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Probability Distribution (2,263 Books)


In probability theory and statistics, a probability distribution identifies either the probability of each value of a random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous). The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

 
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Coupled Hydrogeophysical Parameter Estimation Using a Sequential B...

By: H. Vereecken; J. A. Huisman; J. Rings

Description: ICG 4 – Agrosphere, Forschungszentrum Jülich, Germany. Coupled hydrogeophysical methods infer hydrological and petrophysical parameters directly from geophysical measurements. Widespread methods do not explicitly recognize uncertainty in parameter estimates. Therefore, we apply a sequential Bayesian framework that provides updates of state, parameters and their uncertainty whenever measurements become available. We have coupled a hydrological and an ele...

Archie, G. E.: The electrical resitivity log as an aid in determining some reservoir characteristics, American Institute of Mining and Metallurgical Engineers, 55–62, 1942.; Arulampalam, M. S., Maskell, S., Gordon, N., and Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking, IEEE T. Signal Proces., 50, 174–188, 2002.; Binley, A., Winship, P., West, L. J., Pokar, M., and Middleton, R.: Seasonal variation of moisture content in uns...

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Bayesian Discharge Rating Curves Based on B-spline Smoothing Funct...

By: S. M. Gardarsson; A. Snorrason; B. Hrafnkelsson; K. M. Ingimarsson

Description: Faculty of Industrial Engineering, Mechanical Engineering and Computer Sciences, University of Iceland, Iceland. Discharge in rivers is commonly estimated by the use of a rating curve constructed from pairs of measured water elevations and discharges at a specific location. The Bayesian approach has been successfully applied to estimate discharge rating curves that are based on the standard power-law. In this paper the standard power-law model is extende...

Clarke, R.: Uncertainty in the estimation of mean annual flood due to rating-curve indefinition, J. Hydrol., 222, 185–190, 1999.; Arnason, S.: Estimating nonlinear hydrological rating curves and discharge using the Bayesian approach., Masters thesis, Faculty of Engineering, University of Iceland, 2005.; Di Baldassarre, G. and Montanari, A.: Uncertainty in river discharge observations: a quantitative analysis, Hydrol. Earth Syst. Sci., 13, 913–921, 2009.; Gelman, A., Carl...

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Brief Communication Evaluating European Coastal Evolution Using Ba...

By: M. L. Yates; G. Le Cozannet

Description: BRGM, 3 Avenue Claude Guillemin, BP 36009, 45060 Orleans, France. The coastal zone is a complex environment in which a variety of forcing factors interact causing shoreline evolution. Coastal managers seek to predict coastal evolution and to identify regions vulnerable to erosion. Here, a Bayesian network is developed to identify the primary factors influencing decadal-scale shoreline evolution of European coasts and to reproduce the observed evolution ...

Bayes, T.: An Essay towards Solving a Problem in the Doctrine of Chances, Phil. Trans. Roy. Soc. London, 53, 370–418, doi:10.1098/rstl.1763.0053, 1763.; Berger, J. O.: Bayesian Analysis: A Look at Today and Thoughts of Tomorrow, J. Am. Stat. Assoc., 95, 1269–1276, doi:10.2307/2669768, 2000.; Castelle, B., Bonneton, P., Dupuis, H., and Sénéchal, N.: Double bar beach dynamics...

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Bayesian Hierarchical Modelling of North Atlantic Windiness : Volu...

By: O. N. Breivik; E. Vanem

Description: Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway. Extreme weather conditions represent serious natural hazards to ship operations and may be the direct cause or contributing factor to maritime accidents. Such severe environmental conditions can be taken into account in ship design and operational windows can be defined that limits hazardous operations to less extreme conditions. Nevertheless, possible changes in th...

Caires, S., Swail, V. R., and Wang, X. L.: Projection and Analysis of Extreme Wave Climate, J. Climate, 19, 5581–5605, 2006.; Bader, J., Mesquita, M. D. S., Hodges, K. I., Keenlyside, N., Østerhus, S., and Miles, M.: A review on {N}orthern {H}emisphere sea-ice, storminess and the {N}orth {A}tlantic {O}scillation: Observations and projected changes, Atmos. Res., 101, 809–834, 2011.; Beauchamp, J. J. and Olson, J. S.: Corrections for Bias in Regression Estimates After Loga...

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Using Bayesian Methods for the Parameter Estimation of Deformation...

