Showing papers on "Probability distribution published in 2002"

Shape distributions

Abstract: Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer graphics, computer vision, molecular biology, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes.In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting.We find that the dissimilarities between sampled distributions of simple shape functions (e.g., the distance between two random points on a surface) provide a robust method for discriminating between classes of objects (e.g., cars versus airplanes) in a moderately sized database, despite the presence of arbitrary translations, rotations, scales, mirrors, tessellations, simplifications, and model degeneracies. They can be evaluated quickly, and thus the proposed method could be applied as a pre-classifier in a complete shape-based retrieval or analysis system concerned with finding similar whole objects. The paper describes our early experiences using shape distributions for object classification and for interactive web-based retrieval of 3D models.

Stochastic Neighbor Embedding

Abstract: We describe a probabilistic approach to the task of placing objects, described by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the high-dimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribution as well as possible when the same operation is performed on the low-dimensional "images" of the objects. A natural cost function is a sum of Kullback-Leibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the low-dimensional images. Unlike other dimensionality reduction methods, this probabilistic framework makes it easy to represent each object by a mixture of widely separated low-dimensional images. This allows ambiguous objects, like the document count vector for the word "bank", to have versions close to the images of both "river" and "finance" without forcing the images of outdoor concepts to be located close to those of corporate concepts.

The scaled unscented transformation

Abstract: This paper describes a generalisation of the unscented transformation (UT) which allows sigma points to be scaled to an arbitrary dimension. The UT is a method for predicting means and covariances in nonlinear systems. A set of samples are deterministically chosen which match the mean and covariance of a (not necessarily Gaussian-distributed) probability distribution. These samples can be scaled by an arbitrary constant. The method guarantees that the mean and covariance second order accuracy in mean and covariance, giving the same performance as a second order truncated filter but without the need to calculate any Jacobians or Hessians. The impacts of scaling issues are illustrated by considering conversions from polar to Cartesian coordinates with large angular uncertainties.

Coherent Risk Measures on General Probability Spaces

Abstract: We extend the definition of coherent risk measures, as introduced by Artzner, Delbaen, Eber and Heath, to general probability spaces and we show how to define such measures on the space of all random variables. We also give examples that relates the theory of coherent risk measures to game theory and to distorted probability measures. The mathematics are based on the characterisation of closed convex sets Pσ of probability measures that satisfy the property that every random variable is integrable for at least one probability measure in the set Pσ.

Electric Power Distribution Reliability

Abstract: DISTRIBUTION SYSTEMS Generation, Transmission, and Distribution Distribution Substations Primary Distribution Systems Secondary Distribution Systems Load Characteristics Distribution Operations RELIABILITY METRICS AND INDICES Power Quality, Reliability, and Availability Reliability Indices Customer Cost of Reliability Reliability Targets History of Reliability Indices INTERRUPTION CAUSES Equipment Failures Animals Severe Weather Trees Human Factors Most Common Causes COMPONENT MODELING Component Reliability Parameters Failure Rates and Bathtub Curves Probability Distribution Functions Fitting Curves to Measured Data Component Reliability Data SYSTEM MODELING System Events and System States Event Independence Network Modeling Markov Modeling Analytical Simulation for Radial Systems Analytical Simulation for Network Systems Monte Carlo Simulation Other Methodologies SYSTEM ANALYSIS Model Reduction System Calibration System Analysis Improving Reliability Storm Hardening Conversion of Overhead to Underground Economic Analysis Marginal Benefit-to-Cost Analysis Comprehensive Example SYSTEM OPTIMIZATION Overview of Optimization Discrete Optimization Methods Knowledge-Based Systems Optimization Applications Final Thoughts on Optimization Study Questions AGING INFRASTRUCTURE Equipment Aging Equipment Age Profiles Population Aging Behavior Age and Increasing Failure Rates Inspection, Repair, and Replacement State of the Industry Final Thoughts

A theoretical study on six classifier fusion strategies

Abstract: We look at a single point in feature space, two classes, and L classifiers estimating the posterior probability for class /spl omega//sub 1/. Assuming that the estimates are independent and identically distributed (normal or uniform), we give formulas for the classification error for the following fusion methods: average, minimum, maximum, median, majority vote, and oracle.

