approximations of temporal rainfall from a multidimensional model the feasibility of representing the temporal structure of a multidimensional rainfall process with simpler stochastic models and a study of the effect of parameter robustness on the time scale is investigated here via performing controlled numerical experiments a multidimensional representation for precipitation given in the theory recently proposed by e waymire et al 1984 is used for simulating rainfall in space and time the model produces moving storms with realistic mesoscale meteorological features e g clustering birth and death of cells cell intensity attenuation in time and space etc two year traces of rainfall intensities at fixed gage stations were generated at intervals of 0 1 hours for three climates these traces are then aggregated at different time scales ranging from 1 to 24 hours first and second order statistics are evaluated from the above series at each aggregation level and they are used for estimating the parameters of three one dimensional models of temporal rainfall at a point 1 poisson model with independent marks 2 rectangular pulses with independent intensity and duration and 3 neyman scott with independent marks only at very high levels of aggregation the compound poisson model was able to reproduce the statistical structure of the simulated traces the rectangular pulses model was found to have parameters which vary significantly with the time scale of aggregation and moreover it leads to large distortions in the mean depth and duration of storm events the neyman scott scheme proved to be the most stable model throughout the different time scales and it also reproduced quite well the average storm characteristics at the event level none of these three models was able to reproduce in a satisfactory manner the simulated extreme value distribution of the multidimensional model

rational cohomology of witt groups let k be an algebraically closed field of characteristic p and for each n 0 let w n denote the group of witt vectors of length n w n is a commutative algebraic group for reference see jacobson 2 serre 6 one of the important properties of the witt groups is the following every commutative algebraic k group whose underlying variety is an affine space is a homomorphic image of products of w n we compute the rational cohomology of w n for n 2 h w n k s v n 1 1 l e rn 1 l

bayesian hybrid generative discriminative learning based on finite liouville mixture models recently hybrid generative discriminative approaches have emerged as an efficient knowledge representation and data classification engine however little attention has been devoted to the modeling and classification of non gaussian and especially proportional vectors our main goal in this paper is to discover the true structure of this kind of data by building probabilistic kernels from generative mixture models based on liouville family from which we develop the beta liouville distribution and which includes the well known dirichlet as a special case the beta liouville has a more general covariance structure than the dirichlet which makes it more practical and useful our learning technique is based on a principled purely bayesian approach which resulted models are used to generate support vector machine svm probabilistic kernels based on information divergence in particular we show the existence of closed form expressions of the kullback leibler and renyi divergences between two beta liouville distributions and then between two dirichlet distributions as a special case through extensive simulations and a number of experiments involving synthetic data visual scenes and texture images classification we demonstrate the effectiveness of the proposed approaches

a generalized kernel approach to dissimilarity based classification usually objects to be classified are represented by features in this paper we discuss an alternative object representation based on dissimilarity values if such distances separate the classes well the nearest neighbor method offers a good solution however dissimilarities used in practice are usually far from ideal and the performance of the nearest neighbor rule suffers from its sensitivity to noisy examples we show that other more global classification techniques are preferable to the nearest neighbor rule in such cases for classification purposes two different ways of using generalized dissimilarity kernels are considered in the first one distances are isometrically embedded in a pseudo euclidean space and the classification task is performed there in the second approach classifiers are built directly on distance kernels both approaches are described theoretically and then compared using experiments with different dissimilarity measures and datasets including degraded data simulating the problem of missing values

parameter estimation for point processes with partial observations a filtering approach the estimation of the parameters of a doubly stochastic poisson process driven by a markov chain is considered an ml estimator will be defined by the conditional likelihood ratio given the observations of one path of the point process the filler equation for point processes is used as a tool to solve the corresponding maximisation problem

a deterministic geometric representation of temporal rainfall results for a storm in boston the use of a deterministic fractal multifractal fm representation to model high resolution rainfall time series via projections of fractal interpolating functions weighed by multifractal measures is reported it is shown that the intrinsic shape and variability of an 8 hour boston storm recorded every 15 s on october 25 1980 may be encoded wholistically employing the fractal geometric methodology it is illustrated that the fm methodology provides very faithful descriptions of both major trends and small noisy fluctuations for this storm resulting in preservation of not only classical statistical characteristics of the records but also multifractal and chaotic properties present in them these results and those for other storms suggest that a stochastic framework for rainfall may be bypassed in favor of a deterministic representation based on projections

the mathematical structure of rainfall representations 3 some applications of the point process theory to rainfall processes part 3 constitutes the final part of three parts devoted to the mathematical structure of rainfall the objective is to illustrate the scope of the tools developed in part 2 in the mathematical description of rainfall and rainfall driven processes a general overview of the three part series is given in part 1

information distance while kolmogorov 1965 complexity is the accepted absolute measure of information content in an individual finite object a similarly absolute notion is needed for the information distance between two individual objects for example two pictures we give several natural definitions of a universal information metric based on length of shortest programs for either ordinary computations or reversible dissipationless computations it turns out that these definitions are equivalent up to an additive logarithmic term we show that the information distance is a universal cognitive similarity distance we investigate the maximal correlation of the shortest programs involved the maximal uncorrelation of programs a generalization of the slepian wolf theorem of classical information theory and the density properties of the discrete metric spaces induced by the information distances a related distance measures the amount of nonreversibility of a computation using the physical theory of reversible computation we give an appropriate universal antisymmetric and transitive measure of the thermodynamic work required to transform one object in another object by the most efficient process information distance between individual objects is needed in pattern recognition where one wants to express effective notions of pattern similarity or cognitive similarity between individual objects and in thermodynamics of computation where one wants to analyze the energy dissipation of a computation from a particular input to a particular output