By: K. Felsenstein; M. Yalcinkaya; E. Tanir

Description: Vienna University of Technology, Institute of Geodesy and Geophysics, 1040 Vienna, Austria. In order to investigate the deformations of an area or an object, geodetic observations are repeated at different time epochs and then these observations of each period are adjusted independently. From the coordinate differences between the epochs the input parameters of a deformation model are estimated. The decision about the deformation is given by appropriate ...

Albertella, A., Cazzaniga, N., Sansò, F., Sacerdote, F., Crespi, M., and Luzietti, L.: Deformations detection by a Bayesian approach: prior information representation and testing criteria definition, ISGDM2005 – IAG Symposium volume n 131, 2005.; Caspary, W. F.: Concept of network and deformation analysis, Monograph 11, School of Geomatics Engineering, The University of New South Wales, Australia, 2000.; Felsenstein, K.: Mathematische methoden für die interpretation von ...

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Bayesian Modeling and Significant Features Exploration in Wavelet ...

By: F. Godtliebsen; D. V. Divine

Description: Department of Mathematics and Statistics, Faculty of Science, University of Troms\o, 9037, Norway. This study proposes and justifies a Bayesian approach to modeling wavelet coefficients and finding statistically significant features in wavelet power spectra. The approach utilizes ideas elaborated in scale-space smoothing methods and wavelet data analysis. We treat each scale of the discrete wavelet decomposition as a sequence of independent random variab...

Berger, J. (Ed.): Statistical decision theory and Bayesian analysis, Springer Verlag, 1985.; Box, E., Jenkins, G., and Reinsel, G.: Time series analysis: Forecasting and control, Prentice-Hall, Englewood Cliffs, 1994.; Chaudhuri, P. and Marron, J.: SiZer for exploration of structures in curves, J. Am. Statist. Assoc., 94, 807–823, 1999.; Dansgaard, W., Johnsen, S., Clausen, H., Dahl-Jensen, D., Gundestrup, N., Hammer, C., Hvidberg, C., Steffensen, J., Sveinbjornsdottir, ...

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Bayesian Optimization for Tuning Chaotic Systems : Volume 1, Issue...

By: A. Ilin; H. Järvinen; J. Hakkarainen; A. Solonen; E. Oja; M. Abbas

Description: Aalto University, School of Science, Espoo, Finland. In this work, we consider the Bayesian optimization (BO) approach for tuning parameters of complex chaotic systems. Such problems arise, for instance, in tuning the sub-grid scale parameterizations in weather and climate models. For such problems, the tuning procedure is generally based on a performance metric which measures how well the tuned model fits the data. This tuning is often a...

Annan, J. and Hargreaves, J.: Efficient estimation and ensemble generation in climate modelling, Philos. T. R. Soc. A, 365, 2077–2088, 2007.; Bibov, A.: Variational Kalman filter data assimilation for two-layer Quasi-Geostrophic model, M.S. thesis, Lappeenranta University of Technology, Finland, 2011.; Box, G. E. P. and Draper, N. R.: Empirical model-building and response surfaces, John Wiley & Sons, Oxford, England, 1987.; Boyle, P.: Gaussian Processes for Regression an...

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Efficient Bayesian Inference for Arfima Processes : Volume 2, Issu...

By: N. W. Watkins; R. B. Gramacy; C. L. E. Franzke; T. Graves

Description: URS Corporation, London, UK. Many geophysical quantities, like atmospheric temperature, water levels in rivers, and wind speeds, have shown evidence of long-range dependence (LRD). LRD means that these quantities experience non-trivial temporal memory, which potentially enhances their predictability, but also hampers the detection of externally forced trends. Thus, it is important to reliably identify whether or not a system exhibits LRD. In this paper ...

Abry, P., Flandrin, P., Taqqu, M. S., and Veitch, D.: Self-similarity and long-range dependence through the wavelet lens, in: Theory and Applications of Long-Range Dependence, Birkhäuser, Cambridge, MA, USA, 527–556, 2003.; Adenstedt, R. K.: On large-sample estimation for the mean of a stationary random sequence, Ann. Stat., 2, 1095–1107, 1974.; Barnes, J. A. and Allan, D. W.: A statistical model of flicker noise, Proc. IEEE, 54, 176–178, 1966.; Beran, J.: Statistics for...

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Bayesian Modeling of Nonstationarity in Normal and Lognormal Proce...

By: Velez Arocho, Jorge Ivan, 1947

Civilization

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Plos One : Bayesian Detection of Causal Rare Variants Under Poster...

