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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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Estimates of European Emissions of Methyl Chloroform Using a Bayes...

By: M. Maione; U. Giostra; F. Furlani; J. Arduini; D. R. Blake; S. Reimann; A. Stohl; F. Graziosi; M. K. Vollmer; P. Bonasoni; S. J. O'Doherty; S. A. Montzka; X. Fang

Description: Department of Basic Science and Foundations, University of Urbino, Urbino, Italy. Methyl chloroform (MCF) is a man-made chlorinated solvent contributing to the destruction of stratospheric ozone and is controlled under the Montreal Protocol on Substances that Deplete the Ozone Layer. Long-term, high-frequency observations of MCF carried out at three European sites show a constant decline of the background mixing ratios of MCF. However, we observe p...

Barletta, B., Meinardi, S., Simpson, I. J., Rowland, F. S., Chan, C.-Y., Wang, X., Zou, S., Chan, L. Y., and Blake, D. R.: Ambient halocarbon mixing ratios in 45 Chinese cities, Atmos. Environ., 40, 7706–7719, 2006.; Coll, I., Rousseau, C., Barletta, B., Meinard, S., and Blake, D. R.: Evaluation of an urban NMHC emission inventory by measurements and impact on CTM results, Atmos. Environ., 44, 3843–3855, 2010.; Eckhardt, S., Prata, A. J., Seibert, P., Stebel, K., and Sto...

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Estimates of European Emissions of Methyl Chloroform Using a Bayes...

By: M. Maione; U. Giostra; F. Furlani; J. Arduini; D. R. Blake; S. Reimann; A. Stohl; F. Graziosi; M. K. Vollmer; P. Bonasoni; S. J. O'Doherty; S. A. Montzka; X. Fang

Description: Department of Basic Science and Foundations, University of Urbino, Urbino, Italy. Methyl chloroform (MCF) is a man-made chlorinated solvent contributing to the destruction of stratospheric ozone and is controlled under the Montreal Protocol on Substances that Deplete the Ozone Layer. Long-term, high-frequency observations of MCF carried out at three European sites show a constant decline of the background mixing ratios of MCF. However, we observe p...

Barletta, B., Meinardi, S., Simpson, I. J., Rowland, F. S., Chan, C.-Y., Wang, X., Zou, S., Chan, L. Y., and Blake, D. R.: Ambient halocarbon mixing ratios in 45 Chinese cities, Atmos. Environ., 40, 7706–7719, 2006.; Coll, I., Rousseau, C., Barletta, B., Meinard, S., and Blake, D. R.: Evaluation of an urban NMHC emission inventory by measurements and impact on CTM results, Atmos. Environ., 44, 3843–3855, 2010.; Eckhardt, S., Prata, A. J., Seibert, P., Stebel, K., and Sto...

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Application of the Bayesian Calibration Methodology for the Parame...

By: Y. Conrad; N. Fohrer

Description: Department of Hydrology and Water Resources Management, Ecology Centre at the University of Kiel, Kiel, Germany. This study provides results for the optimization strategy of highly parameterized models, especially with a high number of unknown input parameters and joint problems in terms of sufficient parameter space. Consequently, the uncertainty in model parameterization and measurements must be considered when highly variable nitrogen losses, e.g. N l...

Büchter, M.: Nitratauswaschungen unter Grünland und Silomais in Monokultur auf sandigen Böden Norddeutschlands. Ph.D. thesis, University of Kiel, Germany, Schriftenreihe des Instituts für Pflanzenbau und Pflanzenzüchtung – Grünland und Futterbau/Ökologischer Landbau (in German, English summary), 30, 1–116, 2003.; Casper, M.: Die Identifikation hydrologischer Prozesse im Einzugsgebiet des Dürreychbaches (Nordschwarzwald). Mitteilungen des Instituts für Wasserwirtschaft un...

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Wave-height Hazard Analysis in Eastern Coast of Spain - Bayesian A...

By: V. Pawlowsky-glahn; M. I. Ortego; J. J. Egozcue

Description: Dept. Matemàtica Aplicada III, U. Politècnica de Catalunya, Spain. Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated us...