A Survey of Optimization by Building and Using Probabilistic Models

Abstract: This paper summarizes the research on population-based probabilistic search algorithms based on modeling promising solutions by estimating their probability distribution and using the constructed model to guide the exploration of the search space. It settles the algorithms in the field of genetic and evolutionary computation where they have been originated, and classifies them into a few classes according to the complexity of models they use. Algorithms within each class are briefly described and their strengths and weaknesses are discussed.

Modern statistics for the life sciences

Abstract: Why use this book 1. An introduction to the analysis of variance 2. Regression 3. Models, parameters and GLMs 4. Using more than one explanatory variable 5. Designing experiments - keeping it simple 6. Combining continuous and categorical variables 7. Interactions - getting more complex 8. Checking the models A: Independence 9. Checking the models B: The other three assumptions 10. Model selection I: Principles of model choice and designed experiments 11. Model selection II: Data sets with several explanatory variables 12. Random effects 13. Categorical data 14. What lies beyond? Answers to exercises Revision section: The basics Appendix I: The meaning of p-values and confidence intervals Appendix II: Analytical results about variances of sample means Appendix III: Probability distributions Bibliography

Particle filters for state-space models with the presence of unknown static parameters

Abstract: Particle filters for dynamic state-space models handling unknown static parameters are discussed. The approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered. Such a marginalization can always be applied. However, real-time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low-dimensional sufficient statistics. Such sufficient statistics are present in many of the commonly used state-space models. Marginalizing the static parameters avoids the problem of impoverishment, which typically occurs when static parameters are included as part of the state vector. The filters are tested on several different models, with promising results.

Energy detection of a signal with random amplitude

Abstract: Urkowitz (1967) has discussed the detection of a deterministic signal of unknown structure in the presence of band-limited Gaussian noise. That analysis is developed to the case of a signal with random (Rayleigh, Rice, Nakagami, and other) amplitude. For such amplitude the distribution of a decision statistic of an energy detector is retrieved and expressions for detection probability are obtained.

Monotone Comparative Statics under Uncertainty

Abstract: This paper analyzes monotone comparative statics predictions in several classes of stochastic optimization problems. The main results characterize necessary and sufficient conditions for comparative statics predictions to hold based on properties of primitive functions, that is, utility functions and probability distributions. The results apply when the primitives satisfy one of the following two properties: (i) a single-crossing property, which arises in applications such as portfolio investment problems and auctions, or (ii) log-supermodularity, which arises in the analysis of demand functions, affiliated random variables, stochastic orders, and orders over risk aversion.

Creating superpositions that correspond to efficiently integrable probability distributions

Abstract: We give a simple and efficient process for generating a quantum superposition of states which form a discrete approximation of any efficiently integrable (such as log concave) probability density functions.

Probability distribution of returns in the Heston model with stochastic volatility

Abstract: study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the variance, find an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula is in excellent agreement with the Dow-Jones index for time lags from 1 to 250 trading days. For large returns, the distribution is exponential in log-returns with a time-dependent exponent, whereas for small returns it is Gaussian. For time lags longer than the relaxation time of variance, the probability distribution can be expressed in a scaling form using a Bessel function. The Dow-Jones data for 1982-2001 follow the scaling function for seven orders of magnitude.

Joint Integrated Probabilistic Data Association - JIPDA

Abstract: This paper presents a new algorithm for multi-target tracking. In multi-target situations, multiple tracks may share the same measurement(s). Joint events are formed by creating all possible combinations of track-measurement assignments. The probabilities for these joint events are calculated The expressions for the joint events incorporate the probabilities of track existence of individual tracks, as well as an efficient approximation for the cluster volume and an a-priori probability of the number of clutter measurements in each cluster. From these probabilities the data association and track existence probabilities of individual tracks are obtained These probabilities will allow track update in the classic PDA fashion, as well as automatic track initiation, maintenance and termination. The JIPDA algorithm is recursive and integrates seamlessly with the IPDA algorithm. Simulations are used to verify the performance of the algorithm and compare it with the per performance of the IPDA, IPDA-DLL and IJPDA algorithms in a dense and non-homogenous clutter environment, in crossing target situations.

Analysis of symbolic sequences using the Jensen-Shannon divergence.

