Combining Logistic Regression with Kriging for Mapping the Risk of Occurrence of Unexploded Ordnance (UXO)
|
|
- Duane Briggs
- 5 years ago
- Views:
Transcription
1 Combining Logistic Regression with Kriging for Maing the Risk of Occurrence of Unexloded Ordnance (UXO) H. Saito (), P. Goovaerts (), S. A. McKenna (2) Environmental and Water Resources Engineering, Deartment of Civil and Environmental Engineering, The University of Michigan, 35, Beal Ave., Ann Arbor, Michigan, , U.S.A., (2) Geohydrology Deartment, Sandia National Laboratories, PO Box 58 MS 735, Albuquerque, NM, , U.S.A. Abstract This aer resents a methodology that combines logistic regression with kriging for incororating exhaustive secondary information into the maing of the risk of occurrence of unexloded ordnance (UXO). Logistic regression, which is aroriate for binary data (indicators) analysis, is used to derive the trend comonent in simle kriging with varying local means (). The technique is illustrated using two tyes of information: ) hard indicators samled along transects on a hyothetical UXO site generated using a doubly stochastic Poisson rocess, 2) exhaustive soft information obtained through the rocessing of a series of realizations generated by the same oint rocess. After risks are maed, ixels are flagged for further investigation if the estimated robability exceeds a given threshold. This classification is used to comare the erformance of the roosed technique with traditional cokriging (collocated cokriging). Fewer misclassifications and smaller false ositive rates are obtained for derived from logistic regression. The roortion of false negative is below 5% for both techniques. 2. Introduction Maing the risk of occurrence of unexloded ordnance (UXO) at any military sites is imortant esecially as these sites are reared for return to the ublic sector. Efficient and recise site characterization is necessary. In lace of classical statistical aroaches, geostatistical techniques should be referred because of their ability to take into account satial correlation and many different kinds of ancillary information. It is well recognized that site characterization imroves esecially when the rimary variable, which is often samled sarsely because of cost and time constraints, is sulemented with abundant (exhaustive) additional information (GOOVAERTS 2). A number of geostatistical techniques have been develoed to incororate exhaustive secondary data (GOOVAERTS 997). Among available algorithms, simle kriging with varying local means () rovides flexibility in trend modeling and mathematical simlicity. The basic idea of is the combination of deterministic trend modeling with geostatistical interolation of residuals. Residuals are usually modeled using a stationary random function so that simle kriging can be alied. The remaining question is then what kind of deterministic function should be used for the trend modeling. Linear regression is straightforward but is not aroriate if the rimary data are binary indicators because of several violations against classical linear regression assumtions (ALLISON 999). The logical choice is logistic regression, which has been secifically develoed for binary data. To date, logistic regression has never directly incororated into geostatistical techniques. This aer resents a new methodology to combine logistic regression with kriging for maing the risks of occurrence of UXO. The technique is illustrated using a hyothetical site contaminated with UXO and classification erformances are comared with cokriging results. 3. Stochastic simulation of UXO distribution The satial distribution of UXO should be viewed as a oint rocess since the location of UXO is the variable of interest, and the stochastic simulation of a Poisson rocess can be used to model the satial distribution of UXO.
2 The Poisson rocesses rovide a common class of models for objects distributed in sace according to a uniform intensity (homogeneous Poisson rocess). In reality, however, the satial distribution of UXO is not uniform since its intensity changes satially because of the existence of secific targets. In such a case, one of its variants (the doubly stochastic Poisson rocess or DSPP) is used to model the satial distribution of UXO. A simulator has been develoed to generate non-conditional UXO realizations as the sum of two rocesses:. A homogeneous Poisson rocess describing the background objects that dislay an uniform intensity across the satial domain. 2. DSPP describing the satially varying mean (e.g. higher intensity around targets) Two tyes of bombs can be considered: airborne and mortar bombs, and the satial distribution of both fragments and UXO is simulated. Target-secific arameters can be entered by the user, such as ) targets coordinates, 2) ordnance size, 3) orientation, and 4) intensity, for airborne ordnance. For mortar ordnance, three zones are simulated: a firing zone, a target zone, and a fan zone. One of the realizations generated by the Poisson simulator is used as the hyothetical (true) UXO site and the number of both UXO and fragments using a ixel size of 5 x 5 is maed in Figure (left). # of objects E-tye estimate X X Figure : Ma of the number of objects (UXO and fragments) at the hyothetical site and ma of E-tye estimates. A series of non-conditional realizations (UXO and fragments) is generated by the simulator, each of them being converted into an intensity ma according to a given ixel or block size. Then, for each ixel, the conditional cumulative distribution function (ccdf) of the UXO intensity is numerically aroximated from the series of simulated values. The mean (E-tye) and variance of ccdfs as well as the robability of exceeding an action level are comuted and used as exhaustive secondary information. Figure (right) shows the E-tye estimate ma obtained from a series of realizations using a ixel size of 5 x Geostatistical interolation The risk of occurrence of unexloded ordnance (UXO) at any location within the study area is maed using geostatistical interolation technique. The basic aroach is to estimate the robabilities of occurrence of UXO at unsamled locations using hard data samled from the UXO site. Since hard data are never exhaustive nor % certain, secondary information can hel imroving the site characterization. In the UXO site, samling locations are digged to find out whether or not any UXO is resent. Thus, the rimary data are indicators of 2
