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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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Chapter 1 Discrete Probability Distributions

Mathematics document containing theorems and formulas.

Excerpt: In this chapter, we shall first consider chance experiments with a finite number of possible outcomes !1, !2, . . . , !n. For example, we roll a die and the possible outcomes are 1, 2, 3, 4, 5, 6 corresponding to the side that turns up. We toss a coin with possible outcomes H (heads) and T (tails). It is frequently useful to be able to refer to an outcome of an experiment. For example, we might want to write the mathematical expression which gives the sum of fou...

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Hebrew Pictograms to Latin Letters

Description: Etymology

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Repeatability and Reproducibility Standard Deviations in the Mea...

By: Kacker, R.

Description: Journal of Research of the National Institute of Standards and Technology

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Subjective Prior Probability Distributions and Audit Risk

By: University of Illinois at Urbana-Champaign. College of Commerce and Business Administration

Description: Bibliography: p. 38-41

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Plos One : Using Consensus Bayesian Network to Model the Reactive ...

By: Frank Emmert-streib

Description : Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the Bayesian network from microarray data directly. Although large numbers of Bayesian network learning algorithms have been developed, when applying them to learn Bayesian networks from microarray data, the accuracies are low due to that the databases ...

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Bayesian Network Learning for Natural Hazard Analyses : Volume 14,...

By: C. Riggelsen; F. Scherbaum; O. Korup; K. Vogel

Description: Institute of Earth and Environmental Sciences, University of Potsdam, Germany. Modern natural hazards research requires dealing with several uncertainties that arise from limited process knowledge, measurement errors, censored and incomplete observations, and the intrinsic randomness of the governing processes. Nevertheless, deterministic analyses are still widely used in quantitative hazard assessments despite the pitfall of misestimating the hazard an...

Aguilera, P. A., Fernández, A., Fernández, R., Rumí, R., and Salmerón, A.: Bayesian networks in environmental modelling, Environ. Modell. Softw., 26, 1376–1388, doi:10.1016/j.envsoft.2011.06.004, 2011.; Bayraktarli, Y. Y. and Faber, M. H.: Bayesian probabilistic network approach for managing earthquake risks of cities, Georisk, 5, 2–24, doi:10.1080/174995110036...

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The Application of Bayesian Networks in Natural Hazard Analyses : ...

By: F. Scherbaum; C. Riggelsen; O. Korup; K. Vogel

Description: Institute of Earth and Environmental Sciences, University of Potsdam, Germany. In natural hazards we face several uncertainties due to our lack of knowledge and/or the intrinsic randomness of the underlying natural processes. Nevertheless, deterministic analysis approaches are still widely used in natural hazard assessments, with the pitfall of underestimating the hazard with potentially disastrous consequences.

In this paper we...

Blaser, L., Ohrnberger, M., Riggelsen, C., and Scherbaum, F.: Bayesian Belief Network for Tsunami Warning Decision Support, Lect. Notes. Artif. Int., 5590, 757–768, doi:10.1007/978-3-642-02906-6_65, 2009.; Blaser, L., Ohrnberger, M., Riggelsen, C., Babeyko, A., and Scherbaum, F.: Bayesian networks for tsunami early warning, Geophys. J. Int. 185, 1431–1443, 2011.; Boore, D.: Simulation of ground motion using the s...

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Bayesian Cloud Detection for Meris, Aatsr, and Their Combination :...

By: A. Hollstein; C. Carbajal Henken; J. Fischer; R. Preusker

Description: GeoForschungsZentrum Potsdam (GFZ), Telegrafenberg A17, 14473 Potsdam Germany. A broad range of different of Bayesian cloud detection schemes is applied to measurements from the Medium Resolution Imaging Spectrometer (MERIS), the Advanced Along-Track Scanning Radiometer (AATSR), and their combination. The cloud detection schemes were designed to be numerically efficient and suited for the processing of large numbers of data. Results from the classical an...

Gómez-Chova, L., Camps-Valls, G., Amorós-López, J., Guanter, L., Alonso, L., Calpe, J., and Moreno, J.: New cloud detection algorithm for multispectral and hyperspectral images: Application to ENVISAT/MERIS and PROBA/CHRIS sensors, in: IEEE International Geoscience and Remote Sensing Symposium, IGARSS, 2757–2760, 2006.; Gómez-Chova, L., Camps-Valls, G., Munoz-Marı, J., Calpe, J., and Moreno, J.: Cloud screening methodology for MERIS/AATSR Synergy products, in: Proc. 2nd ...

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Bayesian Cloud Detection for Meris, Aatsr, and Their Combination :...

By: C. Carbajal Henken; R. Preusker; J. Fischer; A. Hollstein

Description: Institute for Space Sciences, Department of Earth Sciences, Freie Universität Berlin, Carl-Heinrich-Becker-Weg 6–10, 12165 Berlin, Germany. A broad range of different of Bayesian cloud detection schemes is applied to measurements from the Medium Resolution Imaging Spectrometer (MERIS), the Advanced Along-Track Scanning Radiometer (AATSR), and their combination. The cloud masks were designed to be numerically efficient and suited for the processing of...

