Topic
Gaussian process
About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: A general accelerated test model is presented in which failure times and degradation measures can be combined for inference about system lifetime, and some specific models when the drift of the Gaussian process depends on the acceleration variable are discussed in detail.
Abstract: An important problem in reliability and survival analysis is that of modeling degradation together with any observed failures in a life test. Here, based on a continuous cumulative damage approach with a Gaussian process describing degradation, a general accelerated test model is presented in which failure times and degradation measures can be combined for inference about system lifetime. Some specific models when the drift of the Gaussian process depends on the acceleration variable are discussed in detail. Illustrative examples using simulated data as well as degradation data observed in carbon-film resistors are presented.
155 citations
••
07 Oct 2001TL;DR: The EM ofGM can be regarded as a special EM of HMM and the EM algorithm of GMM based on symbols is faster in implementation than the EM algorithms based on samples (or on observation) traditionally.
Abstract: The HMM (hidden Markov model) is a probabilistic model of the joint probability of a collection of random variables with both observations and states. The GMM (Gaussian mixture model) is a finite mixture probability distribution model. Although the two models have a close relationship, they are always discussed independently and separately. The EM (expectation-maximum) algorithm is a general method to improve the descent algorithm for finding the maximum likelihood estimation. The EM of HMM and the EM of GMM have similar formulae. Two points are proposed in this paper. One is that the EM of GMM can be regarded as a special EM of HMM. The other is that the EM algorithm of GMM based on symbols is faster in implementation than the EM algorithm of GMM based on samples (or on observation) traditionally.
155 citations
••
TL;DR: In this article, the authors present a general method to analyze reverberation (or echo) mapping data that simultaneously provides estimates for the black hole mass and for the geometry and dynamics of the broad line region (BLR) in active galactic nuclei (AGNs).
Abstract: We present a general method to analyze reverberation (or echo) mapping data that simultaneously provides estimates for the black hole mass and for the geometry and dynamics of the broad-line region (BLR) in active galactic nuclei (AGNs). While previous methods yield a typical scale size of the BLR or a reconstruction of the transfer function, our method directly infers the spatial and velocity distribution of the BLR from the data, from which a transfer function can be easily derived. Previous echo mapping analysis requires an independent estimate of a scaling factor known as the virial coefficient to infer the mass of the black hole, but this is not needed in our more direct approach. We use the formalism of Bayesian probability theory and implement a Markov Chain Monte Carlo algorithm to obtain estimates and uncertainties for the parameters of our BLR models. Fitting of models to the data requires knowledge of the continuum flux at all times, not just the measured times. We use Gaussian Processes to interpolate and extrapolate the continuum light curve data in a fully consistent probabilistic manner, taking the associated errors into account. We illustrate our method using simple models of BLR geometry and dynamics and show that we can recover the parameter values of our test systems with realistic uncertainties that depend upon the variability of the AGN and the quality of the reverberation mapping observing campaign. With a geometry model we can recover the mean radius of the BLR to within ~0.1 dex random uncertainty for simulated data with an integrated line flux uncertainty of 1.5%, while with a dynamical model we can recover the black hole mass and the mean radius to within ~0.05 dex random uncertainty, for simulated data with a line profile average signal-to-noise ratio of 4 per spectral pixel. These uncertainties do not include modeling errors, which are likely to be present in the analysis of real data, and should therefore be considered as lower limits to the accuracy of the method.
155 citations
••
TL;DR: This result shows that the celebrated Schalkwijk-Kailath coding achieves the feedback capacity for the first-order autoregressive moving-average Gaussian channel, positively answering a long-standing open problem studied by Butman, Tiernan-SchalkWijk, Wolfowitz, Ozarow, Ordentlich, Yang-Kavc¿ic¿-Tatikonda, and others.
Abstract: The feedback capacity of additive stationary Gaussian noise channels is characterized as the solution to a variational problem in the noise power spectral density. When specialized to the first-order autoregressive moving-average noise spectrum, this variational characterization yields a closed-form expression for the feedback capacity. In particular, this result shows that the celebrated Schalkwijk-Kailath coding achieves the feedback capacity for the first-order autoregressive moving-average Gaussian channel, positively answering a long-standing open problem studied by Butman, Tiernan-Schalkwijk, Wolfowitz, Ozarow, Ordentlich, Yang-Kavc?ic?-Tatikonda, and others. More generally, it is shown that a k-dimensional generalization of the Schalkwijk-Kailath coding achieves the feedback capacity for any autoregressive moving-average noise spectrum of order k. Simply put, the optimal transmitter iteratively refines the receiver's knowledge of the intended message. This development reveals intriguing connections between estimation, control, and feedback communication.
155 citations
••
TL;DR: In this paper, the random hypersurface model (RHM) is introduced for estimating a shape approximation of an extended object in addition to its kinematic state, where the shape parameters and measurements are related via a measurement equation that serves as the basis for a Gaussian state estimator.
Abstract: The random hypersurface model (RHM) is introduced for estimating a shape approximation of an extended object in addition to its kinematic state. An RHM represents the spatial extent by means of randomly scaled versions of the shape boundary. In doing so, the shape parameters and the measurements are related via a measurement equation that serves as the basis for a Gaussian state estimator. Specific estimators are derived for elliptic and star-convex shapes.
155 citations