Abstract: We study statistical properties of the Jensen-Shannon divergence D, which quantifies the difference between probability distributions, and which has been widely applied to analyses of symbolic sequences. We present three interpretations of D in the framework of statistical physics, information theory, and mathematical statistics, and obtain approximations of the mean, the variance, and the probability distribution of D in random, uncorrelated sequences. We present a segmentation method based on D that is able to segment a nonstationary symbolic sequence into stationary subsequences, and apply this method to DNA sequences, which are known to be nonstationary on a wide range of different length scales.

Comment on "A new method for the nonlinear transformation of means and covariances in filters and estimators" [with authors' reply]

Abstract: The above paper (Julier et al. IEEE Trans. Automat. Contr, vol. 45, pp. 477-82, 2000) generalizes the Kalman filter to nonlinear systems by transforming approximations of the probability distributions through the nonlinear process and measurement functions. This comment derives exactly the same estimator by linearizing the process and measurement functions by a statistical linear regression through some regression points (in contrast with the extended Kalman filter which uses an analytic linearization in one point). This insight allows one: 1) to understand/predict the performance of the estimator for specific applications, and 2) to make adaptations to the estimator (i.e., the choice of the regression points and their weights) in those cases where the original formulation does not assure good results. In reply the authors state that the commenters conclusion is unnecessarily narrow interpretation of results.

Multi-Space Probability Distribution HMM

Abstract: This paper proposes a new kind of hidden Markov model (HMM) based on multi-space probability distribution, and derives a parameter estimation algorithm for the extended HMM HMMs are widely used statistical models for characterizing sequences of speech spectra, and have been successfully applied to speech recognition systems HMMs are categorized into discrete HMMs and continuous HMMs, which can model sequences of discrete symbols and continuous vectors, respectively However, we cannot apply both the conventional discrete and continuous HMMs to observation sequences which consist of continuous values and discrete symbols: F0 pattern modeling of speech is a good illustration The proposed HMM includes discrete HMM and continuous HMM as special cases, and furthermore, can model sequences which consist of observation vectors with variable dimensionality and discrete symbols key words: hidden Markov model, text-to-speech, F0, multispace probability distribution

Minimax analysis of stochastic problems

Abstract: In practical applications of stochastic programming the involved probability distributions are never known exactly. One can try to hedge against the worst expected value resulting from a considered set of permissible distributions. This leads to a min-max formulation of the corresponding stochastic programming problem. We show that, under mild regularity conditions, such a min-max problem generates a probability distribution on the set of permissible distributions with the min-max problem being equivalent to the expected value problem with respect to the corresponding weighted distribution. We consider examples of the news vendor problem, the problem of moments and problems involving unimodal distributions. Finally, we discuss the Monte Carlo sample average approach to solving such min-max problems.

Current Fluctuations for the Totally Asymmetric Simple Exclusion Process

Abstract: The time-integrated current of the TASEP has non-Gaussian fluctuations of order t1/3 The recently discovered connection to random matrices and the Painleve II Riemann-Hilbert problem provides a technique through which we obtain the probability distribution of the current fluctuations, in particular their dependence on initial conditions, and the stationary two-point function Some open problems are explained