3 occurrence of at least one UXO at each location digged ( = at least one UXO, = no UXO). Traditionally robabilities at unsamled locations are estimated from these hard data using indicator kriging (JOURNEL 983). However if exhaustive secondary data are available, variants of indicator kriging can be used. Consider the roblem of estimating the robability of occurrence of an attribute at an unsamled location u, where u is a vector of satial coordinates. The information available consists of hard indicator values (binary data) at n locations u, i(u ), =,2,,n and different tyes of secondary data y j (, j =,2,,S at all estimation grid nodes (exhaustive information). The secondary variable considered in this study is the exhaustive ma of E-tye estimates. The most commonly used aroach to incororate secondary information is cokriging. While a number of variants of cokriging algorithms has been develoed, only collocated cokriging () is considered here because of its numerical stability and simlicity. The basic idea is to incororate only the secondary datum co-located with the location being estimated, that is: n( ( λ ( i( u ) + λ ( [ y( m + m = = where m I and m are the global means of rimary and secondary variables. The second term of equation () corresonds to a rescaling of the secondary variable to the mean of the rimary variable to ensure unbiased estimation. Another aroach consists of redicting the robability as a function of only the co-located secondary datum (e.g. linear relation). This tye of regression however assumes that the residual values are satially uncorrelated, which is not always true. Simle kriging with varying local means () allows one to take the satial correlation of residuals into account. It amounts at relacing the known stationary mean in the simle kriging estimate by known varying means m ( derived from the secondary information: ( m ( = n( λ = ( [ i( u ) m The local means m ( are often derived from linear regression using indeendent variables. However, linear regression is not aroriate when binary data are used as deendent variables because of several violations of underlying assumtions:. Prediction errors are not normally distributed because data take only two values. 2. The errors are heteroscedastic, which occurs when the variance of the deendent variable varies with values of indeendent variables. 3. The redicted robabilities can be greater than or less than if the linear regression model, which is inherently unbounded, is used. Usually those values are set to either or arbitrarily which may lead to non-otimal estimates. Logistic regression overcomes these roblems by using odds ratios O, which are defined as: O = (3) where is the robability that the event occurs. The logistic model is then exressed as: ln = + β X (4) where X is the vector of indeendent variables. Odds ratios are not bounded but estimated robabilities lie between and after the backtransform of estimated ratios: = + ex( β X) (5) ( u )] I ] (2) () 3
4 Unlike traditional linear regression, which minimizes the error variance, arameters β in logistic regression are chosen to maximize the likelihood function (Maximum Likelihood Estimator). Logistic regression is then used to derive the local means m ( in. 5. Site classification Maing of robabilities is not a goal er se, but a reliminary ste towards the delineation of the area where at least one UXO exists. The imact of different robability thresholds and interolation techniques ( and ) on decision-making was investigated using the following rocedure:. The rimary data are indicators of resence of at least one UXO for the ixels of transects ositioned according to rior information. These indicators ( = at least one UXO, = no UXO) are comuted from the true UXO distribution created using the UXO simulator. The secondary information is the exhaustive ma of E-tye estimate. 2. Probabilities of occurrence of at least one UXO are estimated at any ixel using both collocated cokriging and simle kriging with varying local means derived from logistic regression. 3. Pixels are flagged for further geohysical survey if the estimated robability exceeds a given threshold. If the robability is below the threshold, then the ixel is left for no further action. 4. Comarison of classification achieved at the revious ste with the true UXO distribution allows the comutation of roortions of correct classification, false negative, and false ositive. This is done for a series of robability thresholds Hard indicators Figure 2: The location ma of hard data obtained along transects. Closed circles indicate at least one UXO found and oen circles imly no UXO found. Colocated Cokriging SK with varying local means X X Figure 3: Mas of robability of occurrence of at least one UXO estimated using two kriging algorithms: collocated cokriging (left), simle kriging with varying local means (right). The exhaustive ma of E-tye estimates was used as secondary information. 6. Results and discussions Figure 2 shows locations where hard data are collected from the hyothetical UXO site. Six transects are ositioned according to rior information available (e.g. locations of targets). Figure 3 shows robability mas roduced by and. Both techniques reroduce well higher robabilities around targets and lower robabilities in surrounding areas. These 4
5 robability mas are then used for site classification. The roortions of correct classification, false negative and false ositive are comuted for a series of robability thresholds, see Figure 4. The term design reliability, R D is defined as -P UXO where P UXO corresonds to any robability threshold. Until a design reliability of.95, leads to a larger roortion of correct decision and less false ositive than collocated cokriging. Colocated CK SK with varying local means.8.8 Proortion of Decision.6.4 Correct False + Proortion of Decision Figure 4: Proortions of correct classification (solid) and false ositive (dash) as a function of robability threshold. Results are obtained for two kriging algorithms: collocated cokriging (left) and simle kriging with varying local means derived using logistic regression (right). Since the ultimate goal of UXO site remediation is to leave zero UXO after remediation, riority should be given to minimization of the roortion of false negative. Figure 5 deicts the roortion of false negative over a range of design reliability values. The roortions of false negative are basically ket very low (less than 5%). These roortions are relatively higher for than for for a design reliability below.95. In this aer, the combination of logistic regression with geostatistical characterization of UXO site was investigated. Logistic regression was couled with simle kriging to ma the robability of occurrence of at least one UXO. Results indicate the benefit of logistic regression in terms of correct classification and false ositive. The technique can be easily exanded to incororate more than two additional variables. 7. Acknowledgment This work was suorted by the Strategic Environmental Research and Develoment Program (SERDP), UXO Cleanu rogram under grant UX-2. Sandia is a multirogram laboratory oerated by Sandia Cororation, a Lockheed Martin Comany, for the United States Deartment of Energy under contract DE-AC4-94-AL References Goovaerts P., 2: Geostatistical aroach for incororating elevation into the satial interolation of rainfall. Journal of Hydrology, 228, Goovaerts P., 997: Geostatistics for Natural Resources Evaluation. Oxford University Press: New ork (Oxford University Press), Allison, P.D., 999: Logistic Regression Using the SAS System: Theory and Alication. Cary, NC (SAS Institute), Journel, A. G., 983: Non-arametric estimation of satial distributions. Mathematical Geology, 5, Proortion of Decision False negative Figure 5: The imact of design reliability over false negative roduced by two kriging ( and ).
