Measuring Uncertainty in Spatial Data via Bayesian Melding
|
|
- Milo Craig
- 6 years ago
- Views:
Transcription
1 Measuring Uncertainty in Spatial Data via Bayesian Melding Matt Falk Queensland University of Technology (QUT) Joint work with Robert Denham (NRW) and Kerrie Mengersen (QUT) Data Driven and Physically-based Models for Characterization of Processes in Hydrology, Hydraulics, Oceanography and Climate Change, Tuesday 22 Jan 2008
2 Research project called Measuring and Presenting Uncertainty in Complex Natural Resource Monitoring Programs funded by an Australian Research Council grant Focus on Whole of Catchment Water Quality Modelling I am looking at a particular element of the modelling (RUSLE) and trying to characterize the uncertainty within this element The aim is to then apply to the whole model
3 Outline of the Presentation Aims of my research Definition of Uncertainty Measuring Uncertainty - Bayesian Melding Bayesian Melding applied to the Universal Soil Loss Equation
4 Aims of my research Devise methods to measure uncertainty in complex natural resource modelling with an emphasis on water quality Incorporate spatial image data to uncertainty models Ensure methodology is statistically sound Provide uncertainty estimates to assist decision and policy makers Presenting the measured uncertainty
5 Definition of Uncertainty Uncertainty is the inability to determine the true state of affairs of a system - Risk Modeling, Assessment, and Management (Haimes, 2004, p. 237) Components of Uncertainty: Variability - inherent heterogeneity of the process. Temporal Spatial Individual - all other sources Incomplete Knowledge Model Uncertainty - arising from the choice of the particular model used. Parameter Uncertainty - lack of knowledge about empirical quantities in the model. Decision Uncertainty - modelling choices that reflect decisionmaker judgement.
6 Definition of Uncertainty In the context of natural resource models, we choose not to allocate uncertainty to different components because: It s difficult to say whether variability or incomplete knowledge is causing the uncertainty, especially when the true value which may not be available It doesn t matter since we re interested in predictive uncertainty rather than the components of uncertainty Once we find total uncertainty we can then identify which inputs are the main contributors
7 Measuring Uncertainty - Bayesian Melding Background Stems from the Bayesian Synthesis approach (Raftery et al., JASA, 1995), shown by Wolpert to be unsatisfactory Revised by Poole and Raftery (JASA, 2000) to give Bayesian Melding Motivated by work for the International Whaling Commission Takes account of all uncertainty information regarding a models inputs and outputs and places analysis on a sound statistical base So we have four sources of information 1. Knowledge about inputs Prior distribution of inputs q 1 (θ) 2. Data about inputs Likelihood of inputs L 1 (θ) 3. Knowledge about outputs Prior distribution of outputs q 2 (φ) 4. Data about outputs Likelihood of outputs L 2 (φ)
8 Bayesian Melding - Theory Bayesian Melding is then combining the sources of information together M is a model that maps inputs θ to an output φ, i.e. φ = M(θ) M and q 1 (θ) together induce a prior on the output φ, q1 (φ) Estimate q1 (φ) by simulation and nonparametric kernel density estimation Now there are two priors on the output; q 2 (φ) and q1 (φ) which are pooled giving q [φ] (φ) q 1(φ) α q 2 (φ) 1 α Find a pooled prior on the inputs q [θ] (θ) by inverting q [φ] (φ) (complicated when M is non-invertible) Sample from the Bayesian Melding posterior distribution π [θ] (θ) q [θ] (θ)l 1 (θ)l 2 (M(θ)) using the Sampling Importance Resampling algorithm (SIR) Inference about φ occurs by observing the distribution of φ = M(θ), using a Monte Carlo sample
9 Simulating the Posterior Distribution Posterior distribution of θ, π [θ] (θ), simulated using a modified SIR algorithm For each pixel: 1. From the prior q 1 (θ), draw k sample values {θ 1,..., θ k }. 2. For each sampled θ i, obtain φ i = M(θ i ). 3. Estimate q1 (φ), the resulting induced distribution of φ, using nonparametric density estimation. 4. Compute importance sampling weights w i = ( ) q2 (M(θ i )) 1 α q1 (M(θ L 1 (θ i )L 2 (M(θ i )) (1) i)) 5. Draw a sample of l values from the discrete distribution with values θ i and probabilities proportional to w i.
10 The Revised Universal Soil Loss Equation RUSLE (Renard et.al, US Dept. of Ag., 1997) calculates hillslope erosion where: A = R K L S C P (2) A = mean annual soil loss (t/ha.yr) R = rainfall erosivity factor K = soil erodibility factor L = hillslope length factor S = hillslope steepness factor C = ground cover factor P = supporting practice factor, assumed to be 1 due to lack of information Bayesian Melding is appropriate for uncertainty in USLE because we have expert knowledge of the uncertainty regarding inputs and output.