Probability, Statistics, and Reliability for Engineers and Scientists

Abstract: Introduction Introduction Knowledge, Information, and Opinions Ignorance and Uncertainty Aleatory and Epistemic Uncertainties in System Abstraction Characterizing and Modeling Uncertainty Simulation for Uncertainty Analysis and Propagation Simulation Projects Data Description and Treatment Introduction Classification of Data Graphical Description of Data Histograms and Frequency Diagrams Descriptive Measures Applications Analysis of Simulated Data Simulation Projects Fundamentals of Probability Introduction Sets, Sample Spaces, and Events Mathematics of Probability Random Variables and Their Probability Distributions Moments Application: Water Supply and Quality Simulation and Probability Distributions Simulation Projects Probability Distributions for Discrete Random Variables Introduction Bernoulli Distribution Binomial Distribution Geometric Distribution Poisson Distribution Negative Binomial and Pascal Probability Distributions Hypergeometric Probability Distribution Applications Simulation of Discrete Random Variables A Summary of Distributions Simulation Projects Probability Distributions for Continuous Random Variables Introduction Uniform Distribution Normal Distribution Lognormal Distribution Exponential Distribution Triangular Distribution Gamma Distribution Rayleigh Distribution Beta Distribution Statistical Probability Distributions Extreme Value Distributions Applications Simulation and Probability Distributions A Summary of Distributions Simulation Projects Multiple Random Variables Introduction Joint Random Variables and Their Probability Distributions Functions of Random Variables Modeling Aleatory and Epistemic Uncertainty Applications Multivariable Simulation Simulation Projects Simulation Introduction Monte Carlo Simulation Random Numbers Generation of Random Variables Generation of Selected Discrete Random Variables Generation of Selected Continuous Random Variables Applications Simulation Projects Fundamentals of Statistical Analysis Introduction Properties of Estimators Method-of-Moments Estimation Maximum Likelihood Estimation Sampling Distributions Univariate Frequency Analysis Applications Simulation Projects Hypothesis Testing Introduction General Procedure Hypothesis Tests of Means Hypothesis Tests of Variances Tests of Distributions Applications Simulation of Hypothesis Test Assumptions Simulation Projects Analysis of Variance Introduction Test of Population Means Multiple Comparisons in the ANOVA Test Test of Population Variances Randomized Block Design Two-Way ANOVA Experimental Design Applications Simulation Projects Confidence Intervals and Sample-Size Determination Introduction General Procedure Confidence Intervals on Sample Statistics Sample Size Determination Relationship between Decision Parameters and Types I and II Errors Quality Control Applications Simulation Projects Regression Analysis Introduction Correlation Analysis Introduction to Regression Principle of Least Squares Reliability of the Regression Equation Reliability of Point Estimates of the Regression Coefficients Confidence Intervals of the Regression Equation Correlation versus Regression Applications of Bivariate Regression Analysis Simulation and Prediction Models Simulation Projects Multiple and Nonlinear Regression Analysis Introduction Correlation Analysis Multiple Regression Analysis Polynomial Regression Analysis Regression Analysis of Power Models Applications Simulation in Curvilinear Modeling Simulation Projects Reliability Analysis of Components Introduction Time to Failure Reliability of Components First-Order Reliability Method Advanced Second-Moment Method Simulation Methods Reliability-Based Design Application: Structural reliability of a Pressure Vessel Simulation Projects Reliability and Risk Analysis of Systems Introduction Reliability of Systems Risk Analysis Risk-Based Decision Analysis Application: System Reliability of a Post-Tensioned Truss Simulation Projects Bayesian Methods Introduction Bayesian Probabilities Bayesian Estimation of Parameters Bayesian Statistics Applications Appendix A: Probability and Statistics Tables Appendix B: Taylor Series Expansion Appendix C: Data for Simulation Projects Appendix D: Semester Simulation Project Index Problems appear at the end of each chapter

Stochastic lambda calculus and monads of probability distributions

Abstract: Probability distributions are useful for expressing the meanings of probabilistic languages, which support formal modeling of and reasoning about uncertainty. Probability distributions form a monad, and the monadic definition leads to a simple, natural semantics for a stochastic lambda calculus, as well as simple, clean implementations of common queries. But the monadic implementation of the expectation query can be much less efficient than current best practices in probabilistic modeling. We therefore present a language of measure terms, which can not only denote discrete probability distributions but can also support the best known modeling techniques. We give a translation of stochastic lambda calculus into measure terms. Whether one translates into the probability monad or into measure terms, the results of the translations denote the same probability distribution.

Peak Non-Gaussian Wind Effects for Database-Assisted Low-Rise Building Design

Abstract: Current procedures for estimating the peaks of the stochastic response of tall buildings to wind are based on the assumption that the response is Gaussian. Those procedures are therefore inapplicable to low-rise buildings, in which time histories of wind-induced internal forces are generally non-Gaussian. In this paper, an automated procedure is developed for obtaining from such time histories sample statistics of internal force peaks for low-rise building design and codification. The procedure is designed for use in software for calculating internal force time series by the database-assisted design approach. A preliminary step in the development of the procedure is the identification of the appropriate marginal probability distribution of the time series using the probability plot correlation coefficient method. The result obtained is that the gamma distribution and a normal distribution are appropriate for estimating the peaks correspond- ing, respectively, to the longer and shorter tail of the time series' histograms. The distribution of the peaks is then estimated by using the standard translation processes approach. It is found that the peak distribution can be represented by the Extreme Value Type I ~Gumbel! distribution. Because estimates obtained from this approach are based on the entire information contained in the time series, they are more stable than estimates based on observed peaks. The procedure can be used to establish minimum acceptable requirements with respect to the duration and sampling rate of the time series of interest, so that the software used for database-assisted design will be both efficient and accurate.