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Hierarchical Bayesian Space-time Interpolation Versus Spatio-tempo...

By: G. Spoeck; J. Pilz; I. Hussain

Description: Department of Statistics, University of Klagenfurt, Klagenfurt, Austria. The restrictions of the analysis of natural processes which are observed at any point in space or time to a purely spatial or purely temporal domain may cause loss of information and larger prediction errors. Moreover, the arbitrary combinations of purely spatial and purely temporal models may not yield valid models for the space-time domain. For such processes the variation can be...

Brown, P. J., Le, N. D., and Zidek, J. V.: Inference for a covariance matrix, Aspects of Uncertainty: A Tribute to DV Lindley, edited by: Freeman, P. R. and Smith, A. F. M.: Chichester, Wiley, 77–92, 1994.; Chiles, J. P. and Delfiner, P.: Geostatistics, Modeling Spatial Uncertainty, Wiley-Interscience, 1999.; Christakos, G.: Random Field Models in Earth Sciences, Academic Press, 1992.; Christakos, G., Bogaert, P., and Serre, M. L.: it Temporal Gis, Advanced Functions for...

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Mobile Sensor Network Noise Reduction and Re-calibration Using Bay...

By: W. Zhu; Y. Tang; Y. Xiang

Description: College of Information Engineering, Zhejiang University of Technology, Hangzhou, China. People are becoming increasingly interested in mobile air quality sensor network applications. By eliminating the inaccuracies caused by spatial and temporal heterogeneity of pollutant distributions, this method shows great potentials in atmosphere researches. However, such system usually suffers from the problem of sensor noises and drift. For the sensing systems to ...

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Using Bayesian Model Averaging (Bma) to Calibrate Probabilistic Su...

By: G. A. Vakili; I. Soltanzadeh; M. Azadi

Description: Institute of Geophysics, University of Tehran, Tehran, Iran. Using Bayesian Model Averaging (BMA), an attempt was made to obtain calibrated probabilistic numerical forecasts of 2-m temperature over Iran. The ensemble employs three limited area models (WRF, MM5 and HRM), with WRF used with five different configurations. Initial and boundary conditions for MM5 and WRF are obtained from the National Centers for Environmental Prediction (NCEP) Global Foreca...

Bao, L., Gneiting, T., Grimit, E. P., Guttorp, P., and Raftery, A. E.: Bias Correction and Bayesian Model Averaging for Ensemble Forecasts of Surface Wind Direction, Mon. Weather Rev., 138, 1811–1821, 2010.; Dempster, A., Laird, N., and Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc., Series B, 39(1), 1–38, 1977.; Eckel, F. A. and Mass, C. F.: Aspects of effective mesoscale, short-range ensemble forecasting, Wea. Forecasting, 20,...

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Modeling the Vertical Soil Organic Matter Profile Using Bayesian P...

By: C. Beer; T. Wutzler; J. Kattge; M. Schrumpf; B. Kruijt; I. Schöning; M. C. Braakhekke; P. Kabat; M. Reichstein; B. Ahrens; M. R. Hoosbeek

Description: Max Planck Institute for Biogeochemistry, P.O. Box 100164, 07701 Jena, Germany. The vertical distribution of soil organic matter (SOM) in the profile may constitute an important factor for soil carbon cycling. However, the formation of the SOM profile is currently poorly understood due to equifinality, caused by the entanglement of several processes: input from roots, mixing due to bioturbation, and organic matter leaching. In this study we quantified t...

Janssens, I. A., Sampson, D. A., Curiel-Yuste, J., Carrara, A., and Ceulemans, R.: The carbon cost of fine root turnover in a Scots pine forest, Forest Ecol. Manag., 168, 231–240, 2002.; Jenkinson, D. S. and Coleman, K.: The turnover of organic carbon in subsoils. Part 2. Modelling carbon turnover, Eur. J. Soil Sci., 59, 400–413, 2008.; Jobbagy, E. G. and Jackson, R. B.: The vertical distribution of soil organic carbon and its relation to climate and vegetation, Ecol. Ap...