An Analysis of Reliable Classifiers through ROC Isometrics
An Analysis of Reliable Classifiers through ROC Isometrics Stijn Vanderlooy s.vanderlooy@cs.unimaas.nl Ida G. Srinkhuizen-Kuyer kuyer@cs.unimaas.nl Evgueni N. Smirnov smirnov@cs.unimaas.nl MICC-IKAT, Universiteit
More informationScaling Multiple Point Statistics for Non-Stationary Geostatistical Modeling
Scaling Multile Point Statistics or Non-Stationary Geostatistical Modeling Julián M. Ortiz, Steven Lyster and Clayton V. Deutsch Centre or Comutational Geostatistics Deartment o Civil & Environmental Engineering
More informationDeriving Indicator Direct and Cross Variograms from a Normal Scores Variogram Model (bigaus-full) David F. Machuca Mory and Clayton V.
Deriving ndicator Direct and Cross Variograms from a Normal Scores Variogram Model (bigaus-full) David F. Machuca Mory and Clayton V. Deutsch Centre for Comutational Geostatistics Deartment of Civil &
More informationEstimation of the large covariance matrix with two-step monotone missing data
Estimation of the large covariance matrix with two-ste monotone missing data Masashi Hyodo, Nobumichi Shutoh 2, Takashi Seo, and Tatjana Pavlenko 3 Deartment of Mathematical Information Science, Tokyo
More information4. Score normalization technical details We now discuss the technical details of the score normalization method.
SMT SCORING SYSTEM This document describes the scoring system for the Stanford Math Tournament We begin by giving an overview of the changes to scoring and a non-technical descrition of the scoring rules
More informationOn split sample and randomized confidence intervals for binomial proportions
On slit samle and randomized confidence intervals for binomial roortions Måns Thulin Deartment of Mathematics, Usala University arxiv:1402.6536v1 [stat.me] 26 Feb 2014 Abstract Slit samle methods have
More informationMODELING THE RELIABILITY OF C4ISR SYSTEMS HARDWARE/SOFTWARE COMPONENTS USING AN IMPROVED MARKOV MODEL
Technical Sciences and Alied Mathematics MODELING THE RELIABILITY OF CISR SYSTEMS HARDWARE/SOFTWARE COMPONENTS USING AN IMPROVED MARKOV MODEL Cezar VASILESCU Regional Deartment of Defense Resources Management
More informationDistributed Rule-Based Inference in the Presence of Redundant Information
istribution Statement : roved for ublic release; distribution is unlimited. istributed Rule-ased Inference in the Presence of Redundant Information June 8, 004 William J. Farrell III Lockheed Martin dvanced
More informationA Comparison between Biased and Unbiased Estimators in Ordinary Least Squares Regression
Journal of Modern Alied Statistical Methods Volume Issue Article 7 --03 A Comarison between Biased and Unbiased Estimators in Ordinary Least Squares Regression Ghadban Khalaf King Khalid University, Saudi
More informationCharacterizing the Behavior of a Probabilistic CMOS Switch Through Analytical Models and Its Verification Through Simulations
Characterizing the Behavior of a Probabilistic CMOS Switch Through Analytical Models and Its Verification Through Simulations PINAR KORKMAZ, BILGE E. S. AKGUL and KRISHNA V. PALEM Georgia Institute of
More informationEstimation of component redundancy in optimal age maintenance
EURO MAINTENANCE 2012, Belgrade 14-16 May 2012 Proceedings of the 21 st International Congress on Maintenance and Asset Management Estimation of comonent redundancy in otimal age maintenance Jorge ioa
More informationMATHEMATICAL MODELLING OF THE WIRELESS COMMUNICATION NETWORK
Comuter Modelling and ew Technologies, 5, Vol.9, o., 3-39 Transort and Telecommunication Institute, Lomonosov, LV-9, Riga, Latvia MATHEMATICAL MODELLIG OF THE WIRELESS COMMUICATIO ETWORK M. KOPEETSK Deartment
More informationBayesian Spatially Varying Coefficient Models in the Presence of Collinearity
Bayesian Satially Varying Coefficient Models in the Presence of Collinearity David C. Wheeler 1, Catherine A. Calder 1 he Ohio State University 1 Abstract he belief that relationshis between exlanatory
More informationLower Confidence Bound for Process-Yield Index S pk with Autocorrelated Process Data