11 RUSLE - Case Study Area near Emerald (Central Queensland) approx 14 sq km R Factor K Factor L Factor S Factor C Factor Soil Loss (A)
12 Bayesian Melding applied to RUSLE - Differences Inputs and Outputs are spatial GIS images - makes things a little different. No data for either the inputs or output, so no likelihoods w i = ( ) 1 α q2 (M(θ i )) q1 (M(θ i)) All available uncertainty information is conveyed through the prior distributions on inputs and output
13 Bayesian Melding - Application to the USLE Prior Specification for Rainfall (R) Factor R Factor is the average annual sum of individual storm erosion index values EI 30, where E is the total storm kinetic energy per unit area and I 30 is the maximum 30 minute rainfall. Estimated using an equation by u and Rosewell (Aust. J. of Soil Res., 1996). Estimated and actual R Factors compared Prior R i Gamma(r i 2 /se r, r i /se r ) where r i is the mean value from the given surface for pixel i and se r is the standard error from the fitted linear model. Model Pluvio
14 Bayesian Melding - Application to the USLE Prior Specification for Soil Erodibility (K) Factor K Factor is the soil loss rate for a specific soil on a clean tilled fallow plot which is metres in length and on a 9% slope Not feasible to gather enough data for each soil type; large amount of uncertainty Study area contains one soil type, so prior is generated by fitting a shifted beta distribution to all K factors K 0.13 Beta(7.8428, ) Frequency K Factor
15 Bayesian Melding - Application to the USLE Prior Specification for Slope Length (L) and Slope Steepness (S) Factors L Factor is the ratio of soil loss from a particular field slope length, to that from a slope of length metres, with all other conditions identical. S Factor is the ratio of soil loss from a particular field slope gradient, to that from a slope with a gradient of 9%, with all other conditions identical. L and S Factors are calculated from a Digital Elevation Model (DEM) using the raster calculator in ArcGIS Coarse DEM compared to high resolution DEM Linear model fitted and standard error observed
16 Bayesian Melding - Application to the USLE Prior Specification for Slope Length (L) and Slope Steepness (S) Factors S Factor obs L Factor 0.0 obs 2.0 Original DEM is resampled many times assuming pixels are from a N(xi, se) and a new surface fitted L and S Factors are calculated for new DEMs and compared with original L and S Factors Factors are binned and a function is fitted to the 95% confidence interval; Beta distributions are fitted with the same mean and 95% confidence interval mean mean
17 Bayesian Melding - Application to the USLE Prior Specification for Cover (C) Factor C Factor is the ratio of soil loss from an area subject to a specified cover to an otherwise identical area subject to tilled continuous fallow The Bare Ground Index is generated from satellite imagery and used in calculation of C Factor Beta distributions are fitted with the same mean and 95% confidence interval (red line) ObservedBare Mean
18 Bayesian Melding - Application to the USLE Prior Specification for output (mean annual soil loss, A) Lu et. al. (Aust. J. Soil Res., 2003) report on std error comparing modelled with measured soil loss at 3.84 t/ha.yr A N(A i, 3.84), truncated at 0 because soil loss cannot be negative For example, A 33 = Density A
19 Bayesian Melding - Application to the USLE Example results for one pixel Histograms of the posterior samples Solid lines represent the premodel distributions R Gamma( , ) Density Density K 0.13 Beta(7.8428, ) R Factor K Factor L Beta(0.4952, ) Density Density S 3.4 Beta(9.0560, ) L Factor S Factor C Beta(1.2527, ) Density Density A N(6.8843, 3.84) C Factor A
20 Bayesian Melding - Application to the USLE Uncertainty Map - uncertainty measured as the standard deviation of the Bayesian Melding posterior distribution of the output Uncertainty Map
21 Bayesian Melding - Application to the USLE Input Factor Uncertainty Maps R Uncertainty Map K Uncertainty Map L Uncertainty Map S Uncertainty Map C Uncertainty Map
22 Bayesian Melding - Application to the USLE Comparison to analysis completed without a prior on the output Uncertainty Map Uncertainty Map (No Prior on Output)
23 Acknowledgments Uncertainty Map Thanks to Robert Denham, Kerrie Mengersen and all at NRW Remote Sensing Centre
Review Using the Geographical Information System and Remote Sensing Techniques for Soil Erosion Assessment
Polish J. of Environ. Stud. Vol. 19, No. 5 (2010), 881-886 Review Using the Geographical Information System and Remote Sensing Techniques for Soil Erosion Assessment Nuket Benzer* Landscape Architecture
More informationBayesian Melding. Assessing Uncertainty in UrbanSim. University of Washington
Bayesian Melding Assessing Uncertainty in UrbanSim Hana Ševčíková University of Washington hana@stat.washington.edu Joint work with Paul Waddell and Adrian Raftery University of Washington UrbanSim Workshop,
More informationThomas Koellner 1, Adrienne Grét-Regamey 1, Miguel Marchamalo 2, and Raffaele Vignola 3. ETH Zurich, Switzerland. Polytecnica Madrid, Spain