conditional distributions of neyman scott models for storm arrivals and their use in irrigation scheduling count for the widely recognized but often neglected statistical dependence in storm arrivals gabriel and newmann 1957 1962 smith and schreiber 1973 kavvas and delleur 1975 recently authors like kavvas and delleur 1975 and gupta and waymire 1979 have argued that this dependence is due to clustering of rainfall in time and space they suggest modeling storm arrivals with cluster point processes like the neyman scott model this work uses the concept of cluster models for storm arrivals the conditional distribution of the occurrence of future events given a history of the timing of past events is derived for the neyman scott model this new result is then used with a reformulated model of the irrigation scheduling problem now the decision of when and how much to irrigate is based on the time since the last observed storm the effective soil moisture content and the amount of available irrigation water a case study is presented to illustrate the solution significantly there is no important difference between the theoretical net benefits derived from assuming a homogeneous independent poisson model or a dependent neyman scott n s model during the growing season a nonhomogeneous poisson model yields higher theoretical benefits as expected the conditional n s model leads to improved irrigation control as compared to the unconditional n s model from this case study however no definite conclusion can be drawn regarding whether the neyman scott model better represents the process of storm arrivals as opposed to the poisson model however the expected opportunity loss of choosing the wrong model can be significant interesting implications of the results are that data manipulation can have a significant effect on the ultimate model

compatibility of continuous rainfall occurrence models with discrete rainfall observations inferences about the underlying rainfall generating mechanism made through a model fitted to the sampled rainfall series at a particular time scale are meaningful only if they are invariant under the time scale of measurement at which the fitting of the model is made following the work of i rodriguez iturbe et al 1984 this assertion is tested by examining the compatibility of the neyman scott n s model for the continuous underlying rainfall with sampled realizations taken over intervals ranging from one hour to one day the results suggest that the n s model is inconsistent at different time scales and therefore mathematical descriptions of rainfall using this model are inevitably limited to the time scale of measurement at which a description of rainfall is sought these findings are quite general in that they apply to any model with rainfall deposited instantaneously at times described by a n s process regardless of how the amounts associated with the events are distributed and of the dependence structure of the amounts

flood frequency analysis using the cox regression model procedures for incorporating time varying exogenous information into flood frequency analyses are developed using the cox regression model for counting processes in this statistical model the probability of occurrence of a flood peak in a short interval t t dt depends in an explicit manner on the values at t of k covariate processes z1 zk specifically letting dn t be 1 if a flood peak occurs in t t dt and 0 otherwise dn t a t exp j 1kbjzj t dm t where a the baseline intensity is an unknown function b is a vector of unknown regression parameters and the error dm t is conditionally orthogonal to the past history two applications assessment of relative importance of physical processes such as snow melt or soil moisture storage on flood frequency at a site and derivation of time varying flood frequency estimates are considered

a point process model for rainfall further developments a stochastic model for rainfall at a single site is studied in which storms arrive in a poisson process each storm consisting of a cluster of a random number of rain cells each cell having random duration and depth a model studied in an earlier paper is extended to provide a better fit to empirical experience the extension being based on the attachment of a single random variable to each storm to achieve in particular some correlation between the durations of the cells within a single storm the properties of the new model are developed its fitting to two sets of empirical data is described and the examination of adequacy of fit is studied in some detail via properties not used in the fitting procedure finally a theoretical study is made of short term prediction from the model

a cluster model for flood analysis a two level and two dimensional nonhomogeneous point stochastic process is developed to model the flood peaks of a hydrograph the model is a cluster process of the neyman scott type and presents the occurrences of flood generating mechanisms fgm at the precipitation level as the triggers for clusters of flood peaks at the runoff level the fgms are studied in terms of their times of occurrence and their volumes the volume of a fgm corresponds to the volume of precipitation in the precipitation cluster that originates at the occurrence time of the fgm thus each precipitation cluster at the precipitation level is represented by its origin time and by its volume as a point in a time volume plane the fgm points in the time volume plane of the precipitation level form a two dimensional process nc with a nonhomogeneous rate of occurrence it is assumed that nc is a poisson process the fgms in turn generate a two dimensional subsidiary process ns t in the runoff level this process represents the occurrences of flood peaks at time t with magnitude m as a point in the time magnitude plane t t m determined by the conditional rate of occurrence t and is also assumed to be a poisson process the statistical properties of the flood cluster process n t defined as the total number of flood peaks are found in terms of the probability generating functional of the process using a nonparametric methodology the two dimensional parameters and t are estimated the theoretical rate of occurrence the theoretical covariance density and the theoretical probability mass function of the process are compared with the respective empirical functions obtained for several stations located in the ohio river basin a good fit is found for the analyzed stations as the first two moments and the two dimensional probability mass function of the flood peak process are preserved

a hybrid model for point rainfall modeling a hybrid point rainfall model a product of two random processes is presented the model uses a jitter model a general technique for improving the fit of any point process based model we use the nonrandomized bartlett lewis rectangular pulse and an autoregressive model as a jitter first the five parameters of the bartlett lewis model are estimated by the method of moments using the mean of one aggregation level and the dry probabilities of all aggregation levels considered second the parameters of the autoregressive model are derived from the moments of the historical data and those given by the bartlett lewis model without additional cost in terms of parameter calibration using 15 min point rainfall data of capella central queensland australia as a test case the results of the hybrid model were better than the best results given by the randomized bartlett lewis model on its own the nonrandomized bartlett lewis model produced very poor results

two site modeling of rainfall based on the neyman scott process on the basis of the neyman scott process a model is proposed to generate rainfall at two sites simultaneously this model takes into account the correlation which is produced by generating bivariate correlated variates the cross correlation between the sites has been computed in order to estimate the parameters finally the model is validated for three pairs of stations situated in the swiss plateau region

