodiode PPM Gaussian Poisson↗
NASA NTRS2010

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Erkmen, Baris I.↗
DOE OSTI2026

Poisson-response Tensor-on-Tensor Regression and Applications

We introduce Poisson-response tensor-on-tensor regression (PToTR), a novel regression framework designed to handle tensor responses composed element-wise of random Poisson-distributed counts. Tensors, or multi-dimensional arrays, composed of counts are common data in fields such as inter national relations, social networks, epidemiology, and medical imaging, where events occur across multiple dimensions like time, location, and dyads. PToTR accommodates such tensor responses alongside tensor covariates, providing a versatile tool for multi dimensional data analysis. We propose algorithms for maximum likelihood estimation under a canonical polyadic (CP) structure on the regression coefficient tensor that satisfy the positivity of Poisson parameters and then provide an initial theoretical error analysis for PToTR estimators. We also demonstrate the utility of PToTR through three concrete applications: longitudinal data analysis of the Integrated Crisis Early Warning System database, positron emission tomography (PET) image reconstruction, and change-point detection of communication patterns in longitudinal dyadic data. These applications highlight the versatility of PToTR in addressing complex, structured count data across various domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Tensor Decompositions for Count Data that Leverage Stochastic and Deterministic Optimization

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the global maximum likelihood estimator from local minima. Simultaneously, a recent trend in theoretical computer science and numerical linear algebra leverages randomization to solve very large, hard problems. The typical approach is to use randomization for a fast approximation and determinism for refinement to yield effective algorithms with theoretical guarantees. Two popular algorithms for Poisson CPD reflect that emergent dichotomy: CP Alternating Poisson Regression is a deterministic algorithm and Generalized Canonical Polyadic decomposition makes use of stochastic algorithms in several variants. This work extends recent work to develop two new methods that leverage randomized and deterministic algorithms for improved accuracy and performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Analysis of overlapping count data

Counts of a specific characteristic were obtained within regions defined on an object that was manufactured in a proprietary setting. The count regions were altered during production and resulted in misaligned or overlapping count data. A closed-formula maximum likelihood estimator (MLE) of the new region means is derived using all of the available count data and an independent Poisson model. The MLE is shown to be preferable to estimators constructed using generalized linear models for the overlapping data setting. This closed-form estimator extends to over-dispersed overlapping count data as the quasi-MLE and also performs well with correlated overlapping count data. Standard errors for the estimator are approximated and are validated with a simulation study. Additionally, the methods are extended to overlapping multinomial data. Illustrative examples of the methods are provided throughout the paper and are reproducible with the supplemental R code. Additionally, proofs of the paper’s results are also included in the supplemental material.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Adversarial autoencoder ensemble for fast and probabilistic reconstructions of few-shot photon correlation functions for solid-state quantum emitters

Second-order photon correlation measurements [g (2) (τ) functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations – such as quantum dots – by evaluating the value of g (2) (τ = 0). Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free g (2) (τ) functions from noise-dominated, few-shot inputs. The model is trained with simulated g (2) (τ) functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of g (2) (τ = 0) that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot g (2) (τ) functions (~100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free g (2) (τ) functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. Furthermore, this work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1972

Photon counting and Laguerre detection.

In this correspondence maximum-likelihood binary detection theory is applied to an incoherent optical system model employing photodetectors governed by Laguerre counting statistics. It is shown that a maximum-likelihood Laguerre detector corresponds to a count comparison over each signaling interval. Laguerre error probabilities are presented and compared with those for Poisson counting.

Gagliardi, R. M.↗
NASA NTRS1981

Role of the doubly stochastic Neyman type-A and Thomas counting distributions in photon detection

The sums of Meyman type-A and Thomas random variables are shown to retain their form under the constant multiplication parameter constraint. The conditions under which the two random variables converge in distribution to the fixed multiplicative Poisson, and to the Gaussian, are presented. It is shown that the latter result is important, in that it provides a solution to likelihood-ratio detection, estimation and discrimination problems in the presence of many kinds of signal and noise. Among the explicit applications presented are: (1) the photon-counter scintillation detection of nuclear particles when particle flux is low, (2) the photon-counting detection of weak optical signals in the presence of ionizing radiation, and (3) the design of a star-scanner spacecraft guidance system adequate for hostile space environments.