Thomas Koellner 1, Adrienne Grét-Regamey 1, Miguel Marchamalo 2, and Raffaele Vignola 3 1 ETH Zurich, Switzerland 2 Polytecnica Madrid, Spain 3 CATIE, Costa Rica Our concept of human-environment systems
More informationBayesian Methods for Estimating the Reliability of Complex Systems Using Heterogeneous Multilevel Information
Statistics Preprints Statistics 8-2010 Bayesian Methods for Estimating the Reliability of Complex Systems Using Heterogeneous Multilevel Information Jiqiang Guo Iowa State University, jqguo@iastate.edu
More informationUncertainty analysis of nonpoint source pollution modeling:
2013 SWAT Conference Uncertainty analysis of nonpoint source pollution modeling: An important implication for Soil and Water Assessment Tool Professor Zhenyao Shen 2013-07-17 Toulouse Contents 1 2 3 4
More informationCopyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and
Copyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and private study only. The thesis may not be reproduced elsewhere
More informationEffect of land cover / use change on soil erosion assessment in Dubračina catchment (Croatia)
European Water 57: 171-177, 2017. 2017 E.W. Publications Effect of land cover / use change on soil erosion assessment in Dubračina catchment (Croatia) N. Dragičević *, B. Karleuša and N. Ožanić Faculty
More informationSoil Erosion Calculation using Remote Sensing and GIS in Río Grande de Arecibo Watershed, Puerto Rico
Soil Erosion Calculation using Remote Sensing and GIS in Río Grande de Arecibo Watershed, Puerto Rico Alejandra M. Rojas González Department of Civil Engineering University of Puerto Rico at Mayaguez.
More informationLINKING GULLY EROSION AND RAINFALL EROSIVITY
LINKING GULLY EROSION AND RAINFALL EROSIVITY M.A. Campo *, J. Casalí and R. Giménez Department of Projects and Rural Engineering Public University of Navarre Pamplona, Spain. Introduction Gully erosion
More informationBayesian Quadrature: Model-based Approximate Integration. David Duvenaud University of Cambridge
Bayesian Quadrature: Model-based Approimate Integration David Duvenaud University of Cambridge The Quadrature Problem ˆ We want to estimate an integral Z = f ()p()d ˆ Most computational problems in inference
More informationSpatial Inference of Nitrate Concentrations in Groundwater
Spatial Inference of Nitrate Concentrations in Groundwater Dawn Woodard Operations Research & Information Engineering Cornell University joint work with Robert Wolpert, Duke Univ. Dept. of Statistical
More informationSediment yield estimation from a hydrographic survey: A case study for the Kremasta reservoir, Western Greece
Sediment yield estimation from a hydrographic survey: A case study for the Kremasta reservoir, Western Greece 5 th International Conference Water Resources Management in the Era of Transition,, Athens,
More informationConservation Planning evaluate land management alternatives to reduce soil erosion to acceptable levels. Resource Inventories estimate current and
Conservation Planning evaluate land management alternatives to reduce soil erosion to acceptable levels. Resource Inventories estimate current and projected erosion levels and their impact on natural resource
More informationPotential Impacts of Climate Change on Soil Erosion Vulnerability Across the Conterminous U.S.
Potential Impacts of Climate Change on Soil Erosion Vulnerability Across the Conterminous U.S. Catalina Segura 1, Ge Sun 2, Steve McNulty 2, and Yang Zhang 1 1 2 1 Soil Erosion Natural process by which
More informationSTAT 499/962 Topics in Statistics Bayesian Inference and Decision Theory Jan 2018, Handout 01
STAT 499/962 Topics in Statistics Bayesian Inference and Decision Theory Jan 2018, Handout 01 Nasser Sadeghkhani a.sadeghkhani@queensu.ca There are two main schools to statistical inference: 1-frequentist
More informationA Basic Introduction to Geographic Information Systems (GIS) ~~~~~~~~~~
A Basic Introduction to Geographic Information Systems (GIS) ~~~~~~~~~~ Rev. Ronald J. Wasowski, C.S.C. Associate Professor of Environmental Science University of Portland Portland, Oregon 3 September
More informationUSE OF RADIOMETRICS IN SOIL SURVEY
USE OF RADIOMETRICS IN SOIL SURVEY Brian Tunstall 2003 Abstract The objectives and requirements with soil mapping are summarised. The capacities for different methods to address these objectives and requirements
More informationCHAPTER VII FULLY DISTRIBUTED RAINFALL-RUNOFF MODEL USING GIS
80 CHAPTER VII FULLY DISTRIBUTED RAINFALL-RUNOFF MODEL USING GIS 7.1GENERAL This chapter is discussed in six parts. Introduction to Runoff estimation using fully Distributed model is discussed in first
More informationEstimation of sediment yield using Remote Sensing (RS) and Geographic Information System (GIS) technique
Serials Publications Estimation of sediment yield using Remote Sensing (RS)... National Academy of Agricultural Science (NAAS) Rating : 3. 03 Estimation of sediment yield using Remote Sensing (RS) and
More informationAN ASSESSMENT OF THE IMPACT OF RETENTION PONDS
AN ASSESSMENT OF THE IMPACT OF RETENTION PONDS FOR SEDIMENT TRAPPING IN THE ADA CREEK AND LONGWOOD COVE USING REMOTELY SENSED DATA AND GIS ANALYSIS Sudhanshu Sekhar Panda Associate Professor, GIS/Env.
