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Results for “bayes theorem”

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 NTRS2003

Comparison of two weighted integration models for the cueing task: linear and likelihood

In a task in which the observer must detect a signal at two locations, presenting a precue that predicts the location of a signal leads to improved performance with a valid cue (signal location matches the cue), compared to an invalid cue (signal location does not match the cue). The cue validity effect has often been explained with a limited capacity attentional mechanism improving the perceptual quality at the cued location. Alternatively, the cueing effect can also be explained by unlimited capacity models that assume a weighted combination of noisy responses across the two locations. We compare two weighted integration models, a linear model and a sum of weighted likelihoods model based on a Bayesian observer. While qualitatively these models are similar, quantitatively they predict different cue validity effects as the signal-to-noise ratios (SNR) increase. To test these models, 3 observers performed in a cued discrimination task of Gaussian targets with an 80% valid precue across a broad range of SNR's. Analysis of a limited capacity attentional switching model was also included and rejected. The sum of weighted likelihoods model best described the psychophysical results, suggesting that human observers approximate a weighted combination of likelihoods, and not a weighted linear combination.

NASA Program Biomedical Research and Countermeasur↗
NASA NTRS2003

Bayesian estimation of dose thresholds

An example is described of Bayesian estimation of radiation absorbed dose thresholds (subsequently simply referred to as dose thresholds) using a specific parametric model applied to a data set on mice exposed to 60Co gamma rays and fission neutrons. A Weibull based relative risk model with a dose threshold parameter was used to analyse, as an example, lung cancer mortality and determine the posterior density for the threshold dose after single exposures to 60Co gamma rays or fission neutrons from the JANUS reactor at Argonne National Laboratory. The data consisted of survival, censoring times and cause of death information for male B6CF1 unexposed and exposed mice. The 60Co gamma whole-body doses for the two exposed groups were 0.86 and 1.37 Gy. The neutron whole-body doses were 0.19 and 0.38 Gy. Marginal posterior densities for the dose thresholds for neutron and gamma radiation were calculated with numerical integration and found to have quite different shapes. The density of the threshold for 60Co is unimodal with a mode at about 0.50 Gy. The threshold density for fission neutrons declines monotonically from a maximum value at zero with increasing doses. The posterior densities for all other parameters were similar for the two radiation types.

NASA Discipline Radiation Health↗
NASA NTRS1999

Brain segmentation and the generation of cortical surfaces

This paper describes methods for white matter segmentation in brain images and the generation of cortical surfaces from the segmentations. We have developed a system that allows a user to start with a brain volume, obtained by modalities such as MRI or cryosection, and constructs a complete digital representation of the cortical surface. The methodology consists of three basic components: local parametric modeling and Bayesian segmentation; surface generation and local quadratic coordinate fitting; and surface editing. Segmentations are computed by parametrically fitting known density functions to the histogram of the image using the expectation maximization algorithm [DLR77]. The parametric fits are obtained locally rather than globally over the whole volume to overcome local variations in gray levels. To represent the boundary of the gray and white matter we use triangulated meshes generated using isosurface generation algorithms [GH95]. A complete system of local parametric quadratic charts [JWM+95] is superimposed on the triangulated graph to facilitate smoothing and geodesic curve tracking. Algorithms for surface editing include extraction of the largest closed surface. Results for several macaque brains are presented comparing automated and hand surface generation. Copyright 1999 Academic Press.

NASA Discipline Neuroscience↗
NASA NTRS1997

A mathematical model of diurnal variations in human plasma melatonin levels

Studies in animals and humans suggest that the diurnal pattern in plasma melatonin levels is due to the hormone's rates of synthesis, circulatory infusion and clearance, circadian control of synthesis onset and offset, environmental lighting conditions, and error in the melatonin immunoassay. A two-dimensional linear differential equation model of the hormone is formulated and is used to analyze plasma melatonin levels in 18 normal healthy male subjects during a constant routine. Recently developed Bayesian statistical procedures are used to incorporate correctly the magnitude of the immunoassay error into the analysis. The estimated parameters [median (range)] were clearance half-life of 23.67 (14.79-59.93) min, synthesis onset time of 2206 (1940-0029), synthesis offset time of 0621 (0246-0817), and maximum N-acetyltransferase activity of 7.17(2.34-17.93) pmol x l(-1) x min(-1). All were in good agreement with values from previous reports. The difference between synthesis offset time and the phase of the core temperature minimum was 1 h 15 min (-4 h 38 min-2 h 43 min). The correlation between synthesis onset and the dim light melatonin onset was 0.93. Our model provides a more physiologically plausible estimate of the melatonin synthesis onset time than that given by the dim light melatonin onset and the first reliable means of estimating the phase of synthesis offset. Our analysis shows that the circadian and pharmacokinetics parameters of melatonin can be reliably estimated from a single model.

NASA Discipline Number 70-10↗
NASA NTRS1992

The statistical analysis of circadian phase and amplitude in constant-routine core-temperature data

Accurate estimation of the phases and amplitude of the endogenous circadian pacemaker from constant-routine core-temperature series is crucial for making inferences about the properties of the human biological clock from data collected under this protocol. This paper presents a set of statistical methods based on a harmonic-regression-plus-correlated-noise model for estimating the phases and the amplitude of the endogenous circadian pacemaker from constant-routine core-temperature data. The methods include a Bayesian Monte Carlo procedure for computing the uncertainty in these circadian functions. We illustrate the techniques with a detailed study of a single subject's core-temperature series and describe their relationship to other statistical methods for circadian data analysis. In our laboratory, these methods have been successfully used to analyze more than 300 constant routines and provide a highly reliable means of extracting phase and amplitude information from core-temperature data.

