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Results for “marginal likelihood optimization”

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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NASA NTRS2013

Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it-an improved and generalized version of Bayesian Blocks [Scargle 1998]-that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piece- wise linear and piecewise exponential representations, multivariate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by [Arias-Castro, Donoho and Huo 2003]. In the spirit of Reproducible Research [Donoho et al. (2008)] all of the code and data necessary to reproduce all of the figures in this paper are included as auxiliary material.

signal detection↗

NASA NTRS1992

Robustness of solutions to a benchmark control problem

The robustness of 10 solutions to a benchmark control design problem presented at the 1990 American Control Conference has been evaluated. The 10 controllers have second-to-eighth-order transfer functions and have been designed using several different methods, including H-infinity optimization, loop-transfer recovery, imaginary-axis shifting, constrained optimization, structured covariance, game theory, and the internal model principle. Stochastic robustness analysis quantifies the controllers' stability and performance robustness with structured uncertainties in up to six system parameters. The analysis provides insights into system response that are not readily derived from other robustness criteria and provides a common ground for judging controllers produced by alternative methods. One important conclusion is that gain and phase margins are not reliable indicators of the probability of instability. Furthermore, parameter variations actually may improve the likelihood of achieving selected performance metrics, as demonstrated by results for the probability of settling-time exceedance.

Stengel, Robert F.↗

NASA NTRS1982

Using known map category marginal frequencies to improve estimates of thematic map accuracy

By means of two simple sampling plans suggested in the accuracy-assessment literature, it is shown how one can use knowledge of map-category relative sizes to improve estimates of various probabilities. The fact that maximum likelihood estimates of cell probabilities for the simple random sampling and map category-stratified sampling were identical has permitted a unified treatment of the contingency-table analysis. A rigorous analysis of the effect of sampling independently within map categories is made possible by results for the stratified case. It is noted that such matters as optimal sample size selection for the achievement of a desired level of precision in various estimators are irrelevant, since the estimators derived are valid irrespective of how sample sizes are chosen.

Card, D. H.↗

NASA NTRS1995

On the uncertainty in single molecule fluorescent lifetime and energy emission measurements

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least square methods agree and are optimal when the number of detected photons is large however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67% of those can be noise and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous poisson processes, we derive the exact joint arrival time probably density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. the ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background nose and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

Brown, Emery N.↗

NASA NTRS1996

On the Uncertainty in Single Molecule Fluorescent Lifetime and Energy Emission Measurements

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least squares methods agree and are optimal when the number of detected photons is large, however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67 percent of those can be noise, and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous Poisson processes, we derive the exact joint arrival time probability density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. The ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background noise and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

Brown, Emery N.↗

NASA NTRS2015

The Role of Margin in Link Design and Optimization

Link analysis is a system engineering process in the design, development, and operation of communication systems and networks. Link models that are mathematical abstractions representing the useful signal power and the undesirable noise and attenuation effects (including weather effects if the signal path transverses through the atmosphere) that are integrated into the link budget calculation that provides the estimates of signal power and noise power at the receiver. Then the link margin is applied which attempts to counteract the fluctuations of the signal and noise power to ensure reliable data delivery from transmitter to receiver. (Link margin is dictated by the link margin policy or requirements.) A simple link budgeting approach assumes link parameters to be deterministic values typically adopted a rule-of-thumb policy of 3 dB link margin. This policy works for most S- and X-band links due to their insensitivity to weather effects. But for higher frequency links like Ka-band, Ku-band, and optical communication links, it is unclear if a 3 dB link margin would guarantee link closure. Statistical link analysis that adopted the 2-sigma or 3-sigma link margin incorporates link uncertainties in the sigma calculation. (The Deep Space Network (DSN) link margin policies are 2-sigma for downlink and 3-sigma for uplink.) The link reliability can therefore be quantified statistically even for higher frequency links. However in the current statistical link analysis approach, link reliability is only expressed as the likelihood of exceeding the signal-to-noise ratio (SNR) threshold that corresponds to a given bit-error-rate (BER) or frame-error-rate (FER) requirement. The method does not provide the true BER or FER estimate of the link with margin, or the required signalto-noise ratio (SNR) that would meet the BER or FER requirement in the statistical sense. In this paper, we perform in-depth analysis on the relationship between BER/FER requirement, operating SNR, and coding performance curve, in the case when the channel coherence time of link fluctuation is comparable or larger than the time duration of a codeword. We compute the "true" SNR design point that would meet the BER/FER requirement by taking into account the fluctuation of signal power and noise power at the receiver, and the shape of the coding performance curve. This analysis yields a number of valuable insights on the design choices of coding scheme and link margin for the reliable data delivery of a communication system - space and ground. We illustrate the aforementioned analysis using a number of standard NASA error-correcting codes.

Cheung, K.↗

NASA NTRS1997

Nonlinear Dynamic Analysis of Disordered Bladed-Disk Assemblies

In a effort to address current needs for efficient, air propulsion systems, we have developed some new analytical predictive tools for understanding and alleviating aircraft engine instabilities which have led to accelerated high cycle fatigue and catastrophic failures of these machines during flight. A frequent cause of failure in Jets engines is excessive resonant vibrations and stall flutter instabilities. The likelihood of these phenomena is reduced when designers employ the analytical models we have developed. These prediction models will ultimately increase the nation's competitiveness in producing high performance Jets engines with enhanced operability, energy economy, and safety. The objectives of our current threads of research in the final year are directed along two lines. First, we want to improve the current state of blade stress and aeromechanical reduced-ordered modeling of high bypass engine fans, Specifically, a new reduced-order iterative redesign tool for passively controlling the mechanical authority of shroudless, wide chord, laminated composite transonic bypass engine fans has been developed. Second, we aim to advance current understanding of aeromechanical feedback control of dynamic flow instabilities in axial flow compressors. A systematic theoretical evaluation of several approaches to aeromechanical feedback control of rotating stall in axial compressors has been conducted. Attached are abstracts of two .papers under preparation for the 1998 ASME Turbo Expo in Stockholm, Sweden sponsored under Grant No. NAG3-1571. Our goals during the final year under Grant No. NAG3-1571 is to enhance NASA's capabilities of forced response of turbomachines (such as NASA FREPS). We with continue our development of the reduced-ordered, three-dimensional component synthesis models for aeromechanical evaluation of integrated bladeddisk assemblies (i.e., the disk, non-identical bladeing etc.). We will complete our development of component systems design optimization strategies for specified vibratory stresses and increased fatigue life prediction of assembly components, and for specified frequency margins on the Campbell diagrams of turbomachines. Finally, we will integrate the developed codes with NASA's turbomachinery aeromechanics prediction capability (such as NASA FREPS).

McGee, Oliver G., III↗