More informationReducing Uncertainty in Sediment Yield Through Improved Representation of Land Cover: Application to Two Sub-catchments of the Mae Chaem, Thailand
Reducing Uncertainty in Sediment Yield Through Improved Representation of Land Cover: Application to Two Sub-catchments of the Mae Chaem, Thailand Hartcher, M.G. 1 and Post, D. A. 1,2 1 CSIRO Land and
More informationModeling Surface Runoff Path and Soil Erosion in Catchment Area of Hanp River of District Kabeerdham, CG, INDIA, Using GIS
International Journal of Scientific and Research Publications, Volume 6, Issue 5, May 2016 645 Modeling Surface Runoff Path and Soil Erosion in Catchment Area of Hanp River of District Kabeerdham, CG,
More informationDevelopment of single rain storm erosivity models in central plateau and hill zones for Chitrakoot district
218; 7(2): 2961-2965 E-ISSN: 2278-4136 P-ISSN: 2349-8234 JPP 218; 7(2): 2961-2965 Received: 5-1-218 Accepted: 6-2-218 KN Singh A Dalai RR Mohanty Instructor (Agril. Engg.) of Agro Polytechnic Centre, Rourkela,
More informationStatistical Inference for Food Webs
Statistical Inference for Food Webs Part I: Bayesian Melding Grace Chiu and Josh Gould Department of Statistics & Actuarial Science CMAR-Hobart Science Seminar, March 6, 2009 1 Outline CMAR-Hobart Science
More informationUsing MODIS imagery to validate the spatial representation of snow cover extent obtained from SWAT in a data-scarce Chilean Andean watershed
Using MODIS imagery to validate the spatial representation of snow cover extent obtained from SWAT in a data-scarce Chilean Andean watershed Alejandra Stehr 1, Oscar Link 2, Mauricio Aguayo 1 1 Centro
More informationGIS Application in Landslide Hazard Analysis An Example from the Shihmen Reservoir Catchment Area in Northern Taiwan
GIS Application in Landslide Hazard Analysis An Example from the Shihmen Reservoir Catchment Area in Northern Taiwan Chyi-Tyi Lee Institute of Applied Geology, National Central University, No.300, Jungda
More informationEmpirical Risk Minimization is an incomplete inductive principle Thomas P. Minka
Empirical Risk Minimization is an incomplete inductive principle Thomas P. Minka February 20, 2001 Abstract Empirical Risk Minimization (ERM) only utilizes the loss function defined for the task and is
More informationCurve Fitting Re-visited, Bishop1.2.5
Curve Fitting Re-visited, Bishop1.2.5 Maximum Likelihood Bishop 1.2.5 Model Likelihood differentiation p(t x, w, β) = Maximum Likelihood N N ( t n y(x n, w), β 1). (1.61) n=1 As we did in the case of the
More informationPATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 13: SEQUENTIAL DATA
PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 13: SEQUENTIAL DATA Contents in latter part Linear Dynamical Systems What is different from HMM? Kalman filter Its strength and limitation Particle Filter
More informationSpatial Variability of Satellite Derived Rainfall Erosivity Factors (R-Factors) for a Watershed near Allahabad
Vol. 11, pp. 71-78 (2011) Journal of Agricultural Physics ISSN 0973-032X http://www.agrophysics.in Research Article Spatial Variability of Satellite Derived Rainfall Erosivity Factors (R-Factors) for a
More informationInternational Journal of Advance Engineering and Research Development
Scientific Journal of Impact Factor (SJIF): 4.72 International Journal of Advance Engineering and Research Development Volume 4, Issue 5, May -2017 Watershed Delineation of Purna River using Geographical
More informationImplementing a process-based decision support tool for natural resource management - the GeoWEPP example
Implementing a process-based decision support tool for natural resource management - the GeoWEPP example Chris S. Renschler a and Dennis C. Flanagan b a Dept. of Geography, University at Buffalo - The
More informationWhat Is Water Erosion? Aren t they the same thing? What Is Sediment? What Is Sedimentation? How can Sediment Yields be Minimized?