adaptive local linear regression with application to printer color management local learning methods such as local linear regression and nearest neighbor classifiers base estimates on nearby training samples neighbors usually the number of neighbors used in estimation is fixed to be a global ldquooptimalrdquo value chosen by cross validation this paper proposes adapting the number of neighbors used for estimation to the local geometry of the data without need for cross validation the term enclosing neighborhood is introduced to describe a set of neighbors whose convex hull contains the test point when possible it is proven that enclosing neighborhoods yield bounded estimation variance under some assumptions three such enclosing neighborhood definitions are presented natural neighbors natural neighbors inclusive and enclosing k nn the effectiveness of these neighborhood definitions with local linear regression is tested for estimating lookup tables for color management significant improvements in error metrics are shown indicating that enclosing neighborhoods may be a promising adaptive neighborhood definition for other local learning tasks as well depending on the density of training samples

point processes and queues martingale dynamics i martingales 1 histories and stopping times 2 martingales 3 predictability 4 square integrable martingales references solutions to exercises chapter i ii point processes queues and intensities 1 counting processes and queues 2 watanabe s characterization 3 stochastic intensity general case 4 predictable intensities 5 representation of queues 6 random changes of time 7 cryptographic point processes references solutions to exercises chapter ii iii integral representation of point process martingales 1 the structure of internal histories 2 regenerative form of the intensity 3 the representation theorem 4 hilbert space theory of poissonian martingales 5 useful extensions references solutions to exercises chapter iii iv filtering 1 the theory of innovations 2 state estimates for queues and markov chains 3 continuous states and nontrivial prehistory references solutions to exercises chapter iv v flows in markovian networks of queues 1 single station the historical results and the filtering method 2 jackson s networks 3 burke s output theorem for networks 4 cascades and loops in jackson s networks 5 independence and poissonian flows in markov chains references solutions to exercises chapter v vi likelihood ratios 1 radon nikodym derivatives and tests of hypotheses 2 changes of intensities a la girsanov 3 filtering by the method of the probability of reference 4 applications 5 the capacity of a point process channel 6 detection formula187 references189 solutions to exercises chapter vi vii optimal control 1 modeling intensity controls 2 dynamic programming for intensity controls complete observation case 3 input regulation a case study in impulsive control 4 attraction controls 5 existence via likelihood ratio references solutions to exercises chapter vii viii marked point processes 1 counting measure and intensity kernels 2 martingale representation and filtering 3 radon nikodym derivatives 4 towards a general theory of intensity references solutions to exercises chapter viii a1 background in probability and stochastic processes 1 introduction 2 monotone class theorem 3 random variables 4 expectations 5 conditioning and independence 6 convergence 7 stochastic processes 8 markov processes references a2 stopping times and point process histories 1 stopping times 2 changes of time and meyer dellacherie s integration formula 3 point process histories references a3 wiener driven dynamical systems 1 ito s stochastic integral 2 square integrable brownian martingales 3 girsanov s theorem references a4 stieltjes lebesgue calculus 1 the stieltjes lebesgue integral 2 the product and exponential formulas references general bibliography

generalized scale invariance in the atmosphere and fractal models of rain in recent years there has been considerable interest in stochastic rain models by developing new ideas about scale invariance and intermittency we argue that the scope of such models can be greatly extended the notions of scale invariance intermittency and the associated idea of fractal dimension have lately gained considerable ground particularly in the context of extremely variable phenomena such as those found in the mesoscale and in hydrodynamic turbulence we review some relevant work and argue that the atmosphere respects a symmetry principle that we call generalized scale invariance in which the statistical properties of the small and large scale are related to each other by a magnification coupled with a differential stratification due to gravity and differential rotation due to the coriolis force we further argue that the extremely erratic intermittent nature of the atmosphere is characterized by scale invariant fractal measures leading to hyperbolic fat tailed probability distributions of the fluctuations the standard statistical methods based on exponential fall offs in both correlations and probability distributions are inappropriate when the variability is of this type we show how both the scaling and intermittency may be exploited to develop extremely variable stochastic models of rain although the models examined here are the simplest of a family of extremely variable processes depending on only two radar determined parameters they lead to realizations possessing many realistic features of the rainfield including complexity of form clustering and bands at all scales as well as differential stratification and rotation finally we point to weaknesses in the models in particular their monodimensional nature and suggest possible improvements

classification with nonmetric distances image retrieval and class representation a key problem in appearance based vision is understanding how to use a set of labeled images to classify new images systems that model human performance or that use robust image matching methods often use nonmetric similarity judgments but when the triangle inequality is not obeyed most pattern recognition techniques are not applicable exemplar based nearest neighbor methods can be applied to a wide class of nonmetric similarity functions the key issue however is to find methods for choosing good representatives of a class that accurately characterize it we show that existing condensing techniques are ill suited to deal with nonmetric dataspaces we develop techniques for solving this problem emphasizing two points first we show that the distance between images is not a good measure of how well one image can represent another in nonmetric spaces instead we use the vector correlation between the distances from each image to other previously seen images second we show that in nonmetric spaces boundary points are less significant for capturing the structure of a class than in euclidean spaces we suggest that atypical points may be more important in describing classes we demonstrate the importance of these ideas to learning that generalizes from experience by improving performance we also suggest ways of applying parametric techniques to supervised learning problems that involve a specific nonmetric distance functions showing how to generalize the idea of linear discriminant functions in a way that may be more useful in nonmetric spaces

a geomorphologic synthesis of nonlinearity in surface runoff the geomorphic approach leading to a representation of an instantaneous unit hydrograph iuh which we developed earlier is generalized to incorporate nonlinear effects in the rainfall runoff transformation it is demonstrated that the nonlinearity in the transformation enters in part through the dependence of the mean holding time on the rainfall intensity under an assumed first approximation that this dependence is the sole source of nonlinearity an explicit quasi linear representation results for the rainfall runoff transformation the kernel function of this transformation can be termed as the instantaneous response function irf in contradistinction to the notion of an iuh for the case of a linear rainfall runoff transformation the predictions from the quasi linear theory agree very well with predictions from the kinematic wave approach for the one small basin that is analyzed also for two large basins in illinois having areas of about 1100 mi2 the predictions from the quasi linear approach compare very well with the observed flows a measure of nonlinearity naturally arises through the dependence of the mean holding time kb i0 on the rainfall intensity i0via kb i0 i0 computations of for four basins show that approaches as basin size decreases and approaches zero as the basin size increases a semilog plot of versus the square root of the basin area gives a straight line confirmation of this relationship for other basins would be of basic importance in predicting flows from ungaged basins