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

By: T. Wiegand; A. Huth; 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 many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistic...

Beaumont, M. A.: Approximate Bayesian computation in evolution and ecology, Annu. Rev. Ecol. Evol. Syst., 41, 379–406, 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 basis of understanding ecosystems and their development, Ecol. Model., 63, 261–276, 1992.; Bugmann, H. K. M.: A ...

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Bayesian Inversions of a Dynamic Vegetation Model at Four European...

By: E. Laloy; B. Tychon; L. François; J. Minet

Description: Université de Liège, Arlon Campus Environnement, Avenue de Longwy 185, 6700 Arlon, Belgium. Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB (CARbon Assimilation In the Biosphere) dynamic vegetation model (DVM) with 10 unknown parameters, using the DREAM(ZS) (DiffeRential Evolution Adaptive Metropolis) Markov chain Monte Carlo (MCMC) sampler. We focus on comparing model inversions, consider...

Ammann, C., Flechard, C. R., Leifeld, J., Neftel, A., and Fuhrer, J.: The carbon budget of newly established temperate grassland depends on management intensity, Agr. Ecosyst. Environ., 121, 5–20, doi:10.1016/j.agee.2006.12.002, 2007.; Aubinet, M., Vesala, T., and Papale, D. (Eds.): Eddy Covariance: A Practical Guide to Measurement and Data Analysis, Springer, 173–209, 2012.; Ball, Woodrow, I., and Berry, J.: A Mod...

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Bayesian Inversions of a Dynamic Vegetation Model in Four European...

By: L. François; E. Laloy; B. Tychon; J. Minet

Description: Université de Liège, Arlon Campus Environnement, Avenue de Longwy 185, 6700 Arlon, Belgium. Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB dynamic vegetation model (DVM) with ten unknown parameters, using the DREAM(ZS) Markov chain Monte Carlo (MCMC) sampler. We compare model inversions considering both homoscedastic and heteroscedastic eddy covariance residual errors, with varianc...

Ammann, C., Flechard, C. R., Leifeld, J., Neftel, A., and Fuhrer, J.: The carbon budget of newly established temperate grassland depends on management intensity, Agr. Ecosyst. Environ., 121, 5–20, doi:10.1016/j.agee.2006.12.002, 2007.; Aubinet, M., Vesala, T., and Papale, D. (Eds.): Eddy Covariance: A Practical Guide to Measurement and Data Analysis, Springer, 2012.; Ball, J., Woodrow, I., and Berry, J.: A model pr...

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Modeling the Vertical Soil Organic Matter Profile Using Bayesian P...

By: I. Schöning; J. Kattge; C. Beer; M. Reichstein; P. Kabat; M. Schrumpf; M. R. Hoosbeek; M. C. Braakhekke; B. Kruijt; T. Wutzler

Description: Max Planck Institute for Biogeochemistry, P.O. Box 100164, 07701 Jena, Germany. The vertical distribution of soil organic matter (SOM) in the profile may constitute a significant factor for soil carbon cycling. However, the formation of the SOM profile is currently poorly understood due to equifinality, caused by the entanglement of several processes: input from roots, mixing due to bioturbation, and organic matter leaching. In this study we quantified ...

Appleby, P. G. and Oldfield, F.: The calculation of lead-210 dates assuming a constant rate of supply of unsupported 210Pb to the sediment, Catena, 5, 1–8, 1978.; Arai, H. and Tokuchi, N.: Factors contributing to greater soil organic carbon accumulation after afforestation in a Japanese coniferous plantation as determined by stable and radioactive isotopes, Geoderma, 157, 243–251, 2010.; Baisden, W. T., Amundson, R., Brenner, D. L., Cook, A. C., Kendall, C., a...

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Technical Note: Probabilistically Constraining Proxy Age–depth Mod...