Quality Technology & Quantitative Management Vol. 1, No.,. 51-65, 15 QTQM IAQM 15 Lower onfidence Bound for Process-Yield Index with Autocorrelated Process Data Fu-Kwun Wang * and Yeneneh Tamirat Deartment
More informationHotelling s Two- Sample T 2
Chater 600 Hotelling s Two- Samle T Introduction This module calculates ower for the Hotelling s two-grou, T-squared (T) test statistic. Hotelling s T is an extension of the univariate two-samle t-test
More informationShadow Computing: An Energy-Aware Fault Tolerant Computing Model
Shadow Comuting: An Energy-Aware Fault Tolerant Comuting Model Bryan Mills, Taieb Znati, Rami Melhem Deartment of Comuter Science University of Pittsburgh (bmills, znati, melhem)@cs.itt.edu Index Terms
More informationLOGISTIC REGRESSION. VINAYANAND KANDALA M.Sc. (Agricultural Statistics), Roll No I.A.S.R.I, Library Avenue, New Delhi
LOGISTIC REGRESSION VINAANAND KANDALA M.Sc. (Agricultural Statistics), Roll No. 444 I.A.S.R.I, Library Avenue, New Delhi- Chairerson: Dr. Ranjana Agarwal Abstract: Logistic regression is widely used when
More informationUsing the Divergence Information Criterion for the Determination of the Order of an Autoregressive Process
Using the Divergence Information Criterion for the Determination of the Order of an Autoregressive Process P. Mantalos a1, K. Mattheou b, A. Karagrigoriou b a.deartment of Statistics University of Lund
More informationOn Wald-Type Optimal Stopping for Brownian Motion
J Al Probab Vol 34, No 1, 1997, (66-73) Prerint Ser No 1, 1994, Math Inst Aarhus On Wald-Tye Otimal Stoing for Brownian Motion S RAVRSN and PSKIR The solution is resented to all otimal stoing roblems of
More informationCHAPTER-II Control Charts for Fraction Nonconforming using m-of-m Runs Rules
CHAPTER-II Control Charts for Fraction Nonconforming using m-of-m Runs Rules. Introduction: The is widely used in industry to monitor the number of fraction nonconforming units. A nonconforming unit is
More informationGeneral Linear Model Introduction, Classes of Linear models and Estimation
Stat 740 General Linear Model Introduction, Classes of Linear models and Estimation An aim of scientific enquiry: To describe or to discover relationshis among events (variables) in the controlled (laboratory)
More informationAn Outdoor Recreation Use Model with Applications to Evaluating Survey Estimators
United States Deartment of Agriculture Forest Service Southern Research Station An Outdoor Recreation Use Model with Alications to Evaluating Survey Estimators Stanley J. Zarnoch, Donald B.K. English,
More informationGenetic Algorithms, Selection Schemes, and the Varying Eects of Noise. IlliGAL Report No November Department of General Engineering
Genetic Algorithms, Selection Schemes, and the Varying Eects of Noise Brad L. Miller Det. of Comuter Science University of Illinois at Urbana-Chamaign David E. Goldberg Det. of General Engineering University
More informationState Estimation with ARMarkov Models
Deartment of Mechanical and Aerosace Engineering Technical Reort No. 3046, October 1998. Princeton University, Princeton, NJ. State Estimation with ARMarkov Models Ryoung K. Lim 1 Columbia University,
More informationLinear diophantine equations for discrete tomography
Journal of X-Ray Science and Technology 10 001 59 66 59 IOS Press Linear diohantine euations for discrete tomograhy Yangbo Ye a,gewang b and Jiehua Zhu a a Deartment of Mathematics, The University of Iowa,
More informationYixi Shi. Jose Blanchet. IEOR Department Columbia University New York, NY 10027, USA. IEOR Department Columbia University New York, NY 10027, USA
Proceedings of the 2011 Winter Simulation Conference S. Jain, R. R. Creasey, J. Himmelsach, K. P. White, and M. Fu, eds. EFFICIENT RARE EVENT SIMULATION FOR HEAVY-TAILED SYSTEMS VIA CROSS ENTROPY Jose
More informationRadial Basis Function Networks: Algorithms
Radial Basis Function Networks: Algorithms Introduction to Neural Networks : Lecture 13 John A. Bullinaria, 2004 1. The RBF Maing 2. The RBF Network Architecture 3. Comutational Power of RBF Networks 4.