Teich, M. C.↗
NASA NTRS2013

The Atacama Cosmology Telescope: Likelihood for Small-Scale CMB Data

The Atacama Cosmology Telescope has measured the angular power spectra of microwave fluctuations to arcminute scales at frequencies of 148 and 218 GHz, from three seasons of data. At small scales the fluctuations in the primordial Cosmic Microwave Background (CMB) become increasingly obscured by extragalactic foregounds and secondary CMB signals. We present results from a nine-parameter model describing these secondary effects, including the thermal and kinematic Sunyaev-Zel'dovich (tSZ and kSZ) power; the clustered and Poisson-like power from Cosmic Infrared Background (CIB) sources, and their frequency scaling; the tSZ-CIB correlation coefficient; the extragalactic radio source power; and thermal dust emission from Galactic cirrus in two different regions of the sky. In order to extract cosmological parameters, we describe a likelihood function for the ACT data, fitting this model to the multi-frequency spectra in the multipole range 500 < l < 10000. We extend the likelihood to include spectra from the South Pole Telescope at frequencies of 95, 150, and 220 GHz. Accounting for different radio source levels and Galactic cirrus emission, the same model provides an excellent fit to both datasets simultaneously, with χ2/dof= 675/697 for ACT, and 96/107 for SPT. We then use the multi-frequency likelihood to estimate the CMB power spectrum from ACT in bandpowers, marginalizing over the secondary parameters. This provides a simplified 'CMB-only' likelihood in the range 500 < l < 3500 for use in cosmological parameter estimation

Cosmology↗
DOE OSTI2025

Large deviations of ionic currents in dilute electrolytes

Here, we evaluate the exponentially rare fluctuations of the ionic current for a dilute electrolyte by means of macroscopic fluctuation theory. We consider the fluctuating hydrodynamics of a fluid electrolyte described by a stochastic Poisson–Nernst–Planck equation. We derive the Euler–Lagrange equations that dictate the optimal concentration profiles of ions conditioned on exhibiting a given current, whose form determines the likelihood of that current in the long-time limit. For a symmetric electrolyte under small applied voltages, number density fluctuations are small, and ionic current fluctuations are Gaussian with a variance determined by the Nernst–Einstein conductivity. Under large applied potentials, the ionic current distribution is generically non-Gaussian. Its structure is constrained thermodynamically by Gallavotti–Cohen symmetry and the thermodynamic uncertainty principle.

Farhadi, Jafar [University of California, Berkeley↗
NASA NTRS2012

Experimental Validation of Pulse Phase Tracking for X-Ray Pulsar Based

Pulsars are a form of variable celestial source that have shown to be usable as aids for autonomous, deep space navigation. Particularly those sources emitting in the X-ray band are ideal for navigation due to smaller detector sizes. In this paper X-ray photons arriving from a pulsar are modeled as a non-homogeneous Poisson process. The method of pulse phase tracking is then investigated as a technique to measure the radial distance traveled by a spacecraft over an observation interval. A maximum-likelihood phase estimator (MLE) is used for the case where the observed frequency signal is constant. For the varying signal frequency case, an algorithm is used in which the observation window is broken up into smaller blocks over which an MLE is used. The outputs of this phase estimation process were then looped through a digital phase-locked loop (DPLL) in order to reduce the errors and produce estimates of the doppler frequency. These phase tracking algorithms were tested both in a computer simulation environment and using the NASA Goddard Space flight Center X-ray Navigation Laboratory Testbed (GXLT). This provided an experimental validation with photons being emitted by a modulated X-ray source and detected by a silicon-drift detector. Models of the Crab pulsar and the pulsar B1821-24 were used in order to generate test scenarios. Three different simulated detector trajectories were used to be tracked by the phase tracking algorithm: a stationary case, one with constant velocity, and one with constant acceleration. All three were performed in one-dimension along the line of sight to the pulsar. The first two had a constant signal frequency and the third had a time varying frequency. All of the constant frequency cases were processed using the MLE, and it was shown that they tracked the initial phase within 0.15% for the simulations and 2.5% in the experiments, based on an average of ten runs. The MLE-DPLL cascade version of the phase tracking algorithm was used in the varying frequency case. This resulted in tracking of the phase and frequency by the DPLL outputs in both the simulation and experimental environments. The crab pulsar was experimentally tested with a trajectory with a higher acceleration. In this case the phase error tended toward zero as the observation extended to 250 seconds and the doppler frequency error tended to zero in under 100 seconds.

Experimental↗