By: Kai Wang

Description : Identification of causal rare variants that are associated with complex traits poses a central challenge on genome-wide association studies. However, most current research focuses only on testing the global association whether the rare variants in a given genomic region are collectively associated with the trait. Although some recent work, e.g., the Bayesian risk index method, have tried to address this problem, it is unclear whether the causal rare variant...

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Plos One : Source Reconstruction Accuracy of Meg and Eeg Bayesian ...

By: Jérémie Bourdon

Description : Electro- and magnetoencephalography allow for non-invasive investigation of human brain activation and corresponding networks with high temporal resolution. Still, no correct network detection is possible without reliable source localization. In this paper, we examine four different source localization schemes under a common Variational Bayesian framework. A Bayesian approach to the Minimum Norm Model (MNM), an Empirical Bayesian Beamformer (EBB) and two it...

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Plos Computational Biology : Risk-sensitivity in Bayesian Sensorim...

By: Jordi Grau-moya

Description : Information processing in the nervous system during sensorimotor tasks with inherent uncertainty has been shown to be consistent with Bayesian integration. Bayes optimal decision-makers are, however, risk-neutral in the sense that they weigh all possibilities based on prior expectation and sensory evidence when they choose the action with highest expected value. In contrast, risk-sensitive decision-makers are sensitive to model uncertainty and bias their de...

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Plos Computational Biology : Bayesian Phylogeography Finds Its Roo...

By: Philippe Lemey

Description : As a key factor in endemic and epidemic dynamics, the geographical distribution of viruses has been frequently interpreted in the light of their genetic histories. Unfortunately, inference of historical dispersal or migration patterns of viruses has mainly been restricted to model-free heuristic approaches that provide little insight into the temporal setting of the spatial dynamics. The introduction of probabilistic models of evolution, however, offers uni...

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Plos Genetics : a Flexible Bayesian Model for Studying Gene– Envir...

By: Nicholas J. Schork

Description : An important follow-up step after genetic markers are found to be associated with a disease outcome is a more detailed analysis investigating how the implicated gene or chromosomal region and an established environment risk factor interact to influence the disease risk. The standard approach to this study of gene–environment interaction considers one genetic marker at a time and therefore could misrepresent and underestimate the genetic contribution to the ...

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Plos One : a Bayesian Interpretation of the Particle Swarm Optimiz...

By: Cedric Sueur

Description : Particle swarm optimization is a popular method for solving difficult optimization problems. There have been attempts to formulate the method in formal probabilistic or stochastic terms (e.g. bare bones particle swarm) with the aim to achieve more generality and explain the practical behavior of the method. Here we present a Bayesian interpretation of the particle swarm optimization. This interpretation provides a formal framework for incorporation of prior...

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Plos Computational Biology : Collective Animal Behavior from Bayes...

By: Pérez-escudero Alfonso

Description : Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is mainly based on empirical fits to observations, with less emphasis in obtaining first-principles approaches that allow their derivation. Here we show that patterns of collective decisions can be derived from the basic ability of animals to make probabilistic est...

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Plos Computational Biology : Approximate Bayesian Computation, Vol...

By: Mikael Sunnaker

Description : Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for...

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Plos Computational Biology : Bayesian Inference of Spatial Organiz...

By: Ming Hu

Description : Knowledge of spatial chromosomal organizations is critical for the study of transcriptional regulation and other nuclear processes in the cell. Recently, chromosome conformation capture (3C) based technologies, such as Hi-C and TCC, have been developed to provide a genome-wide, three-dimensional (3D) view of chromatin organization. Appropriate methods for analyzing these data and fully characterizing the 3D chromosomal structure and its structural variation...

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Plos One : a Novel Bayesian Seamless Phase I, Volume 8

By: Wenge Guo

Description : This paper proposes a novel bayesian phase I/II design featuring using a hybrid mTPI method in phase I for targeting the MTD level and a randomization allocation schema for adaptively assigning patients to desirable doses in phase II. The mechanism of simultaneously escalating dose in phase I and expanding promising doses to phase II is inherited from a design proposed in literature. Extensive simulation studies indicate that our proposed design can vastly ...

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AutoClass: A Bayesian classification system

By: Cheeseman, Peter; Self, Matthew; Stutz, John; Taylor, Will; Freeman, Do; Kelly, James

Supplemental catalog subcollection information: NASA Publication Collection; Astrophysics and Technical Documents; A program, AutoClass 2, for automatically discovering (inducing) classes from a database is described that is based on a Bayesian statistica

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