More informationProbability Estimates for Multi-class Classification by Pairwise Coupling
Probability Estimates for Multi-class Classification by Pairwise Couling Ting-Fan Wu Chih-Jen Lin Deartment of Comuter Science National Taiwan University Taiei 06, Taiwan Ruby C. Weng Deartment of Statistics
More informationA New Asymmetric Interaction Ridge (AIR) Regression Method
A New Asymmetric Interaction Ridge (AIR) Regression Method by Kristofer Månsson, Ghazi Shukur, and Pär Sölander The Swedish Retail Institute, HUI Research, Stockholm, Sweden. Deartment of Economics and
More informationx and y suer from two tyes of additive noise [], [3] Uncertainties e x, e y, where the only rior knowledge is their boundedness and zero mean Gaussian
A New Estimator for Mixed Stochastic and Set Theoretic Uncertainty Models Alied to Mobile Robot Localization Uwe D. Hanebeck Joachim Horn Institute of Automatic Control Engineering Siemens AG, Cororate
More informationPaper C Exact Volume Balance Versus Exact Mass Balance in Compositional Reservoir Simulation
Paer C Exact Volume Balance Versus Exact Mass Balance in Comositional Reservoir Simulation Submitted to Comutational Geosciences, December 2005. Exact Volume Balance Versus Exact Mass Balance in Comositional
More informationLower bound solutions for bearing capacity of jointed rock
Comuters and Geotechnics 31 (2004) 23 36 www.elsevier.com/locate/comgeo Lower bound solutions for bearing caacity of jointed rock D.J. Sutcliffe a, H.S. Yu b, *, S.W. Sloan c a Deartment of Civil, Surveying
More informationSystem Reliability Estimation and Confidence Regions from Subsystem and Full System Tests
009 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June 0-, 009 FrB4. System Reliability Estimation and Confidence Regions from Subsystem and Full System Tests James C. Sall Abstract
More informationSAS for Bayesian Mediation Analysis
Paer 1569-2014 SAS for Bayesian Mediation Analysis Miočević Milica, Arizona State University; David P. MacKinnon, Arizona State University ABSTRACT Recent statistical mediation analysis research focuses
More informationMinimax Design of Nonnegative Finite Impulse Response Filters
Minimax Design of Nonnegative Finite Imulse Resonse Filters Xiaoing Lai, Anke Xue Institute of Information and Control Hangzhou Dianzi University Hangzhou, 3118 China e-mail: laix@hdu.edu.cn; akxue@hdu.edu.cn
More informationMultivariable Generalized Predictive Scheme for Gas Turbine Control in Combined Cycle Power Plant
Multivariable Generalized Predictive Scheme for Gas urbine Control in Combined Cycle Power Plant L.X.Niu and X.J.Liu Deartment of Automation North China Electric Power University Beiing, China, 006 e-mail
More informationPERFORMANCE BASED DESIGN SYSTEM FOR CONCRETE MIXTURE WITH MULTI-OPTIMIZING GENETIC ALGORITHM
PERFORMANCE BASED DESIGN SYSTEM FOR CONCRETE MIXTURE WITH MULTI-OPTIMIZING GENETIC ALGORITHM Takafumi Noguchi 1, Iei Maruyama 1 and Manabu Kanematsu 1 1 Deartment of Architecture, University of Tokyo,
More informationAlgorithms for Air Traffic Flow Management under Stochastic Environments
Algorithms for Air Traffic Flow Management under Stochastic Environments Arnab Nilim and Laurent El Ghaoui Abstract A major ortion of the delay in the Air Traffic Management Systems (ATMS) in US arises
More informationFactors Effect on the Saturation Parameter S and there Influences on the Gain Behavior of Ytterbium Doped Fiber Amplifier
Australian Journal of Basic and Alied Sciences, 5(12): 2010-2020, 2011 ISSN 1991-8178 Factors Effect on the Saturation Parameter S and there Influences on the Gain Behavior of Ytterbium Doed Fiber Amlifier
More informationAI*IA 2003 Fusion of Multiple Pattern Classifiers PART III
AI*IA 23 Fusion of Multile Pattern Classifiers PART III AI*IA 23 Tutorial on Fusion of Multile Pattern Classifiers by F. Roli 49 Methods for fusing multile classifiers Methods for fusing multile classifiers
More informationA MIXED CONTROL CHART ADAPTED TO THE TRUNCATED LIFE TEST BASED ON THE WEIBULL DISTRIBUTION
O P E R A T I O N S R E S E A R C H A N D D E C I S I O N S No. 27 DOI:.5277/ord73 Nasrullah KHAN Muhammad ASLAM 2 Kyung-Jun KIM 3 Chi-Hyuck JUN 4 A MIXED CONTROL CHART ADAPTED TO THE TRUNCATED LIFE TEST
More informationResearch of PMU Optimal Placement in Power Systems
Proceedings of the 5th WSEAS/IASME Int. Conf. on SYSTEMS THEORY and SCIENTIFIC COMPUTATION, Malta, Setember 15-17, 2005 (38-43) Research of PMU Otimal Placement in Power Systems TIAN-TIAN CAI, QIAN AI
More informationFeedback-error control
Chater 4 Feedback-error control 4.1 Introduction This chater exlains the feedback-error (FBE) control scheme originally described by Kawato [, 87, 8]. FBE is a widely used neural network based controller
More informationASSESSMENT OF NUMERICAL UNCERTAINTY FOR THE CALCULATIONS OF TURBULENT FLOW OVER A BACKWARD FACING STEP
Submitted to Worsho on Uncertainty Estimation October -, 004, Lisbon, Portugal ASSESSMENT OF NUMERICAL UNCERTAINTY FOR THE CALCULATIONS OF TURBULENT FLOW OVER A BACKWARD FACING STEP ABSTRACT Ismail B.