An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches

Abstract: Deterministic optimum designs that are obtained without consideration of uncertainty could lead to unreliable designs, which call for a reliability approach to design optimization, using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in an original random space (X-space) and reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mapping between X- and U-spaces for a various probability distributions. Therefore, the nonlinearity of RBDO problem will depend on the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity to reliability-based performance measures evaluated during the RBDO process. Evaluation of probabilistic constraints in RBDO can be carried out in two different ways: the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity of RIA and PMA in the RBDO process. In this paper, it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of highly nonlinear transformations involved. However, PMA is rather independent of probability distributions because of little involvement of the nonlinear transformation.Copyright © 2002 by ASME

An Introduction to Probabilistic Graphical Models

Abstract: In this chapter we will introduce two probabilistic graphical models -Bayesian networks and Gaussian networks-that will be used to carry out factorization of the probability distribution of the selected individuals in the Estimation of Distribution Algorithms based approaches. For both paradigms we will present different algorithms to induce the underlying model from data, as well as some methods to simulate such models.

Modifying advertisement scores based on advertisement response probabilities

Abstract: Advertisement response probabilities are utilized to alter advertisement scores. A plurality of possible advertisements is accessed from, for example, an advertisement database or advertisement pipeline. A response probability for each advertisement is determined. A response probability may be a probability that a user will “click,” or otherwise select an advertisement. Advertisements may be associated with probabilistic prediction models that take advertisement recipient attribute values as inputs and provide a probability distribution as output. A score associated with each of the possible advertisements is altered based on the response probability for each of the advertisements. Statistical prediction is used to determine how scores are to be altered. Advertisements with response probabilities less than a mean probability may have associated scores decreased. Conversely, advertisements with response probabilities greater than a mean probability may have associated scores increased.

PhFit: A General Phase-Type Fitting Tool

Abstract: PhFit, a new Phase-type fitting tool is presented in this paper. The presented tool is novel from several aspects. It allows for approximating distributions or set of samples not only by continuous but by discrete Phase-type distributions as well. The implemented algorithms separate the fitting of the body and the tail part of the distribution which results in satisfactory fitting also for heavy-tail distributions. Moreover, PhFit allows the user to choose the distance measure according to which the fitting is performed.

Probability Distribution of Solution Time in GRASP: An Experimental Investigation

Abstract: A GRASP (greedy randomized adaptive search procedure) is a multi-start metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a sub-optimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. Standard methodology for graphical analysis is used to compare the empirical and theoretical distributions and estimate the parameters of the distributions. We conclude that the solution time to a sub-optimal target value fits a two-parameter exponential distribution. Hence, it is possible to approximately achieve linear speed-up by implementing GRASP in parallel.

Probability Distribution of Low Streamflow Series in the United States

Abstract: Estimates of low streamflow statistics are required for a variety of water resource applications. At gauged river sites, the estimation of low streamflow statistics requires estimation of annual n-day minimum streamflows, selection of a probability distribution to describe annual minimums, and estimation of the distribution's parameters. Using L-moment diagrams, the ability of various probabil- ity distributions to describe low streamflow series was examined at 1,505 gauged river sites in the United States. A weighted distance statistic was developed to compare the goodness-of-fit of different probability distributions for describing low streamflow series. Com- pared to perennial streamflow sites, a shift of L-moments ratios was observed at intermittent river sites where discharge is sometimes reported as zero. An analytical experiment compared the observed shifts in L-moment ratios at intermittent sites with theoretical L-moment ratio shifts for a number of real- and log-spaced probability distributions. Results of these experiments indicate that Pearson Type III and the 3-parameter lognormal distributions should be the recommended distributions for describing low streamflow statistics in the United States at intermittent and nonintermittent ~perennial! sites, respectively.