a nonparametric wet dry spell model for resampling daily precipitation a nonparametric wet dry spell model is developed for resampling daily precipitation at a site the model considers alternating sequences of wet and dry days in a given season of the year all marginal joint and conditional probability densities of interest e g dry spell length wet spell length precipitation amount and wet spell length given prior to dry spell length are estimated nonparametrically using at site data and kernel probability density estimators procedures for the disaggregation of wet spell precipitation into daily precipitation and for the generation of synthetic sequences are proffered an application of the model for generating synthetic precipitation traces at a site in utah is presented

an entropic stochastic representation of rainfall intermittency the origin of clustering and persistence 1 the well established physical and mathematical principle of maximum entropy interpreted as maximum uncertainty is used to explain the observed dependence properties of the rainfall occurrence process including the clustering behavior and persistence the conditions used for the maximization of entropy are as simple as possible i e that the rainfall processes is intermittent with dependent occurrences intermittency is quantified by the probability that a time interval is dry and dependence is quantified by the probability that two consecutive intervals are dry these two probabilities are used as constraints in a multiple scale entropy maximization framework which determines any conditional or unconditional probability of any sequence of dry and wet intervals at any timescale thus the rainfall occurrence process including its dependence structure is described by only two parameters this dependence structure appears to be non markovian application of this theoretical framework to the rainfall data set of athens indicates good agreement of theoretical predictions and empirical data at the entire range of scales for which probabilities dry and wet can be estimated from one hour to several months

on binary time series obtained from continuous time point processes describing rainfall recent work on modeling rainfall occurrence has used continuous time point process models in many cases the available data is not sufficiently precise to properly fit such a model for example if only occurrence or nonoccurrence of precipitation is given daily a more appropriate model would be a binary time series in this work we relate some parameters of the time series thus obtained to parameters of the underlying but not observed continuous time process we carry out the details for several models proposed in the literature such as the neyman scott poisson cluster process and the smith karr renewal cox process an application of the theory is illustrated on some washington state rainfall data

an smo algorithm for the potential support vector machine we describe a fast sequential minimal optimization smo procedure for solving the dual optimization problem of the recently proposed potential support vector machine p svm the new smo consists of a sequence of iteration steps in which the lagrangian is optimized with respect to either one single smo or two dual smo of the lagrange multipliers while keeping the other variables fixed an efficient selection procedure for lagrange multipliers is given and two heuristics for improving the smo procedure are described block optimization and annealing of the regularization parameter e a comparison of the variants shows that the dual smo including block optimization and annealing performs efficiently in terms of computation time in contrast to standard support vector machines svms the p svm is applicable to arbitrary dyadic data sets but benchmarks are provided against libsvm s e svr and c svc implementations for problems that are also solvable by standard svm methods for those problems computation time of the p svm is comparable to or somewhat higher than the standard svm the number of support vectors found by the p svm is usually much smaller for the same generalization performance

a spectral theory of rainfall intensity at the meso β scale the available empirical descriptions of extratropical cyclonic storms are employed to formulate a physically realistic stochastic representation of the ground level rainfall intensity field in space and time the stochastic representation is based on three component stochastic point processes which possess the general features of the embedding of rain cells within small mesoscale areas within large mesoscale areas within synoptic storms certain scale idealizations and assumptions on functional forms which qualitatively reflect the physical features lead to a closed form expression for the covariance function i e the real space time spectrum of the rainfall intensity field the theoretical spectrum explains the empirical spectral features observed by zawadzki almost a decade ago of particular interest and importance in this connection is an explanation of the empirical observation that the taylorian propogation of the fine scale structure via a transformation of time to space through the storm velocity holds only for a small time lag and not throughout the results here indicate the extent of this lag in terms of the characteristic scales associated with cell durations cellular birthrates and velocities etc

similarity measures with complex multimedia data we see the emergence of database systems in which the fundamental operation is similarity assessment before database issues can be addressed it is necessary to give a definition of similarity as an operation we develop a similarity measure based on fuzzy logic that exhibits several features that match experimental findings in humans the model is dubbed fuzzy feature contrast ffc and is an extension to a more general domain of the feature contrast model due to tversky 1977 we show how the ffc model can be used to model similarity assessment from fuzzy judgment of properties and we address the use of fuzzy measures to deal with dependencies among the properties

continuous time versus discrete time point process models for rainfall occurrence series several authors have had apparent success in applying continuous time point process models to rainfall occurrence sequences in this paper it is shown that if rainfall occurrences are interpreted as the events of a point process and not as a censored sample the continuous time point process methodology and estimation procedures are not directly applicable since they fail to account for the time discreteness of the sample process this is demonstrated analytically by studying the effects of discretization on selected statistical properties of a poisson process a neyman scott process and a renewal cox process with markovian intensity in general the study of rainfall occurrences under the continuous time point process framework may result in misleading inferences regarding clustering dispersion and consequently incorrect interpretations of the underlying rainfall generating mechanisms for example daily rainfall occurrence structures underdispersed relative to the poisson process are usually overdispersed relative to the bernoulli process the discrete time analogue of the poisson these findings are confirmed by the statistical analysis of six daily rainfall records representative of a range of u s climates two of which are described in detail