More informationMorten Frydenberg Section for Biostatistics Version :Friday, 05 September 2014
Morten Frydenberg Section for Biostatistics Version :Friday, 05 Setember 204 All models are aroximations! The best model does not exist! Comlicated models needs a lot of data. lower your ambitions or get
More informationDeveloping A Deterioration Probabilistic Model for Rail Wear
International Journal of Traffic and Transortation Engineering 2012, 1(2): 13-18 DOI: 10.5923/j.ijtte.20120102.02 Develoing A Deterioration Probabilistic Model for Rail Wear Jabbar-Ali Zakeri *, Shahrbanoo
More informationPerformance of lag length selection criteria in three different situations
MPRA Munich Personal RePEc Archive Performance of lag length selection criteria in three different situations Zahid Asghar and Irum Abid Quaid-i-Azam University, Islamabad Aril 2007 Online at htts://mra.ub.uni-muenchen.de/40042/
More informationChapter 7 Sampling and Sampling Distributions. Introduction. Selecting a Sample. Introduction. Sampling from a Finite Population
Chater 7 and s Selecting a Samle Point Estimation Introduction to s of Proerties of Point Estimators Other Methods Introduction An element is the entity on which data are collected. A oulation is a collection
More informationUncertainty Modeling with Interval Type-2 Fuzzy Logic Systems in Mobile Robotics
Uncertainty Modeling with Interval Tye-2 Fuzzy Logic Systems in Mobile Robotics Ondrej Linda, Student Member, IEEE, Milos Manic, Senior Member, IEEE bstract Interval Tye-2 Fuzzy Logic Systems (IT2 FLSs)
More informationPositivity, local smoothing and Harnack inequalities for very fast diffusion equations
Positivity, local smoothing and Harnack inequalities for very fast diffusion equations Dedicated to Luis Caffarelli for his ucoming 60 th birthday Matteo Bonforte a, b and Juan Luis Vázquez a, c Abstract
More informationOn Fractional Predictive PID Controller Design Method Emmanuel Edet*. Reza Katebi.**
On Fractional Predictive PID Controller Design Method Emmanuel Edet*. Reza Katebi.** * echnology and Innovation Centre, Level 4, Deartment of Electronic and Electrical Engineering, University of Strathclyde,
More informationNotes on Instrumental Variables Methods
Notes on Instrumental Variables Methods Michele Pellizzari IGIER-Bocconi, IZA and frdb 1 The Instrumental Variable Estimator Instrumental variable estimation is the classical solution to the roblem of
More informationAn Improved Generalized Estimation Procedure of Current Population Mean in Two-Occasion Successive Sampling
Journal of Modern Alied Statistical Methods Volume 15 Issue Article 14 11-1-016 An Imroved Generalized Estimation Procedure of Current Poulation Mean in Two-Occasion Successive Samling G. N. Singh Indian
More informationDETC2003/DAC AN EFFICIENT ALGORITHM FOR CONSTRUCTING OPTIMAL DESIGN OF COMPUTER EXPERIMENTS
Proceedings of DETC 03 ASME 003 Design Engineering Technical Conferences and Comuters and Information in Engineering Conference Chicago, Illinois USA, Setember -6, 003 DETC003/DAC-48760 AN EFFICIENT ALGORITHM
More informationarxiv: v1 [physics.data-an] 26 Oct 2012
Constraints on Yield Parameters in Extended Maximum Likelihood Fits Till Moritz Karbach a, Maximilian Schlu b a TU Dortmund, Germany, moritz.karbach@cern.ch b TU Dortmund, Germany, maximilian.schlu@cern.ch
More informationAsymptotic Properties of the Markov Chain Model method of finding Markov chains Generators of..
IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578, -ISSN: 319-765X. Volume 1, Issue 4 Ver. III (Jul. - Aug.016), PP 53-60 www.iosrournals.org Asymtotic Proerties of the Markov Chain Model method of
More informationMULTIVARIATE STATISTICAL PROCESS OF HOTELLING S T CONTROL CHARTS PROCEDURES WITH INDUSTRIAL APPLICATION
Journal of Statistics: Advances in heory and Alications Volume 8, Number, 07, Pages -44 Available at htt://scientificadvances.co.in DOI: htt://dx.doi.org/0.864/jsata_700868 MULIVARIAE SAISICAL PROCESS
More informationCHAPTER 5 STATISTICAL INFERENCE. 1.0 Hypothesis Testing. 2.0 Decision Errors. 3.0 How a Hypothesis is Tested. 4.0 Test for Goodness of Fit
Chater 5 Statistical Inference 69 CHAPTER 5 STATISTICAL INFERENCE.0 Hyothesis Testing.0 Decision Errors 3.0 How a Hyothesis is Tested 4.0 Test for Goodness of Fit 5.0 Inferences about Two Means It ain't
More informationTests for Two Proportions in a Stratified Design (Cochran/Mantel-Haenszel Test)
Chater 225 Tests for Two Proortions in a Stratified Design (Cochran/Mantel-Haenszel Test) Introduction In a stratified design, the subects are selected from two or more strata which are formed from imortant
More informationVIBRATION ANALYSIS OF BEAMS WITH MULTIPLE CONSTRAINED LAYER DAMPING PATCHES
Journal of Sound and Vibration (998) 22(5), 78 85 VIBRATION ANALYSIS OF BEAMS WITH MULTIPLE CONSTRAINED LAYER DAMPING PATCHES Acoustics and Dynamics Laboratory, Deartment of Mechanical Engineering, The
More informationBrownian Motion and Random Prime Factorization
Brownian Motion and Random Prime Factorization Kendrick Tang June 4, 202 Contents Introduction 2 2 Brownian Motion 2 2. Develoing Brownian Motion.................... 2 2.. Measure Saces and Borel Sigma-Algebras.........