NASA Discipline Regulatory Physiology↗
NASA NTRS2004

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Neural Networks (Computer)↗
NASA NTRS2004

A Bayesian approach to tracking patients having changing pharmacokinetic parameters

This paper considers the updating of Bayesian posterior densities for pharmacokinetic models associated with patients having changing parameter values. For estimation purposes it is proposed to use the Interacting Multiple Model (IMM) estimation algorithm, which is currently a popular algorithm in the aerospace community for tracking maneuvering targets. The IMM algorithm is described, and compared to the multiple model (MM) and Maximum A-Posteriori (MAP) Bayesian estimation methods, which are presently used for posterior updating when pharmacokinetic parameters do not change. Both the MM and MAP Bayesian estimation methods are used in their sequential forms, to facilitate tracking of changing parameters. Results indicate that the IMM algorithm is well suited for tracking time-varying pharmacokinetic parameters in acutely ill and unstable patients, incurring only about half of the integrated error compared to the sequential MM and MAP methods on the same example.

Bayes Theorem↗
NASA NTRS2004

Molecular evidence for a terrestrial origin of snakes

Biologists have debated the origin of snakes since the nineteenth century. One hypothesis suggests that snakes are most closely related to terrestrial lizards, and reduced their limbs on land. An alternative hypothesis proposes that snakes are most closely related to Cretaceous marine lizards, such as mosasaurs, and reduced their limbs in water. A presumed close relationship between living monitor lizards, believed to be close relatives of the extinct mosasaurs, and snakes has bolstered the marine origin hypothesis. Here, we show that DNA sequence evidence does not support a close relationship between snakes and monitor lizards, and thus supports a terrestrial origin of snakes.

Environment↗
NASA NTRS2004

Perceptual learning through optimization of attentional weighting: human versus optimal Bayesian learner

Human performance in visual detection, discrimination, identification, and search tasks typically improves with practice. Psychophysical studies suggest that perceptual learning is mediated by an enhancement in the coding of the signal, and physiological studies suggest that it might be related to the plasticity in the weighting or selection of sensory units coding task relevant information (learning through attention optimization). We propose an experimental paradigm (optimal perceptual learning paradigm) to systematically study the dynamics of perceptual learning in humans by allowing comparisons to that of an optimal Bayesian algorithm and a number of suboptimal learning models. We measured improvement in human localization (eight-alternative forced-choice with feedback) performance of a target randomly sampled from four elongated Gaussian targets with different orientations and polarities and kept as a target for a block of four trials. The results suggest that the human perceptual learning can occur within a lapse of four trials (<1 min) but that human learning is slower and incomplete with respect to the optimal algorithm (23.3% reduction in human efficiency from the 1st-to-4th learning trials). The greatest improvement in human performance, occurring from the 1st-to-2nd learning trial, was also present in the optimal observer, and, thus reflects a property inherent to the visual task and not a property particular to the human perceptual learning mechanism. One notable source of human inefficiency is that, unlike the ideal observer, human learning relies more heavily on previous decisions than on the provided feedback, resulting in no human learning on trials following a previous incorrect localization decision. Finally, the proposed theory and paradigm provide a flexible framework for future studies to evaluate the optimality of human learning of other visual cues and/or sensory modalities.

Non-NASA Center↗
NASA NTRS2023

Efficient Calibration of Expensive Computational Models

Accounting for uncertainty when calibrating expensive computational models is a common challenge faced by scientists and engineers. Often Bayesian techniques are adopted to estimate a probability density function over the model parameters given noisy empirical data. The methods used to perform this type of probabilistic calibration are computationally prohibitive in that they require a large number of evaluations of the expensive model. In these cases, surrogate modeling -- that is, using a fast-to-evaluate, lower fidelity stand-in for the original computational model -- may be the only option to alleviate this computational burden. However, the upfront cost of generating training data to build a surrogate model can itself be expensive. As such, it is important to be judicious when selecting training points at which the full-fidelity model is evaluated. Here, an active learning approach is proposed that enables efficient selection of training points using approximate samples of the calibrated parameter probability density function. In this way, the training points can be concentrated in regions where the calibration algorithm requires high model accuracy.

active learning↗
NASA NTRS1994

Data Analysis with Graphical Models: Software Tools

Probabilistic graphical models (directed and undirected Markov fields, and combined in chain graphs) are used widely in expert systems, image processing and other areas as a framework for representing and reasoning with probabilities. They come with corresponding algorithms for performing probabilistic inference. This paper discusses an extension to these models by Spiegelhalter and Gilks, plates, used to graphically model the notion of a sample. This offers a graphical specification language for representing data analysis problems. When combined with general methods for statistical inference, this also offers a unifying framework for prototyping and/or generating data analysis algorithms from graphical specifications. This paper outlines the framework and then presents some basic tools for the task: a graphical version of the Pitman-Koopman Theorem for the exponential family, problem decomposition, and the calculation of exact Bayes factors. Other tools already developed, such as automatic differentiation, Gibbs sampling, and use of the EM algorithm, make this a broad basis for the generation of data analysis software.

Buntine, Wray L.↗