on space time scaling of cumulated rainfall fields in the study of space time rainfall it is particularly important to establish characteristic properties to guide both theoretical and modeling research efforts in the present paper new observational analyses on the scaling properties of time evolving cumulated rainfall fields are presented and a theoretical framework for their interpretation is introduced it is found that the time evolution of the spatial organization of a cumulated rainfall field produces scaling relationships of spatial variance versus time and characteristic values for the scaling exponent the reproduction of these values constitutes a basic requirement for spatial temporal field generators in order to model important properties of real rainfall fields it is then shown on theoretical grounds what properties the instantaneous rainfall intensity fields must obey in order to reproduce the experimental observations and how the size of the observation domain affects the scaling relationships some current stochastic models of space time precipitation are finally discussed and analyzed in the light of the tools introduced to show under what circumstances the models considered give acceptable results furthermore it is shown that the assumption of an exponential time correlation function used in many current rainfall models is not compatible with observations

generative models for similarity based classification a maximum entropy approach to generative similarity based classifiers model is proposed first a descriptive set of similarity statistics is assumed to be sufficient for classification then the class conditional distributions of these descriptive statistics are estimated as the maximum entropy distributions subject to empirical moment constraints the resulting exponential class conditional distributions are used in a maximum a posteriori decision rule forming the similarity discriminant analysis sda classifier simulated and real data experiments compare performance to the k nearest neighbor classifier the nearest centroid classifier and the potential support vector machine psvm

the mathematical structure of rainfall representations 2 a review of the theory of point processes part 2 constitutes the second of three parts devoted to the mathematical structure of rainfall an expository yet current treatment of those features of point process theory which are essential to descriptions of the hydrologic processes is developed a general overview of this three part series is given in part 1

experimental study on prototype optimisation algorithms for prototype based classification in vector spaces prototype based classification relies on the distances between the examples to be classified and carefully chosen prototypes a small set of prototypes is of interest to keep the computational complexity low while maintaining high classification accuracy an experimental study of some old and new prototype optimisation techniques is presented in which the prototypes are either selected or generated from the given data these condensing techniques are evaluated on real data represented in vector spaces by comparing their resulting reduction rates and classification performance usually the determination of prototypes is studied in relation with the nearest neighbour rule we will show that the use of more general dissimilarity based classifiers can be more beneficial an important point in our study is that the adaptive condensing schemes here discussed allow the user to choose the number of prototypes freely according to the needs if such techniques are combined with linear dissimilarity based classifiers they provide the best trade off of small condensed sets and high classification accuracy

the effect of certain restrictions imposed on the interarrival times of flood events on the poisson distribution used for modeling flood counts in the application of partial duration series models of flood analysis it is occasionally observed that successive exceedances are correlated to reduce this correlation some investigators tend to impose certain restrictions on the interarrival times of flood events in order that these events will not occur close together in bunches we show analytically how such restrictions interfere with the underlying hypotheses of the poisson process commonly used to model flood counts and we caution against imposing restrictions that may render this simple and appealing model inapplicable

the mathematical structure of rainfall representations 1 a review of the stochastic rainfall models this is the first of a three part series on the mathematical structure of rainfall models several important attempts at modeling rainfall are reviewed special attention is given to the mathematical structures that arise in the rainfall descriptions a general overview of the three part series is given as preface to this part

seasonal generalized exponential probability models with application to interstorm and storm durations a simple generalization of the exponential probability model is presented which provides a flexible method for identifying and fitting probability distributions when coupled with likelihood based estimation this approach enables a parsimonious description of seasonal dependence using harmonic functions a case study involving modeling of interstorm and storm durations for several australian state capitals illustrates practical issues in calibration and identification because the rainfall data were stored in a binned format consisting of rainfall depths accumulated over fixed time intervals the start and end times of storms were known only to the resolution of the fixed time interval a likelihood function is developed which properly makes use of such information likelihood ratio statistics along with monthly distribution plots are used to select the number of harmonics necessary to model seasonal dependence it is shown for melbourne that a single harmonic adequately describes seasonal dependence thereby reducing the number of parameters from 48 to 6

multiscaling pulse representation of temporal rainfall 1 we develop a pulse based representation of temporal rainfall with multifractal properties in the small scale limit the representation combines a traditional model for the exterior process at the synoptic scale with a novel hierarchical pulse model for the event interiors for validation we apply the model to a temporal rainfall record from florence italy although the model has only six parameters four for the exterior process and two for the event interiors it accurately reproduces a wide range of empirical statistics including the distribution of dry and wet periods the distribution of rainfall intensity up to extreme fractiles the spectral density the moment scaling function k q and the distribution of the partition coefficients for rainfall disaggregation the model also reproduces observed deviations of physical rainfall from perfect scaling multiscaling behavior

hessian optimal design for image retrieval recently there has been a considerable interest in active learning from the perspective of optimal experimental design oed oed selects the most informative samples to minimize the covariance matrix of the parameters so that the expected prediction error of the parameters as well as the model output can be minimized most of the existing oed methods are based on either linear regression or laplacian regularized least squares laprls models although laprls has shown a better performance than linear regression it suffers from the fact that the solution is biased towards a constant and the lack of extrapolating power in this paper we propose a novel active learning algorithm called hessian optimal design hod hod is based on the second order hessian energy for semi supervised regression which overcomes the drawbacks of laplacian based methods specifically hod selects those samples which minimize the parameter covariance matrix of the hessian regularized regression model the experimental results on content based image retrieval have demonstrated the effectiveness of our proposed approach

support vector machines for dyadic data we describe a new technique for the analysis of dyadic data where two sets of objects row and column objects are characterized by a matrix of numerical values that describe their mutual relationships the new technique called potential support vector machine p svm is a large margin method for the construction of classifiers and regression functions for the column objects contrary to standard support vector machine approaches the p svm minimizes a scale invariant capacity measure and requires a new set of constraints as a result the p svm method leads to a usually sparse expansion of the classification and regression functions in terms of the row rather than the column objects and can handle data and kernel matrices that are neither positive definite nor square we then describe two complementary regularization schemes the first scheme improves generalization performance for classification and regression tasks the second scheme leads to the selection of a small informative set of row support objects and can be applied to feature selection benchmarks for classification regression and feature selection tasks are performed with toy data as well as with several real world data sets the results show that the new method is at least competitive with but often performs better than the benchmarked standard methods for standard vectorial as well as true dyadic data sets in addition a theoretical justification is provided for the new approach