Jerald S. Fifield, Ph.D. CISEC HydroDynamics Incorporated Parker, CO 303-841-0377 Aren t they the same thing? What Is Sediment? Soil particles deposited or suspended in water or air The process of depositing
More informationClassification of Erosion Susceptibility
GEO327G: GIS & GPS Applications in Earth Sciences Classification of Erosion Susceptibility Denali National Park, Alaska Zehao Xue 12 3 2015 2 TABLE OF CONTENTS 1 Abstract... 3 2 Introduction... 3 2.1 Universal
More informationEVALUATION OF MIGRATION OF HEAVY METAL CONTAINING SEDIMENT RESULTING FROM WATER EROSION USING A GEO- INFORMATION MODEL
EVALUATION OF MIGRATION OF HEAVY METAL CONTAINING SEDIMENT RESULTING FROM WATER EROSION USING A GEO- INFORMATION MODEL János Tamás, Elza Kovács University of Debrecen, Centre of Agricultural Sciences Department
More informationOther Noninformative Priors
Other Noninformative Priors Other methods for noninformative priors include Bernardo s reference prior, which seeks a prior that will maximize the discrepancy between the prior and the posterior and minimize
More informationEfficient Likelihood-Free Inference
Efficient Likelihood-Free Inference Michael Gutmann http://homepages.inf.ed.ac.uk/mgutmann Institute for Adaptive and Neural Computation School of Informatics, University of Edinburgh 8th November 2017
More informationComputer Emulation With Density Estimation
Computer Emulation With Density Estimation Jake Coleman, Robert Wolpert May 8, 2017 Jake Coleman, Robert Wolpert Emulation and Density Estimation May 8, 2017 1 / 17 Computer Emulation Motivation Expensive
More informationGIS model & modeling
GIS model & modeling Model : a simplified representation of a phenomenon or a system. GIS modeling : the use of GIS in the process of building models with spatial data. Basic requirement in modeling :
More informationRelative soil vulnerability and patterns of erosion during the muddy floods of on the South Downs, Sussex, UK
Relative soil vulnerability and patterns of erosion during the muddy floods of 2000-2001 on the South Downs, Sussex, UK Hazel Faulkner, Jose Luis Ruiz & John Boardman South Downs East Sussex Due to a long
More informationThe Jackknife-Like Method for Assessing Uncertainty of Point Estimates for Bayesian Estimation in a Finite Gaussian Mixture Model
Thai Journal of Mathematics : 45 58 Special Issue: Annual Meeting in Mathematics 207 http://thaijmath.in.cmu.ac.th ISSN 686-0209 The Jackknife-Like Method for Assessing Uncertainty of Point Estimates for
More informationURBAN WATERSHED RUNOFF MODELING USING GEOSPATIAL TECHNIQUES
URBAN WATERSHED RUNOFF MODELING USING GEOSPATIAL TECHNIQUES DST Sponsored Research Project (NRDMS Division) By Prof. M. GOPAL NAIK Professor & Chairman, Board of Studies Email: mgnaikc@gmail.com Department
More informationDEVELOPMENT AND APPLICATION OF HIGH- RESOLUTION GIS-BASED ATLAS TO ENHANCE WATERSHED MANAGEMENT IN THE PHILIPPINES
DEVELOPMENT AND APPLICATION OF HIGH- RESOLUTION GIS-BASED ATLAS TO ENHANCE WATERSHED MANAGEMENT IN THE PHILIPPINES Nathaniel C. Bantayan Institute of Renewable Natural Resources College of Forestry and
More informationSediment- yield estimation, by M-PSIAC method in a GIS environment, case study:jonaghn river sub basin(karun basin)
Sediment- yield estimation, by M-PSIAC method in a GIS environment, case study:jonaghn river sub basin(karun basin) Yavari-shahla *,Khdabakhsh-Saeed,Mohseni-Hasan, Rezai- Khalil Corresponding author: a
More informationThe Generalized Likelihood Uncertainty Estimation methodology
CHAPTER 4 The Generalized Likelihood Uncertainty Estimation methodology Calibration and uncertainty estimation based upon a statistical framework is aimed at finding an optimal set of models, parameters
More informationStable Limit Laws for Marginal Probabilities from MCMC Streams: Acceleration of Convergence
Stable Limit Laws for Marginal Probabilities from MCMC Streams: Acceleration of Convergence Robert L. Wolpert Institute of Statistics and Decision Sciences Duke University, Durham NC 778-5 - Revised April,
More informationSoil erosion susceptibility and coastal evolution: examples in southern New Caledonia
Pacific Island Countries GIS /RS User Conference Soil erosion susceptibility and coastal evolution: examples in southern New Caledonia Pascal DUMAS et Olivier COHEN University of New-Caledonia (EA 4242/
More informationNatural hazards in Glenorchy Summary Report May 2010
Natural hazards in Glenorchy Summary Report May 2010 Contents Glenorchy s hazardscape Environment setting Flood hazard Earthquakes and seismic hazards Hazards Mass movement Summary Glossary Introduction