By: M. P. Tingley; J. P. Werner

Description: Department for Earth Science and Bjerknes Centre for Climate Research, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway. Reconstructions of the late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurements of tree rings, ice cores, and varved lake sediments. Considerable advances could be achieved if time-uncertain proxies were able to be included within these multiproxy recons...

Altekar, G., Dwarkadas, S., Huelsenbeck, J. P., and Ronquist, F.: Parallel Metropolis coupled Markov chain Monte Carlo for Bayesian phylogenetic inference, Bioinformatics, 20, 407–415, 2004.; Anchukaitis, K. J. and Tierney, J. E.: Identifying coherent spatiotemporal modes in time-uncertain proxy paleoclimate records, Clim. Dynam., 41, 1291–1306, 2013.; Banerjee, S., Carlin, B. P., and Gelfand, A. E.: Hierarchical Modeling and Analysis for Spatial Data, Chapman & Hall/CRC...

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Bayesian Parameter Estimation and Interpretation for an Intermedia...

By: M. N. Evans; K. J. Anchukaitis; S. E. Tolwinski-ward

Description: Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, Boulder, CO, USA. We present a Bayesian model for estimating the parameters of the VS-Lite forward model of tree-ring width for a particular chronology and its local climatology. The scheme also provides information about the uncertainty of the parameter estimates, as well as the model error in representing the observed proxy time series. By inferring VS-Lite's pa...

Boreux, J.-J., Naveau, P., Guin, O., Perreault, L., and Bernier, J.: Extracting a common high frequency signal from Northern Quebec black spruce tree-rings with a Bayesian hierarchical model, Clim. Past, 5, 607–613, doi:10.5194/cp-5-607-2009, 2009.; Carrer, M. and Urbinati, C.: Long-term change in the sensitivity of tree-ring growth to climate forcing in Larix decidua, New Phytol., 170, 861–872, 2006.; Chib, S. a...

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Technical Note: Probabilistically Constraining Proxy Age–depth Mod...

By: J. P. Werner; M. P. Tingley

Description: Department for Earth Science and Bjerknes Centre for Climate Research, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway. Reconstructions of late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurement on tree rings, ice cores, and varved lake sediments. Considerable advances may be achievable if time uncertain proxies could be included within these multiproxy reconstructions, a...

Altekar, G., Dwarkadas, S., Huelsenbeck, J. P., and Ronquist, F.: Parallel Metropolis coupled Markov chain Monte Carlo for Bayesian phylogenetic inference, Bioinformatics, 20, 407–415, doi:10.1093/bioinformatics/btg427, 2004.; Anchukaitis, K. J. and Tierney, J. E.: Identifying coherent spatiotemporal modes in time-uncertain proxy paleoclimate records, Clim. Dynam., 41, 1291–1306, 2013.; Banerjee, S., Carlin, B. ...

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Bayesian Parameter Estimation and Interpretation for an Intermedia...

By: S. E. Tolwinski-ward; M. N. Evans; K. J. Anchukaitis

Description: Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, Boulder, CO, USA. We present a Bayesian model for estimating the parameters of the VS-Lite forward model of tree-ring width. The scheme also provides information about the uncertainty of the parameter estimates, as well as the uncertainty of VS-Lite itself. By inferring VS-Lite's parameters for synthetically-generated ring-width series at several h...

Misson, L.: {MAIDEN}: a model for analyzing ecosystem processes in dendroecology, Can. J. Forest Res., 34, 874–887, doi:10.1139/x03-252, 2004.; Misson, L., Rathgerber, C., and Guiot, J.: Dendroecological analysis of climatic effects on Quercus petraea and Pinus halepensis radial growth using the process-based MAIDEN model, Can. J. Forest Res., 34, 888–898, doi:10.1139/x03-253, 200...

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Re-evaluating Luminescence Burial Doses and Bleaching of Fluvial D...

By: N. Hobo; H. Middelkoop; A. J. Versendaal; A. C. Cunningham; J. Wallinga; B. Makaske

Description: School of Geosciences, University of the Witwatersrand, Johannesburg, South Africa. The optically stimulated luminescence (OSL) signal from fluvial sediment often contains a remnant from the previous deposition cycle, leading to a partially bleached equivalent-dose distribution. Although identification of the burial dose is of primary concern, the degree of bleaching could potentially provide insights into sediment transport processes. However, comparis...