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

on the information and representation of non euclidean pairwise data two common data representations are mostly used in intelligent data analysis namely the vectorial and the pairwise representation pairwise data which satisfy the restrictive conditions of euclidean spaces can be faithfully translated into a euclidean vectorial representation by embedding non metric pairwise data with violations of symmetry reflexivity or triangle inequality pose a substantial conceptual problem for pattern recognition since the amount of predictive structural information beyond what can be measured by embeddings is unclear we show by systematic modeling of non euclidean pairwise data that there exists metric violations which can carry valuable problem specific information furthermore euclidean and non metric data can be unified on the level of structural information contained in the data stable component analysis selects linear subspaces which are particularly insensitive to data fluctuations experimental results from different domains support our pattern recognition strategy

further developments of the neyman scott clustered point process for modeling rainfall this paper provides some useful results for modeling rainfall it extends work on the neyman scott cluster model for simulating rainfall time series several important properties have previously been found for the model for example the expectation and variance of the amount of rain captured in an arbitrary time interval rodriguez iturbe et al 1987a in this paper additional properties are derived such as the probability of an arbitrary interval of any chosen length being dry in applications this is a desirable property to have and is often used for fitting stochastic rainfall models to field data the model is currently being used in rainfall time series research directed toward improving sewage systems in the united kingdom to illustrate the model s performance an example is given where the model is fitted to 10 years of hourly data taken from blackpool england

some models for discretized series of events a discretized series of events is a binary time series that indicates whether or not events of a point process in the line occur in successive intervals such data are common in environmental applications we describe a class of models for them based on an unobserved continuous time discrete state markov process which determines the rate of a doubly stochastic poisson process from which the binary time series is constructed by discretization we discuss likelihood inference for these processes and their second order properties and extend them to multiple series an application involves modeling the times of exposures to air pollution at a number of receptors in western europe

the similarity metric a new class of distances appropriate for measuring similarity relations between sequences say one type of similarity per distance is studied we propose a new normalized information distance based on the noncomputable notion of kolmogorov complexity and show that it is in this class and it minorizes every computable distance in the class that is it is universal in that it discovers all computable similarities we demonstrate that it is a metric and call it the similarity metric this theory forms the foundation for a new practical tool to evidence generality and robustness we give two distinctive applications in widely divergent areas using standard compression programs like gzip and gencompress first we compare whole mitochondrial genomes and infer their evolutionary history this results in a first completely automatic computed whole mitochondrial phylogeny tree secondly we fully automatically compute the language tree of 52 different languages

a stochastic cluster model of daily rainfall sequences a two level point stochastic model for the rainfall occurrences at a given rainfall station is constructed in the time dimension the model is a cluster process of the neyman scott type the model has the rainfall generating mechanisms as its primary level and the rainfalls that are generated by these mechanisms as the secondary level it uses infinite superposition of rainfalls and has a very flexible dependence structure the model is fitted to daily rainfall sequences in indiana after these are stationarized by a transformation the fit of the model is then tested in terms of its correlation and marginal probability characteristics the present form of the neyman scott cluster model is time homogeneous therefore the neyman scott process as presented in this paper may be of practical use only for modeling the stationary rainfall occurrences

analytically derived runoff models based on rainfall point processes this work introduces four stochastic and lumped in space rainfall runoff models they arise combining two stochastic rainfall models with two conceptualizations of a basin s response rainfall is given by rectangular pulses whose arrivals are described by poisson and neyman scott models runoff is obtained routing such pulses via two alternative conceptualizations both based on simple linear reservoirs general expressions for the first and second order moments are given for both the instantaneous and locally averaged processes the mathematical structure of the alternative parameterizations is illustrated via computer simulations

prototype selection for dissimilarity based classifiers a conventional way to discriminate between objects represented by dissimilarities is the nearest neighbor method a more efficient and sometimes a more accurate solution is offered by other dissimilarity based classifiers they construct a decision rule based on the entire training set but they need just a small set of prototypes the so called representation set as a reference for classifying new objects such alternative approaches may be especially advantageous for non euclidean or even non metric dissimilarities the choice of a proper representation set for dissimilarity based classifiers is not yet fully investigated it appears that a random selection may work well in this paper a number of experiments has been conducted on various metric and non metric dissimilarity representations and prototype selection methods several procedures like traditional feature selection methods here effectively searching for prototypes mode seeking and linear programming are compared to the random selection in general we find out that systematic approaches lead to better results than the random selection especially for a small number of prototypes although there is no single winner as it depends on data characteristics the k centres works well in general for two class problems an important observation is that our dissimilarity based discrimination functions relying on significantly reduced prototype sets 3 10 of the training objects offer a similar or much better classification accuracy than the best k nn rule on the entire training set this may be reached for multi class data as well however such problems are more difficult

statistical modeling of daily rainfall occurrences in this paper likelihood based inference procedures for discrete point process models are developed and a new family of discrete point process models for daily rainfall occurrences is proposed the model which is termed a markov bernoulli process can be viewed as a sequence of bernoulli trials with randomized success probabilities contained within the family of markov bernoulli models are markov chain and bernoulli trial models asymptotic properties of maximum likelihood estimators of markov bernoulli model parameters are derived these results provide the basis for assessing standard errors and correlation of parameter estimators and for developing likelihood ratio tests to choose among markov bernoulli markov chain and bernoulli trial models inference procedures are applied to a data set from washington d c