More informationEagle Creek Post Fire Erosion Hazard Analysis Using the WEPP Model. John Rogers & Lauren McKinney
Eagle Creek Post Fire Erosion Hazard Analysis Using the WEPP Model John Rogers & Lauren McKinney Columbia River Gorge at Risk: Using LiDAR and GIS-based predictive modeling for regional-scale erosion susceptibility
More informationParameter Estimation in the Spatio-Temporal Mixed Effects Model Analysis of Massive Spatio-Temporal Data Sets
Parameter Estimation in the Spatio-Temporal Mixed Effects Model Analysis of Massive Spatio-Temporal Data Sets Matthias Katzfuß Advisor: Dr. Noel Cressie Department of Statistics The Ohio State University
More informationStatistical Rock Physics
Statistical - Introduction Book review 3.1-3.3 Min Sun March. 13, 2009 Outline. What is Statistical. Why we need Statistical. How Statistical works Statistical Rock physics Information theory Statistics
More informationGaussian Process Approximations of Stochastic Differential Equations
Gaussian Process Approximations of Stochastic Differential Equations Cédric Archambeau Centre for Computational Statistics and Machine Learning University College London c.archambeau@cs.ucl.ac.uk CSML
More informationStrong Lens Modeling (II): Statistical Methods
Strong Lens Modeling (II): Statistical Methods Chuck Keeton Rutgers, the State University of New Jersey Probability theory multiple random variables, a and b joint distribution p(a, b) conditional distribution
More informationImperfect Data in an Uncertain World
Imperfect Data in an Uncertain World James B. Elsner Department of Geography, Florida State University Tallahassee, Florida Corresponding author address: Dept. of Geography, Florida State University Tallahassee,
More informationSummary Description Municipality of Anchorage. Anchorage Coastal Resource Atlas Project
Summary Description Municipality of Anchorage Anchorage Coastal Resource Atlas Project By: Thede Tobish, MOA Planner; and Charlie Barnwell, MOA GIS Manager Introduction Local governments often struggle
More informationCOMMON GIS TECHNIQUES FOR VECTOR AND RASTER DATA PROCESSING. Ophelia Wang, Department of Geography and the Environment, University of Texas
COMMON GIS TECHNIQUES FOR VECTOR AND RASTER DATA PROCESSING Ophelia Wang, Department of Geography and the Environment, University of Texas PART I: BASIC VECTOR TOOLS CLIP A FEATURE BASED ON THE EXTENT
More informationPresented at the FIG Working Week 2017, May 29 - June 2, 2017 in Helsinki, Finland. Denny LUMBAN RAJA Adang SAPUTRA Johannes ANHORN
Presented at the FIG Working Week 2017, May 29 - June 2, 2017 in Helsinki, Finland Denny LUMBAN RAJA Adang SAPUTRA Johannes ANHORN MAIN RESULTS Most of the surroundings of Cipongkor is dominated by very
More informationPhysician Performance Assessment / Spatial Inference of Pollutant Concentrations
Physician Performance Assessment / Spatial Inference of Pollutant Concentrations Dawn Woodard Operations Research & Information Engineering Cornell University Johns Hopkins Dept. of Biostatistics, April
More informationThe Bayesian Choice. Christian P. Robert. From Decision-Theoretic Foundations to Computational Implementation. Second Edition.
Christian P. Robert The Bayesian Choice From Decision-Theoretic Foundations to Computational Implementation Second Edition With 23 Illustrations ^Springer" Contents Preface to the Second Edition Preface
More information1. Introduction. 2. Study area. Arun Babu Elangovan 1+ and Ravichandran Seetharaman 2
2011 International Conference on Environmental and Computer Science IPCBEE vol.19(2011) (2011) IACSIT Press, Singapore Estimating Rainfall Erosivity of the Revised Universal Soil Loss Equation from daily
More informationImpact of DEM Resolution on Topographic Indices and Hydrological Modelling Results
Impact of DEM Resolution on Topographic Indices and Hydrological Modelling Results J. Vaze 1, 2 and J. Teng 1, 2 1 Department of Water and Energy, NSW, Australia 2 ewater Cooperative Research Centre, Australia
More informationA distributed runoff model for flood prediction in ungauged basins
Predictions in Ungauged Basins: PUB Kick-off (Proceedings of the PUB Kick-off meeting held in Brasilia, 2 22 November 22). IAHS Publ. 39, 27. 267 A distributed runoff model for flood prediction in ungauged
More informationObnoxious lateness humor
Obnoxious lateness humor 1 Using Bayesian Model Averaging For Addressing Model Uncertainty in Environmental Risk Assessment Louise Ryan and Melissa Whitney Department of Biostatistics Harvard School of
More informationSéminaire de l'umr Economie Publique. Spatial Disaggregation of Agricultural. Raja Chakir. February 21th Spatial Disaggregation.