Arnold, L. J., Roberts, R. G., Galbraith, R. F., and DeLong, S. B.: A revised burial dose estimation procedure for optical dating of youngand modern-age sediments, Quatern. Geochronol., 4, 306–325, doi:10.1016/j.quageo.2009.02.017, 2009.; Bailey, R. M. and Arnold, L. J.: Statistical modelling of single grain quartz De distributions and an assessment of procedures for estimating burial dose, Quaternary Sci. Rev., ...

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Bayesian Calibration of the Thermosphere-ionosphere Electrodynamic...

By: A. Maute; A. D. Richmond; J. Rougier; S. Guillas; C. D. Linkletter

Description: Department of Statistical Science & Aon Benfield UCL Hazard Research Centre, University College London, London, UK. In this paper, we demonstrate a procedure for calibrating a complex computer simulation model having uncertain inputs and internal parameters, with application to the NCAR Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM). We compare simulated magnetic perturbations with observations at two ground locations for var...

Bayarri, M. J., Berger, J. O., Cafeo, J., Garcia-Donato, G., Liu, F., Palomo, J., Parthasarathy, R. J., Paulo, R., Sacks, J., and Walsh, D.: Computer model validation with functional output, Ann. Stat., 35, 1874–1906, 2007.; Fang, T., Richmond, A., Liu, J., Maute, A., Lin, C., Chen, C., and Harper, B.: Model simulation of the equatorial electrojet in the Peruvian and Philippine sectors, J. Atmos. Sol.-Terr. Phy., 70, 2203–2211, 2008.; Fesen, C. G., Crowley, G., Roble, R....

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Bayesian Calibration of the Thermosphere-ionosphere Electrodynamic...

By: A. Maute; J. Rougier; S. Guillas; C. D. Linkletter; A. D. Richmond

Description: Department of Statistical Science & Aon Benfield UCL Hazard Research Centre, University College London, UK. In this paper, we demonstrate a procedure for calibrating a complex computer simulation model having uncertain inputs and internal parameters, with application to the NCAR Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM). We compare simulated magnetic perturbations with observations at two ground locations for various com...

Higdon, D., Gattiker, J., Williams, B., and Rightley, M.: Computer model calibration using high-dimensional output, J. Am. Stat. Assoc., 103, 570–583, 2008.; Bayarri, M. J., Berger, J. O., Cafeo, J., Garcia-Donato, G., Liu, F., Palomo, J., Parthasarathy, R. J., Paulo, R., Sacks, J., and Walsh, D.: Computer model validation with functional output, Ann. Statist., 35, 1874–1906, 2007.; Fang, T., Richmond, A., Liu, J., Maute, A., Lin, C., Chen, C., and Harper, B.: Model simu...

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A User-friendly Forest Model with a Multiplicative Mathematical St...

By: D. Gianelle; M. Van Oijen; M. Sottocornola; D. Cameron; F. Magnani; M. Bagnara

Description: Fondazione Edmund Mach, Research and Innovation Centre, Sustainable Agro-ecosystems and Bioresources Department, via E. Mach, 1, S. Michele all'Adige (TN), Italy. Forest models are being increasingly used to study ecosystem functioning, through the reproduction of carbon fluxes and productivity in very different forests all over the world. Over the last two decades, the need for simple and easy to use models for practical applications, characterized ...

Allen, R. G., Pereira, L. S., Raes, D., and Smith, M.: Crop evapotranspiration guidelines for computing crop water requirements, Irrig. Drain. Pap. 65, 300 pp., United Nations Food Agric. Organ., Rome, Italy, 1998.; Bagnara, M., Sottocornola, M., Cescatti, A., Minerbi, S., Montagnani, L., Gianelle, D., and Magnani, F.: Bayesian optimization of a light use efficiency model for the estimation of daily gross primary productivity in a range of Italian forest ecosystems, Ecol...

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