evaluation of cluster based rectangular pulses point process models for rainfall this technical note presents a comparison of cluster based point rainfall models using the historical hourly rainfall data observed between 1949 and 1976 at denver colorado the denver data are used to analyze the performance of three classes of models namely the bartlett lewis model the geometric neyman scott model and the poisson neyman scott model the original formulation of the structure of each model as well as the modified description developed in order to improve the zero depth probability is considered in this study rodriguez iturbe et al 1987a concluded that it is unlikely that empirical analysis of rainfall data can be used to choose between the bartlett lewis model and the neyman scott model in a subsequent paper rodriguez iturbe et al 1987b argued that the choice of the distribution of the number of cells per storm for the neyman scott model either geometric or poisson has no general bias effect on the stochastic structure some investigators e g burlando and rosso 1991 however reported results contradictory to those of the previous authors in light of these observations this note investigates the performance of the cluster based models for the denver data the geometric neyman scott model yields better results compared to the poisson neyman scott model moreover the bartlett lewis model is shown to be very sensitive to the sets of moment equations used in the parameter estimation this sensitivity is not observed in the neyman scott scheme and is believed to be a drawback for applying the bartlett lewis model in hydrologic simulation studies

daily precipitation modeling by discrete autoregressive moving average processes to account for the statistical dependence among the daily precipitation magnitudes and among the daily precipitation occurrence times various models from the discrete autoregressive moving average darma family are constructed for and applied to the daily precipitation data in indiana the structure of the darma family is specified by the marginal distribution of independent identically distributed i i d discrete random variables and by their random linear combination a fundamental property of the darma family is that its correlation structure can be specified independently of its marginal density the darma correlation structure remains invariant under transformation of the marginal density this property is satisfied by the indiana daily precipitation data and it facilitates their modeling by the darma family of processes it is shown that the markov chain a popular model for the daily precipitation sequences is a specified model within darma family the indiana daily precipitation data is transformed into a multistate discrete precipitation sequence by discretizing the daily precipitation amount into a number of magnitude states the stochastic process of the daily precipitation sequences is analyzed in terms of the locally stationary seasons defined within the paper in each season the candidate darma models are identified in terms of the covariance function within the season the parameter estimation of these candidate models is done by fitting their theoretical autocorrelation functions to their empirical counterparts and the state probabilities are obtained through the multistate mean run lengths the theoretical run length distributions of the candidate models are derived for each of the precipitation magnitude states including the dry state the goodness of fit tests of the candidate models and the best model selection are based on the theoretical multistate run length distributions of the daily precipitation data supplement data tables calculations etc is available with entire article on microfiche order from american geophysical union 2000 florida avenue n w washington dc 20009 document w84 001 2 50 payment must accompany order

a comparative copula based bivariate frequency analysis of observed and simulated storm events a case study on bartlett lewis modeled rainfall 1 because of a lack of historical rainfall time series of considerable length one often has to rely on simulated rainfall time series e g in the design of hydraulic structures one way to simulate such time series is by means of stochastic point process rainfall models such as the bartlett lewis type of model for the evaluation of model performance with a focus on the reproduction of extreme rainfall events often a univariate extreme value analysis is performed recently developed concepts in statistical hydrology now offer other means of evaluating the overall performance of such models in this study a copula based frequency analysis of storms is proposed as a tool to evaluate differences between the return periods of several types of observed and modeled storms first this study performs an analysis of several storm variables which indicates a problem with the modeling of the temporal structure of rainfall by the models thereafter the bivariate frequency analysis of storms defined by their duration and volume illustrates the underestimation and overestimation of the return period of the storms simulated by the models which is partially explained by a large difference in the marginal distribution functions of the storm duration and storm volume the difference in the degree of association between the latter and a different mean storm interarrival time the proposed methodology allows for the identification of some problems with the rainfall simulations from which recommendations for possible improvements to rainfall models can be made

a space time neyman scott model of rainfall empirical analysis of extremes 1 a spatial temporal model of rainfall based on a neyman scott stochastic point process is fitted to hourly data taken from nine sites in the arno basin italy the stochastic model is an extension of the temporal neyman scott rectangular pulses model into two dimensional space and introduces a further parameter into the model in the model storms arrive in a poisson process where each storm consists of discs representing rain cells with centers distributed over an area according to a spatial poisson process the cells have a random radius lifetime and intensity with the intensity remaining constant over the area of the disc and cell lifetime a fitting procedure is proposed which couples the results obtained in two preceding papers the second order properties of the spatial temporal model and the third moment function of the single site model cowpertwait 1995 1998 the model is validated by comparing extreme historical hourly data and equivalent data simulated using the fitted spatial temporal model these comparisons are made using a regional frequency analysis based on l moments and log log plots of the upper distribution tail the results indicate that the model is able to preserve regional extremes and support the use of the model in hydrological applications

on parameter estimation of temporal rainfall models characteristics and moment estimators of temporal rainfall models such as poisson rectangular pulse prp neyman scott white noise nswn and neyman scott rectangular pulse nsrp are investigated it is shown that prp and nswn have a correlation structure like that of an autoregressive moving average arma 1 1 model whereas the nsrp has a dependence structure like that of an arma 2 2 the admissible regions of lag 1 and lag 2 autocorrelations are derived to demonstrate that in general they are more restricted than their arma counterparts an additional property denoted as variance ratio which is intimately related to the scale of fluctuation of a process is defined and used for model comparison the bias and mean square error properties of the moment estimators are investigated with emphasis on the nswn model for which it is suggested that the temporal scale t defined by t 1 provides the most efficient estimators of the parameters parameter defines the arrival of rain bursts relative to the origin of storm systems all three models are fitted to an extensive data set covering hourly precipitation data at 38 stations in northeastern colorado the correlation and variance ratio plots are used to select the appropriate model for each month however it is shown that the diurnal periodicity of storm occurrence is predominant during the summer months which is a characteristic not built into any of the temporal models used here