Carbajal Henken, C. K., Lindstrot, R., Preusker, R., and Fischer, J.: FAME-C: cloud property retrieval using synergistic AATSR and MERIS observations, Atmos. Meas. Tech. Discuss., 7, 4909–4947, doi:10.5194/amtd-7-4909-2014, 2014.; Coppo, P., Ricciarelli, B., Brandani, F., Delderfield, J., Ferlet, M., Mutlow, C., Munro, G., Nightingale, T., Smith, D., Bianchi, S., Nicol, P., Kirschstein, S., Hennig, T., Engel, W., Fre...

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Bayesian Trend Analysis for Daily Rainfall Series of Barcelona : V...

By: J. J. Egozcue; R. Tolosana-delgado; M. I. Ortego; M. C. Llasat; J. Gibergans-báguena

Description: Universitat Politècnica de Catalunya, Departament de Matemàtica Aplicada III, Barcelona, Spain. A Point-Over-Threshold approach using a reparameterization of the Generalized Pareto Distribution (GPD) has been used to assess changes in the daily rainfall Barcelona series (1854–2006). A Bayesian approach, considering the suitable scale and physical features of the phenomenon, has been used to look for these alterations. Two different models have been asses...

Grandell, J.: Mixed Poisson processes, Chapman & Hall, London, GB, 268~pp., 1997.; Katz, R W., Parlange, M B., and Naveau, P.: Statistics of extremes in hydrology, Adv. Water Res., 25, 1287–1304, 2002.; Barrera-Escoda, A.: Evolución de los extremos hídricos en Catalunya en los \'ultimos 500 años y su modelización regional. (Evolution of hydric extrems in Catalonia during the last 500 years and its regional modelling), Ph.D. thesis, Universitat de Barcelona, Barcelona, Sp...

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Dimensionality Reduction in Bayesian Estimation Algorithms : Volum...

By: G. W. Petty

Description: Department of Atmospheric and Oceanic Sciences, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA. An idealized synthetic database loosely resembling 3-channel passive microwave observations of precipitation against a variable background is employed to examine the performance of a conventional Bayesian retrieval algorithm. For this dataset, algorithm performance is found to be poor owing to an irreconcilable conflict between the need to fin...

Di Michele, S., Tassa, A., Mugnai, A., Marzano, F., Bauer, P., and Baptista, J.: Bayesian algorithm for microwave-based precipitation retrieval: Description and application to TMI measurements over ocean, IEEE T. Geosci. Remote, 43, 778–791, 2005.; Grecu, M. and Olson, W.: Bayesian estimation of precipitation from satellite passive microwave observations using combined radar-radiometer retrievals, J. Appl. Meteorol. Clim., 45, 416–433, 2006.; Bauer, P., Amayenc, P., Kumm...

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Dimensionality Reduction in Bayesian Estimation Algorithms : Volum...

By: G. W. Petty

Description: Department of Atmospheric and Oceanic Sciences, University of Wisconsin-Madison, USA. An idealized synthetic database loosely resembling 3-channel passive microwave observations of precipitation against a variable background is employed to examine the performance of a conventional Bayesian retrieval algorithm. For this dataset, algorithm performance is found to be poor owing to an irreconcilable conflict between the need to find matches i...

Bauer, P., Amayenc, P., Kummerow, C., and Smith, E.: Over-ocean rainfall retrieval from multisensor data of the Tropical Rainfall Measuring Mission. Part II: Algorithm implementation, J. Atmos. Ocean Tech., 18, 1838–1855, 2001.; Bayes, T. and Price, R.: An {e}ssay towards solving a {p}roblem in the {d}octrine of {c}hance, by the late {R}ev., {M}r. {B}ayes, F. R. S. communicated by {M}r. {P}rices, in a letter to {J}ohn {C}anton, A. M. F. R. S., Philos. T. R. Soc. Lond., 5...

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Technical Note: Approximate Bayesian Parameterization of a Complex...

By: A. Huth; T. Wiegand; C. Dislich; F. Hartig

Description: UFZ – Helmholtz Centre for Environmental Research, Department of Ecological Modelling, Permoserstr. 15, 04318 Leipzig, Germany. Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inv...

Beaumont, M. A.: Approximate Bayesian computation in evolution and ecology, Annu. Rev. Ecol. Evol. Syst., 41, 379–406, doi:10.1146/annurev-ecolsys-102209-144621, 2010.; Blum, M. G. B., Nunes, M. A., Prangle, D., and Sisson, S. A.: A comparative review of dimension reduction methods in approximate Bayesian computation, Stat. Sci., 28, 189–208, 2013.; Bossel, H.: Real-structure process description as the b...

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Analysis of Cosima Spectra: Bayesian Approach : Volume 4, Issue 1 ...