Séminaire de l'umr Economie Publique : An : An February 21th 2006 Outline : An 1 2 3 4 : An The latest reform the Common Policy (CAP) aims to encourage environmentally friendly farming practices in order
More informationDr. S.SURIYA. Assistant professor. Department of Civil Engineering. B. S. Abdur Rahman University. Chennai
Hydrograph simulation for a rural watershed using SCS curve number and Geographic Information System Dr. S.SURIYA Assistant professor Department of Civil Engineering B. S. Abdur Rahman University Chennai
More informationThe impact of slope length on the discharge of sediment by rain impact induced saltation and suspension
EARTH SURFACE PROCESSES AND LANDFORMS Earth Surf. Process. Landforms 34, 1393 1407 (2009) Copyright 2009 John Wiley & Sons, Ltd. Published online 16 June 2009 in Wiley InterScience (www.interscience.wiley.com).1828
More informationA GIS-based Subcatchments Division Approach for SWMM
Send Orders for Reprints to reprints@benthamscience.ae The Open Civil Engineering Journal, 2015, 9, 515-521 515 A GIS-based Subcatchments Division Approach for SWMM Open Access Shen Ji and Zhang Qiuwen
More informationWarwick Business School Forecasting System. Summary. Ana Galvao, Anthony Garratt and James Mitchell November, 2014
Warwick Business School Forecasting System Summary Ana Galvao, Anthony Garratt and James Mitchell November, 21 The main objective of the Warwick Business School Forecasting System is to provide competitive
More informationData Analysis and Uncertainty Part 2: Estimation
Data Analysis and Uncertainty Part 2: Estimation Instructor: Sargur N. University at Buffalo The State University of New York srihari@cedar.buffalo.edu 1 Topics in Estimation 1. Estimation 2. Desirable
More information1 INTRODUCTION. 1.1 Context
1 INTRODUCTION 1.1 Context During the last 30 years ski run construction has been one of the major human activities affecting the Alpine environment. The impact of skiing on environmental factors and processes,
More informationUrban Erosion Potential Risk Mapping with GIS
Urban Erosion Potential Risk Mapping with GIS ESRI Water Conference San Diego, CA Jan 29-Feb 1, 2018 Dr. Randy Dymond, PE, F.ASCE, D.WRE Co-investigators: Amanda Weikmann, MS Student Dr. Clay Hodges, PE
More informationTropics & Sub-Tropics. How can predictive approaches be improved: Data Sparse Situations
Tropics & Sub-Tropics How can predictive approaches be improved: Data Sparse Situations 1. Protocol for catchment function diagnostics and model setup. Use of a decision tree as a preliminary stage to
More informationRainfall Lab. Forest Water Resources Spring 20XX
Rainfall Lab Forest Water Resources Spring 20XX Introduction The most simplistic way to understand rainfall in a particular area is to look at the area s average annual rainfall. That simple statistic
More informationApplication of USLE Model & GIS in Estimation of Soil Erosion for Tandula Reservoir
Application of USLE Model & GIS in Estimation of Soil Erosion for Tandula Reservoir Ishtiyaq Ahmad 1, Dr. M. K. Verma 2 1 Ph.D. Research Scholar, Dept. of Civil Engg. NIT Raipur (C.G.) - India 2 Prof.
More informationExisting NWS Flash Flood Guidance
Introduction The Flash Flood Potential Index (FFPI) incorporates physiographic characteristics of an individual drainage basin to determine its hydrologic response. In flash flood situations, the hydrologic
More informationTopographical Change Monitoring for Susceptible Landslide Area Determination by Using Multi-Date Digital Terrain Models and LiDAR
Topographical Change Monitoring for Susceptible Landslide Area Determination by Using Multi-Date Digital Terrain Models and Chanist PRASERTBURANAKUL 1, Parkorn SUWANICH 2, Kanchana NAKHAPAKORN 3, and Sukit
More informationA Bayesian Nonparametric Approach to Monotone Missing Data in Longitudinal Studies with Informative Missingness
A Bayesian Nonparametric Approach to Monotone Missing Data in Longitudinal Studies with Informative Missingness A. Linero and M. Daniels UF, UT-Austin SRC 2014, Galveston, TX 1 Background 2 Working model
More informationDeriving Uncertainty of Area Estimates from Satellite Imagery using Fuzzy Land-cover Classification
International Journal of Information and Computation Technology. ISSN 0974-2239 Volume 3, Number 10 (2013), pp. 1059-1066 International Research Publications House http://www. irphouse.com /ijict.htm Deriving
More informationSPATIAL AND TEMPORAL MODELLING OF ECOSYSTEM SERVICES
SPATIAL AND TEMPORAL MODELLING OF ECOSYSTEM SERVICES Solen Le Clec h, T.Decaëns, S. Dufour, M. Grimaldi, N. Jégou and J. Oszwald ACES Conference 2016 Jacksonville, Florida (USA). December, 5-9th : issues
More informationBayesian model selection: methodology, computation and applications
Bayesian model selection: methodology, computation and applications David Nott Department of Statistics and Applied Probability National University of Singapore Statistical Genomics Summer School Program
More informationOutline. Remote Sensing, GIS and DEM Applications for Flood Monitoring. Introduction. Satellites and their Sensors used for Flood Mapping
Outline Remote Sensing, GIS and DEM Applications for Flood Monitoring Prof. D. Nagesh Kumar Chairman, Centre for Earth Sciences Professor, Dept. of Civil Engg. Indian Institute of Science Bangalore 560