More informationTemperature, current and doping dependence of non-ideality factor for pnp and npn punch-through structures
Indian Journal of Pure & Alied Physics Vol. 44, December 2006,. 953-958 Temerature, current and doing deendence of non-ideality factor for n and nn unch-through structures Khurshed Ahmad Shah & S S Islam
More informationEvaluating Circuit Reliability Under Probabilistic Gate-Level Fault Models
Evaluating Circuit Reliability Under Probabilistic Gate-Level Fault Models Ketan N. Patel, Igor L. Markov and John P. Hayes University of Michigan, Ann Arbor 48109-2122 {knatel,imarkov,jhayes}@eecs.umich.edu
More informationEffective conductivity in a lattice model for binary disordered media with complex distributions of grain sizes
hys. stat. sol. b 36, 65-633 003 Effective conductivity in a lattice model for binary disordered media with comlex distributions of grain sizes R. PIASECKI Institute of Chemistry, University of Oole, Oleska
More informationSupplementary Materials for Robust Estimation of the False Discovery Rate
Sulementary Materials for Robust Estimation of the False Discovery Rate Stan Pounds and Cheng Cheng This sulemental contains roofs regarding theoretical roerties of the roosed method (Section S1), rovides
More informationAnalysis of M/M/n/K Queue with Multiple Priorities
Analysis of M/M/n/K Queue with Multile Priorities Coyright, Sanjay K. Bose For a P-riority system, class P of highest riority Indeendent, Poisson arrival rocesses for each class with i as average arrival
More informationRatio Estimators in Simple Random Sampling Using Information on Auxiliary Attribute
ajesh Singh, ankaj Chauhan, Nirmala Sawan School of Statistics, DAVV, Indore (M.., India Florentin Smarandache Universit of New Mexico, USA atio Estimators in Simle andom Samling Using Information on Auxiliar
More informationResearch Note REGRESSION ANALYSIS IN MARKOV CHAIN * A. Y. ALAMUTI AND M. R. MESHKANI **
Iranian Journal of Science & Technology, Transaction A, Vol 3, No A3 Printed in The Islamic Reublic of Iran, 26 Shiraz University Research Note REGRESSION ANALYSIS IN MARKOV HAIN * A Y ALAMUTI AND M R
More informationAn Improved Calibration Method for a Chopped Pyrgeometer
96 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 An Imroved Calibration Method for a Choed Pyrgeometer FRIEDRICH FERGG OtoLab, Ingenieurbüro, Munich, Germany PETER WENDLING Deutsches Forschungszentrum
More informationUncorrelated Multilinear Principal Component Analysis for Unsupervised Multilinear Subspace Learning
TNN-2009-P-1186.R2 1 Uncorrelated Multilinear Princial Comonent Analysis for Unsuervised Multilinear Subsace Learning Haiing Lu, K. N. Plataniotis and A. N. Venetsanooulos The Edward S. Rogers Sr. Deartment
More informationHidden Predictors: A Factor Analysis Primer
Hidden Predictors: A Factor Analysis Primer Ryan C Sanchez Western Washington University Factor Analysis is a owerful statistical method in the modern research sychologist s toolbag When used roerly, factor
More informationAN OPTIMAL CONTROL CHART FOR NON-NORMAL PROCESSES
AN OPTIMAL CONTROL CHART FOR NON-NORMAL PROCESSES Emmanuel Duclos, Maurice Pillet To cite this version: Emmanuel Duclos, Maurice Pillet. AN OPTIMAL CONTROL CHART FOR NON-NORMAL PRO- CESSES. st IFAC Worsho
More informationOptimal Recognition Algorithm for Cameras of Lasers Evanescent
Otimal Recognition Algorithm for Cameras of Lasers Evanescent T. Gaudo * Abstract An algorithm based on the Bayesian aroach to detect and recognise off-axis ulse laser beams roagating in the atmoshere
More informationModelling of non-uniform DC driven glow discharge in argon gas
Physics Letters A 367 (2007) 114 119 www.elsevier.com/locate/la Modelling of non-uniform DC driven glow discharge in argon gas I.R. Rafatov,1, D. Akbar, S. Bilikmen Physics Deartment, Middle East Technical
More informationIntroduction to Probability and Statistics
Introduction to Probability and Statistics Chater 8 Ammar M. Sarhan, asarhan@mathstat.dal.ca Deartment of Mathematics and Statistics, Dalhousie University Fall Semester 28 Chater 8 Tests of Hyotheses Based
More informationThe Noise Power Ratio - Theory and ADC Testing
The Noise Power Ratio - Theory and ADC Testing FH Irons, KJ Riley, and DM Hummels Abstract This aer develos theory behind the noise ower ratio (NPR) testing of ADCs. A mid-riser formulation is used for
More informationSTABILITY ANALYSIS AND CONTROL OF STOCHASTIC DYNAMIC SYSTEMS USING POLYNOMIAL CHAOS. A Dissertation JAMES ROBERT FISHER
STABILITY ANALYSIS AND CONTROL OF STOCHASTIC DYNAMIC SYSTEMS USING POLYNOMIAL CHAOS A Dissertation by JAMES ROBERT FISHER Submitted to the Office of Graduate Studies of Texas A&M University in artial fulfillment
More informationOn parameter estimation in deformable models
Downloaded from orbitdtudk on: Dec 7, 07 On arameter estimation in deformable models Fisker, Rune; Carstensen, Jens Michael Published in: Proceedings of the 4th International Conference on Pattern Recognition
More informationMODEL-BASED MULTIPLE FAULT DETECTION AND ISOLATION FOR NONLINEAR SYSTEMS
MODEL-BASED MULIPLE FAUL DEECION AND ISOLAION FOR NONLINEAR SYSEMS Ivan Castillo, and homas F. Edgar he University of exas at Austin Austin, X 78712 David Hill Chemstations Houston, X 77009 Abstract A
More informationAsymptotically Optimal Simulation Allocation under Dependent Sampling
Asymtotically Otimal Simulation Allocation under Deendent Samling Xiaoing Xiong The Robert H. Smith School of Business, University of Maryland, College Park, MD 20742-1815, USA, xiaoingx@yahoo.com Sandee
More informationInformation collection on a graph