By: T. Lönnberg; K. M. Lehto; J. Rynö; J. Silén; H. Krüger; B. Zaprudin; H. J. Lehto; J. Kissel; M. Hilchenbach

Description: Tuorla Observatory, Department of Physics and Astronomy, University of Turku, Väisäläntie 20, 21500 Piikkiö, Finland. We describe the use of Bayesian analysis methods applied to time-of-flight secondary ion mass spectrometer (TOF-SIMS) spectra. The method is applied to the COmetary Secondary Ion Mass Analyzer (COSIMA) TOF-SIMS mass spectra where the analysis can be broken into subgroups of lines close to integer mass values. The effects of the instrum...

Batir, N.: Very Accurate approximation for the factorial function, J. Math. Inequal., 4, 335–344, 2010.; Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B.: Bayesian Data Analysis, Chapman & Hall, London, 1995.; Glassmeier, K. H., Boehnhardt, H., Koschny, D., Kührt, E., and Richter, I.: The Rosetta mission: flying towards the origin of the Solar System, Space Sci. Rev., 128, 1–21, 2007.; Haario, H., Saksman, E., and Tamminen, J.: An adaptive Metropolis algorithm, ...

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Analysis of Cosima Spectra: Bayesian Approach : Volume 4, Issue 2 ...

By: H. J. Lehto; H. Krüger; J. Kissel; J. Silén; M. Hilchenbach; J. Rynö; T. Lönnberg; K. M. Lehto; B. Zaprudin

Description: Tuorla Observatory, Department of Physics and Astronomy, University of Turku, Väisäläntie 20, 21500 Piikkiö, Finland. We describe the use of Bayesian analysis methods applied to TOF-SIMS spectra. The method finds the probability density functions of measured line parameters (number of lines, and their widths, peak amplitudes, integrated amplitudes, positions) in mass intervals over the whole spectrum. We discuss the results we can expect from this ...

Batir, N.: Very Accurate approximation for the factorial function, J. Math. Inequal., 4, 335–344, 2010.; Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B.: Bayesian Data Analysis, Chapman & Hall, London, 1995.; Haario, H., Saksman, E., and Tamminen, J.: An adaptive Metropolis algorithm, Bernoulli, 7, 223–242, 2001.; Glassmeier, K. H., Boehnhardt, H., Koschny, D., Kührt, E., and Richter, I.: The Rosetta mission: flying towards the origin of the Solar System, Space...

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Objectified Quantification of Uncertainties in Bayesian Atmospheri...

By: F. Chevallier; A. Berchet; J.-l. Bonne; J.-d. Paris; P. Bousquet; I. Pison

Description: Laboratoire des Sciences du Climat et de l'Environnement, CEA-CNRS-UVSQ, IPSL, Gif-sur-Yvette, France. Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. When data pieces are sparse, inversion results ar...

Michalak, A. M., Hirsch, A., Bruhwiler, L., Gurney, K. R., Peters, W., and Tans, P. P.: Maximum likelihood estimation of covariance parameters for Bayesian atmospheric trace gas surface flux inversions, J. Geophys. Res.-Atmos., 110, published online first, doi:10.1029/2005JD005970, 2005.; Olivier, J. G. J., Van Aardenne, J. A., Dentener, F. J., Pagliari, V., Ganzeveld, L. N., and Peters, J. A. H. W.: Recent trends in glo...

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Objectified Quantification of Uncertainties in Bayesian Atmospheri...

By: I. Pison; P. Bousquet; F. Chevallier; J.-l. Bonne; A. Berchet; J.-d. Paris

Description: Laboratoire des Sciences du Climat et de l'Environnement, CEA-CNRS-UVSQ, IPSL, Gif-sur-Yvette, France. Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. At the meso-scale, inversion resul...

Ahmadov, R., Gerbig, C., Kretschmer, R., Koerner, S., Neininger, B., Dolman, A. J., and Sarrat, C.: Mesoscale covariance of transport and CO2 fluxes: evidence from observations and simulations using the WRF-VPRM coupled atmosphere-biosphere model, J. Geophys. Res.-Atmos., 112, D22107, doi:10.1029/2007JD008552, 2007.; Amante, C. and Eakins, B. W.: ETOPO1 1 Arc-minute Global Relief Model: Procedures, Data Source...

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A Bayesian Decision Approach to Rainfall Thresholds Based Flood Wa...

By: A. Libralon; E. Todini; M. L. V. Martina

Description: Dept. of Earth and Geo-Environmental Sciences, Univ. of Bologna, Piazza di Porta San Donato, 1, Bologna, 40126, Italy. Operational real time flood forecasting systems generally require a hydrological model to run in real time as well as a series of hydro-informatics tools to transform the flood forecast into relatively simple and clear messages to the decision makers involved in flood defense. The scope of this paper is to set forth the possibility of pr...

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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 Estimation of Parameters in a Regional Hydrological Model...

By: K. Engeland; L. Gottschalk

Description: Norwegian Water Resources and Energy Directorate, P.O. Box 5091,Majorstua, 0301 Oslo, Norway. This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The ...

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