non power law scale properties of rainfall in space and time 1 the identification of general relationships linking statistical properties of rainfall aggregated at different temporal and spatial scales possesses clear theoretical and practical relevance among other properties it is important to characterize the scale dependence of rainfall variability which may for many purposes be summarized by its variance this paper presents theoretical results and observational analyses connecting the variance of temporal and spatial rainfall to the scale of observation under an assumption of second order stationarity previous results regarding the theoretical form of the temporal variance as a function of aggregation are refined and extended to the spatial case it is shown that the variance of aggregated rainfall exhibits an overall nonscaling form within the range of scales of usual hydrological interest it is further shown that the theoretically derived form of the variance as a function of scale is incompatible with power law relations usually assumed for the second order statistical moment within multiscaling approaches to rainfall modeling predictions of the theoretical derivations are validated by use of observations representing a wide variety of resolutions from 2 s to 1 hour in time and 4 km in space climates and measurement instruments the validation shows a good agreement between observations and the theoretically predicted forms of the variance as a function of aggregation the proposed theoretical framework thus provides a useful context for rainfall analysis modeling and downscaling in space and time and suggests careful reexaminations of usual multiscaling assumptions

scaling limits and self similarity in precipitation fields it has been recognized in the literature on rainfall models in hydrology that the exact calculations of probabilities for models which incorporate cluster structure is typically not possible consequently one is led to considerations of limiting approximations however because of the presence of dependencies and or fat tails in several of the current models the nature of the approximations involves some important issues for both theoretical as well as experimental consideration in precipitation research the objective of the present paper is to systematically describe these issues as they pertain to rainfall models some specific large scale approximations are given for models of the type currently in the literature

probabilistic representation of the temporal rainfall process by a modified neyman scott rectangular pulses model parameter estimation and validation the capability of the neyman scott clustered stochastic point process model of rainfall to preserve various observed statistics is considered randomization of the cell duration parameter from storm to storm is shown to considerably improve the wet dry period joint distribution and extreme value statistics a simple procedure for parameter estimation is introduced and applied

bayesian quadratic discriminant analysis quadratic discriminant analysis is a common tool for classification but estimation of the gaussian parameters can be ill posed this paper contains theoretical and algorithmic contributions to bayesian estimation for quadratic discriminant analysis a distribution based bayesian classifier is derived using information geometry using a calculus of variations approach to define a functional bregman divergence for distributions it is shown that the bayesian distribution based classifier that minimizes the expected bregman divergence of each class conditional distribution also minimizes the expected misclassification cost a series approximation is used to relate regularized discriminant analysis to bayesian discriminant analysis a new bayesian quadratic discriminant analysis classifier is proposed where the prior is defined using a coarse estimate of the covariance based on the training data this classifier is termed bda7 results on benchmark data sets and simulations show that bda7 performance is competitive with and in some cases significantly better than regularized quadratic discriminant analysis and the cross validated bayesian quadratic discriminant analysis classifier quadratic bayes

a markov renewal model for rainfall occurrences a probabilistic model for the temporal description of daily rainfall occurrences at a single location is presented by defining an event as a day with measurable precipitation the model is cast into the discrete time point process framework in the proposed model the sequence of times between events is formed by sampling from two geometric distributions according to transition probabilities specified by a markov chain the model belongs to the class of markov renewal processes and exhibits clustering relative to the independent bernoulli process as a special case it reduces to a renewal model with a mixture distribution for the interarrival times the rainfall occurrence model coupled with a mixed exponential distribution for the nonzero daily rainfall amounts was applied to the daily rainfall series for snoqualmie falls washington and was successful in preserving the short term structure of the occurrence process as well as the distributional properties of the seasonal rainfall amounts

the combinatorics of steenrod operations on the cohomology of grassmannians abstract the study of the action of the steenrod algebra on the mod p cohomology of spaces has many applications to the topological structure of those spaces in this paper we present combinatorial formulas for the action of steenrod operations on the cohomology of grassmannians both in the borel and the schubert picture we consider integral lifts of steenrod operations which lie in a certain hopf algebra of differential operators the latter has been considered recently as a realization of the landweber novikov algebra in complex cobordism theory it also has connections with the action of the virasoro algebra on the boson fock space our formulas for steenrod operations are based on methods which have not been used before in this area namely hammond operators and the combinatorics of schur functions we also discuss applications of our formulas to the geometry of grassmannians

the relationship between a continuous time renewal model and a discrete markov chain model of precipitation occurrence a relationship between a continuous wet dry renewal model with gamma distributed dry intervals and a markov chain model for daily rainfall is derived the relationship requires numerical evaluation for the general case but closed form solutions are available for the markov process case in which dry intervals are exponentially distributed the markov process equations are equivalent to those derived by j r green 1964 for first order transition probabilities but are presented in a simplified nonrecursive form the markov process relationships are examined for convergence and accuracy with simulation studies and comparison to observed rainfall records the markov process model is shown to provide a good representation in certain parts of the united states in other areas where the markov property is inappropriate due to event clustering or other phenomena the gamma model provides an improved characterization of the relationship between continuous and discrete rainfall occurrence

statistical inference for point process models of rainfall in this paper we develop maximum likelihood procedures for parameter estimation and model selection that apply to a large class of point process models that have been used to model rainfall occurrences including cox processes neyman scott processes and renewal processes the statistical inference procedures are based on the stochastic intensity t lims 0 s 0 1 s e n t s n t n u u t the likelihood function of a point process is shown to have a simple expression in terms of the stochastic intensity the main result of this paper is a recursive procedure for computing stochastic intensities the procedure is applicable to a broad class of point process models including renewal cox process with markovian intensity processes and an important class of neyman scott processes the model selection procedure we propose which is based on likelihood ratios allows direct comparison of two classes of point processes to determine which provides a better model for a given data set the estimation and model selection procedures are applied to two data sets of simulated cox process arrivals and a data set of daily rainfall occurrences in the potomac river basin