Information collection on a grah Ilya O. Ryzhov Warren Powell February 10, 2010 Abstract We derive a knowledge gradient olicy for an otimal learning roblem on a grah, in which we use sequential measurements
More informationChapter 10. Supplemental Text Material
Chater 1. Sulemental Tet Material S1-1. The Covariance Matri of the Regression Coefficients In Section 1-3 of the tetbook, we show that the least squares estimator of β in the linear regression model y=
More informationEvaluation of the critical wave groups method for calculating the probability of extreme ship responses in beam seas
Proceedings of the 6 th International Shi Stability Worsho, 5-7 June 207, Belgrade, Serbia Evaluation of the critical wave grous method for calculating the robability of extreme shi resonses in beam seas
More informationA PEAK FACTOR FOR PREDICTING NON-GAUSSIAN PEAK RESULTANT RESPONSE OF WIND-EXCITED TALL BUILDINGS
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-1, 009, Taiei, Taiwan A PEAK FACTOR FOR PREDICTING NON-GAUSSIAN PEAK RESULTANT RESPONSE OF WIND-EXCITED TALL BUILDINGS M.F. Huang 1,
More informationObserver/Kalman Filter Time Varying System Identification
Observer/Kalman Filter Time Varying System Identification Manoranjan Majji Texas A&M University, College Station, Texas, USA Jer-Nan Juang 2 National Cheng Kung University, Tainan, Taiwan and John L. Junins
More informationSession 5: Review of Classical Astrodynamics
Session 5: Review of Classical Astrodynamics In revious lectures we described in detail the rocess to find the otimal secific imulse for a articular situation. Among the mission requirements that serve
More informationModeling and Estimation of Full-Chip Leakage Current Considering Within-Die Correlation
6.3 Modeling and Estimation of Full-Chi Leaage Current Considering Within-Die Correlation Khaled R. eloue, Navid Azizi, Farid N. Najm Deartment of ECE, University of Toronto,Toronto, Ontario, Canada {haled,nazizi,najm}@eecg.utoronto.ca
More informationThe Nottingham eprints service makes this work by researchers of the University of Nottingham available open access under the following conditions.
Harvey, David I. and Leybourne, Stehen J. and Taylor, A.M. Robert (04) On infimum Dickey Fuller unit root tests allowing for a trend break under the null. Comutational Statistics & Data Analysis, 78..
More informationEstimating function analysis for a class of Tweedie regression models
Title Estimating function analysis for a class of Tweedie regression models Author Wagner Hugo Bonat Deartamento de Estatística - DEST, Laboratório de Estatística e Geoinformação - LEG, Universidade Federal
More information%(*)= E A i* eiujt > (!) 3=~N/2
CHAPTER 58 Estimating Incident and Reflected Wave Fields Using an Arbitrary Number of Wave Gauges J.A. Zelt* A.M. ASCE and James E. Skjelbreia t A.M. ASCE 1 Abstract A method based on linear wave theory
More informationAn Investigation on the Numerical Ill-conditioning of Hybrid State Estimators
An Investigation on the Numerical Ill-conditioning of Hybrid State Estimators S. K. Mallik, Student Member, IEEE, S. Chakrabarti, Senior Member, IEEE, S. N. Singh, Senior Member, IEEE Deartment of Electrical
More informationCovariance Matrix Estimation for Reinforcement Learning
Covariance Matrix Estimation for Reinforcement Learning Tomer Lancewicki Deartment of Electrical Engineering and Comuter Science University of Tennessee Knoxville, TN 37996 tlancewi@utk.edu Itamar Arel
More informationApplied Mathematics and Computation
Alied Mathematics and Comutation 217 (2010) 1887 1895 Contents lists available at ScienceDirect Alied Mathematics and Comutation journal homeage: www.elsevier.com/locate/amc Derivative free two-oint methods
More informationTowards understanding the Lorenz curve using the Uniform distribution. Chris J. Stephens. Newcastle City Council, Newcastle upon Tyne, UK
Towards understanding the Lorenz curve using the Uniform distribution Chris J. Stehens Newcastle City Council, Newcastle uon Tyne, UK (For the Gini-Lorenz Conference, University of Siena, Italy, May 2005)
More informationAdaptive estimation with change detection for streaming data
Adative estimation with change detection for streaming data A thesis resented for the degree of Doctor of Philosohy of the University of London and the Diloma of Imerial College by Dean Adam Bodenham Deartment
More informationUniform Law on the Unit Sphere of a Banach Space
Uniform Law on the Unit Shere of a Banach Sace by Bernard Beauzamy Société de Calcul Mathématique SA Faubourg Saint Honoré 75008 Paris France Setember 008 Abstract We investigate the construction of a
More informationMULTIVARIATE SHEWHART QUALITY CONTROL FOR STANDARD DEVIATION
MULTIVARIATE SHEWHART QUALITY CONTROL FOR STANDARD DEVIATION M. Jabbari Nooghabi, Deartment of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad-Iran. and H. Jabbari
More informationOne-way ANOVA Inference for one-way ANOVA
One-way ANOVA Inference for one-way ANOVA IPS Chater 12.1 2009 W.H. Freeman and Comany Objectives (IPS Chater 12.1) Inference for one-way ANOVA Comaring means The two-samle t statistic An overview of ANOVA
More informationChapter 1 Fundamentals
Chater Fundamentals. Overview of Thermodynamics Industrial Revolution brought in large scale automation of many tedious tasks which were earlier being erformed through manual or animal labour. Inventors
More informationPlotting the Wilson distribution
, Survey of English Usage, University College London Setember 018 1 1. Introduction We have discussed the Wilson score interval at length elsewhere (Wallis 013a, b). Given an observed Binomial roortion
More information