摘要:

In this paper, we address the problem of frequency estimation when multiple stationary nonsinusoidal resonances oscillate about a trend in nonuniformly sampled data when the number and shape of the resonances are unknown. To solve this problem we postulate a model that relates the resonances to the data and then apply Bayesian probability theory to derive the posterior probability for the number of resonances. The calculation is implemented using simulated annealing in a Markov chain Monte Carlo simulation to draw samples from this posterior distribution. From these samples, using Monte Carlo integration, we compute the posterior probability for the resonance frequencies given the model indicators as well as a number of other posterior distributions of interest. For a single sinusoidal resonance, the Bayesian sufficient statistic is numerically equal to the Lomb‐Scargle periodogram. For a nonsinusoidal resonance this statistic is a straightforward generalization of both the discrete Fourier transform and the Lomb‐Scargle periodogram. Finally, we illustrate the calculations using data taken from two different astrophysical sources. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570531

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Accurate measurement of single‐trial responses is key to a definitive use of complex electromagnetic and hemodynamic measurements in the investigation of brain dynamics. We developed the multiple component, Event‐Related Potential (mcERP) approach to single‐trial response estimation to improve our resolution of dynamic interactions between neuronal ensembles located in different layers within a cortical region and/or in different cortical regions. The mcERP model asserts that multiple components defined as stereotypic waveforms comprise the stimulus‐evoked response and that these components may vary in amplitude and latency from trial to trial.Maximum a posteriori(MAP) solutions for the model are obtained by iterating a set of equations derived from the posterior probability. Our first goal was to use the mcERP algorithm to analyze interactions (specifically latency and amplitude correlation) between responses in different layers within a cortical region. Thus, we evaluated the model by applying the algorithm to synthetic data containing two correlated local components and one independent far‐field component. Three cases were considered: the local components were correlated by an interaction in their single‐trial amplitudes, by an interaction in their single‐trial latencies, or by an interaction in both amplitude and latency. We then analyzed the accuracy with which the algorithm estimated the component waveshapes and the single‐trial parameters as a function of these relationships. Extensions of these analyses to real data are discussed as well as ongoing work to incorporate more detailed prior information. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570532

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

An important emerging issue in fisheries biology is the health of free‐ranging populations of fish, particularly with respect to the prevalence of certain pathogens. For many years, pathologists focused on captive populations and interest was in the presence or absence of certain pathogens, so it was economically attractive to test pooled samples of fish. Recently, investigators have begun to study individual fish prevalence from pooled samples. Estimation of disease prevalence from pooled samples is straightforward when assay sensitivity and specificity are perfect, but this assumption is unrealistic. Here we illustrate the use of a Bayesian approach for estimating disease prevalence from pooled samples when sensitivity and specificity are not perfect. We also focus on diagnostic plots to monitor the convergence of the Gibbs‐sampling‐based Bayesian analysis. The methods are illustrated with a sample data set. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570533

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Estimation of the population mean, and variance is generally carried out using sample estimates. Given normality of the parent population, the distribution of sample mean and sample variance is straightforward. However, when normality cannot be assumed, inference is usually based on approximations through the use of the Central Limit theorem. In addition, the data generated from many real populations may be naturally bounded, i.e. weights, heights, etc. Thus, the unbounded normal probability model may not be appropriate. Utilizing Bayesian analysis and maximum entropy, procedures are developed which produce nonparametric distributions for both the mean and the mean/standard deviation combination. These methods require no assumptions on the form of the parent distribution or the size of the sample and inherently make use of existing bounds. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570534

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Chernoff’s bound binds a tail probability (ie.Pr(X⩾a), wherea⩾EX). Assuming that the distribution ofXisQ, the logarithm of the bound is known to be equal to the value of relative entropy (or minus Kullback‐Leibler distance) forI‐projectionP⁁ofQon a setH≜ {P : EPX = a}. Here, Chernoff’s bound is related to Maximum Likelihood on exponential form and consequently implications for the notion of complementarity are discussed. Moreover, a novel form of the bound is proposed, which expresses the value of the Chernoff’s bound directly in terms of theI‐projection (or generalizedI‐projection). © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570535

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the first problem. Here we explore its use to tackle the second problem. We show how this use of maximum entropy leads to the Bogoliuvob variational principle which we generalize, apply to density functional theory, and use it to develop a mean field theory for classical fluids. Numerical calculations for Argon gas are compared with experimental data. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570536

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three‐dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter‐American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two‐dimensional object and use these estimates to later examine its three‐dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570537

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Onsager’s [1,2] and Prigogine’s [3,4] type minimum principles can be treated for irreversible processes in the frame of classical irreversible thermodynamics (CIT). Results agree with Gyarmati’s [5] integral principle. It is especially worthy to investigate the irreversible heat conduction process for the case of a stationary state for which new quasilinear elliptic type PDEs derived from the principles of minimal energy dissipation and minimum entropy production. Evaluating these PDEs through the aid of the Dirichlet Integral Principle yields the first, second and third type boundary condition solutions for each minimum principle. Here the interpretation of the Dirichlet Integral Principle essentially differs from the usually known “conservative” type approach using Laplace’s equation in conjunction with potential theory. Dissipation potentials of Rayleigh and Onsager type also agree with stated results. The evolution of the process towards a stationary state can be explained with the Glanssdorff‐Prigogine criterion. Boundary conditions of thefourth kinddefine the process of conduction between a single body, or system of bodies and their surroundings. The bodies are assumed to be in perfect contact where and when the surfaces in contact have the same temperature. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570538

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

We examine a first order differential equation with respect to time used to describe magnetic islands in magnetically confined plasmas. The free parameters of this equation are obtained by employing Bayesian probability theory. Additionally, a typical Bayesian change point is solved in the process of obtaining the data. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570539

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Most learning algorithms rely on the assumption that the input training data contains no noise or uncertainty. However, when collecting data under an identification experiment it may not be possible to avoid noise when measuring the input. The use of the errors‐in‐variable model to describe the data in this case is more appropriate. However, learning based on maximum likelihood estimation is far from straightforward because of the high number of unknown parameters. In this paper, to overcome the problems associated to the estimation with high number of unknown parameters, the nonlinear errors‐in‐variable estimation problem is treated under a Bayesian formulation. In order to compute the necessary maximuma posterioriestimate we use the restoration maximization algorithms where the true but unknown training inputs are treated as hidden variables. In order to accelerate the convergence of the algorithm a modified version of the stochastic EM algorithm is proposed. A simulation example on learning a nonlinear parametric function and an example on learning feedforward neural networks are presented to illustrate the effectiveness of the proposed learning method. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1570540

出版商:AIP    

年代:1903

数据来源: AIP