More informationAn Application of Bayesian Melding to Ecological Networks. Joshua Michael Gould. A research paper presented to the. University of Waterloo
An Application of Bayesian Melding to Ecological Networks by Joshua Michael Gould A research paper presented to the University of Waterloo In partial fulfillment of the requirements for the degree of Master
More informationINTRODUCTION TO ARCGIS 10
Department of Irrigation, Drainage and Landscape Engineering, Faculty of Civil Engineering, CTU Prague Institute of Hydraulics and Rural Water Management BOKU Vienna INTRODUCTION TO ARCGIS 10 MAIN WINDOW
More informationEVALUATION OF RAINFALL EROSIVITY INDICES MODELS BASED ON DAILY, MONTHLY AND ANNUAL RAINFALL FOR DEDIAPADA REGION OF GUJARAT
EVALUATION OF RAINFALL EROSIVITY INDICES MODELS BASED ON DAILY, MONTHLY AND ANNUAL RAINFALL FOR DEDIAPADA REGION OF GUJARAT 1 BABARIYA, V.; 1 JADAV, C.; 2 LAKKAD, A. P. AND * 3 OJHA, S. COLLEGE OF AGRICULTURAL
More informationTempered Stable and Pareto Distributions: Predictions Under Uncertainty
Tempered Stable and Pareto Distributions: Predictions Under Uncertainty Robert L Wolpert & Kerrie L Mengersen Duke University & Queensland University of Technology Session 2A: Foundations I Thu 1:50 2:15pm
More informationRemote sensing technique to monitoring the risk of soil degradation using NDVI
Remote sensing technique to monitoring the risk of soil degradation using NDVI Ahmed Asaad Zaeen Remote sensing Unit, College of Science, University of Baghdad, Iraq ahmed_a_z@scbaghdad.com Abstract. In
More informationAssessing Uncertainty in Urban Simulations Using Bayesian Melding
Assessing Uncertainty in Urban Simulations Using Bayesian Melding Hana Ševčíková, Adrian E. Raftery and Paul A. Waddell University of Washington Working Paper no. 57 Center for Statistics and the Social
More informationStochastic Hydrology. a) Data Mining for Evolution of Association Rules for Droughts and Floods in India using Climate Inputs
Stochastic Hydrology a) Data Mining for Evolution of Association Rules for Droughts and Floods in India using Climate Inputs An accurate prediction of extreme rainfall events can significantly aid in policy
More informationGoverning Rules of Water Movement
Governing Rules of Water Movement Like all physical processes, the flow of water always occurs across some form of energy gradient from high to low e.g., a topographic (slope) gradient from high to low
More informationDirect Simulation Methods #2
Direct Simulation Methods #2 Econ 690 Purdue University Outline 1 A Generalized Rejection Sampling Algorithm 2 The Weighted Bootstrap 3 Importance Sampling Rejection Sampling Algorithm #2 Suppose we wish
More informationNatural Susceptibility to Coastal Erosion: Methodology and Mapping Summary
Natural Susceptibility to Coastal Erosion: Methodology and Mapping Summary. Introduction The Flood Risk Management (Scotland) Act 2009 (FRM Act) introduced a coordinated and partnership approach to how
More informationEXPERT AGGREGATION WITH DEPENDENCE
EXPERT AGGREGATION WITH DEPENDENCE M. J. Kallen, R.M. Cooke 2 Department of Mathematics, Delft University of Technology, Delft, The Netherlands 2 Department of Mathematics, Delft University of Technology,
More informationCromwell's principle idealized under the theory of large deviations
Cromwell's principle idealized under the theory of large deviations Seminar, Statistics and Probability Research Group, University of Ottawa Ottawa, Ontario April 27, 2018 David Bickel University of Ottawa
More informationDynamic Land Cover Dataset Product Description
Dynamic Land Cover Dataset Product Description V1.0 27 May 2014 D2014-40362 Unclassified Table of Contents Document History... 3 A Summary Description... 4 Sheet A.1 Definition and Usage... 4 Sheet A.2
More informationHydrologic Modelling of the Upper Malaprabha Catchment using ArcView SWAT
Hydrologic Modelling of the Upper Malaprabha Catchment using ArcView SWAT Technical briefs are short summaries of the models used in the project aimed at nontechnical readers. The aim of the PES India
More informationAlaska, USA. Sam Robbins
Using ArcGIS to determine erosion susceptibility within Denali National Park, Alaska, USA Sam Robbins Introduction Denali National Park is six million acres of wild land with only one road and one road
More informationCreation of high resolution soil parameter data by use of artificial neural network technologies (advangeo )
Creation of high resolution soil parameter data by use of artificial neural network technologies (advangeo ) A. Knobloch 1, F. Schmidt 1, M.K. Zeidler 1, A. Barth 1 1 Beak Consultants GmbH, Freiberg /
More informationUrban storm water management
Urban storm water management Cooperation between geologists and land-use planners Philipp Schmidt-Thomé Geological Survey of Finland Background Urban flood modeling has become more topical during 21 st
More information3 Joint Distributions 71
2.2.3 The Normal Distribution 54 2.2.4 The Beta Density 58 2.3 Functions of a Random Variable 58 2.4 Concluding Remarks 64 2.5 Problems 64 3 Joint Distributions 71 3.1 Introduction 71 3.2 Discrete Random
More information