on association schemes with thin thin residue abstract let s be a scheme of finite valency and assume that o s o s it is known that s is schurian which means that s arises from a finite group if the normal closed subsets normal subgroups of o s are linearly ordered with respect to set theoretic inclusion cf m hirasaka p h zieschang sufficient conditions for a scheme to originate from a group j combin theory ser a 104 2003 17 27 in this note it is shown that s is schurian if o s is direct product of two simple closed subsets finite simple groups of different order

bayesian estimation of uncertainty in runoff prediction and the value of data an application of the glue approach this paper addresses the problem of evaluating the predictive uncertainty of topmodel using the bayesian generalised likelihood uncertainty estimation glue methodology in an application to the small ringelbach research catchment in the vosges france the wide range of parameter sets giving acceptable simulations is demonstrated and uncertainty bands are presented based on different likelihood measures it is shown how the distributions of predicted discharges are non gaussian and vary in shape through time and with discharge updating of the likelihood weights using bayes equation is demonstrated after each year of record and it is shown how the additional data can be evaluated in terms of the way they constrain the uncertainty bands

on wreath products of c algebras table algebras and association schemes abstract in this paper we will first present characterizations of wreath products of c algebras and show that the dual of the wreath product of c algebras is isomorphic to the wreath product of the duals of those c algebras in the reverse order then we prove the krull schmidt type theorems for the wreath products of table algebras as well as for the wreath products of association schemes

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

on structures of quasi thin table algebras and applications to association schemes abstract in this paper we develop a structure theory for a class of table algebras i e the so called quasi thin table algebras they are direct generalizations of quasi thin association schemes although this class of table algebras is rather close to finite groups its structural properties are quite different from those of finite groups the thin radical and thin residue give rise to two group structures for every table algebra they play the central role in our discussions applications to association schemes are also discussed and some new results about quasi thin association schemes are obtained in particular we will give necessary and sufficient conditions under which a commutative quasi thin association scheme has multiplicities 1 or 2 we will need these results in the study of the characterization and classification of double quasi thin association schemes in 22

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

identification of temporal consistency in rating curve data bidirectional reach breach in this paper a methodology is developed to identify consistency of rating curve data based on a quality analysis of model results this methodology called bidirectional reach breach evaluates results of a rating curve model with randomly sampled parameter sets in each observation the combination of a parameter set and an observation is classified as nonacceptable if the deviation between the accompanying model result and the measurement exceeds observational uncertainty based on this classification conditions for satisfactory behavior of a model in a sequence of observations are defined subsequently a parameter set is evaluated in a data point by assessing the span for which it behaves satisfactory in the direction of the previous or following chronologically sorted observations this is repeated for all sampled parameter sets and results are aggregated by indicating the endpoint of the largest span called the maximum left right reach this temporal reach should not be confused with a spatial reach indicating a part of a river the same procedure is followed for each data point and for different definitions of satisfactory behavior results of this analysis enable the detection of changes in data consistency the methodology is validated with observed data and various synthetic stage discharge data sets and proves to be a robust technique to investigate temporal consistency of rating curve data it provides satisfying results despite of low data availability errors in the estimated observational uncertainty and a rating curve model that is known to cover only a limited part of the observations

water quality modeling a review of the analysis of uncertainty this paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction more specifically four problem areas are examined in detail uncertainty about model structure uncertainty in the estimated model parameter values the propagation of prediction errors and the design of experiments in order to reduce the critical uncertainties associated with a model the review is rather lengthy and it has therefore been prepared in effect as two papers there is a shorter largely nontechnical version which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling enclosed by this shorter discussion is the main body of the review dealing in turn with 1 identifiability and experimental design 2 the generation of preliminary model hypotheses under conditions of sparse grossly uncertain field data 3 the selection and evaluation of model structure 4 parameter estimation model calibration 5 checks and balances on the identified model i e model verification and model discrimination and 6 prediction error propagation much time is spent in discussing the algorithms of system identification in particular the methods of recursive estimation and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first order error analysis there are two obvious omissions from the review it is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty although clearly some reference must be made to these topics in brief the review concludes not surprisingly that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality and much remains to be done a lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior and there is ample evidence to show that the larger more comprehensive models are easily capable of generating highly uncertain predictions of future behavior for the future of the subject it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification a need for new questions to be posed in the problem of prediction and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence

dynamic rating curve assessment in unstable rivers using ornstein uhlenbeck processes 1 the procedure of fitting rating curves in channels where the stage discharge relationship is subject to changes driven by morphological processes remains one of the major unsolved problems in hydrometry this paper addresses this issue by formulating the stage discharge relationship as a steady flow one segmented power law model with parameters that are viewed as stochastic processes with characteristics associated with the temporal instabilities of the channel elements governing the stage discharge relationship a bayesian analysis with informative priors and time stage discharge measurements as forcing data is used to determine the most plausible model and its posterior parameter distributions using markov chain monte carlo simulation techniques and particle filtering the proposed framework is applied to data from gauging stations in two unstable rivers and one stable river in norway

ensemble evaluation of hydrological model hypotheses it is demonstrated for the first time how model parameter structural and data uncertainties can be accounted for explicitly and simultaneously within the generalized likelihood uncertainty estimation glue methodology as an example application 72 variants of a single soil moisture accounting store are tested as simplified hypotheses of runoff generation at six experimental grassland field scale lysimeters through model rejection and a novel diagnostic scheme the fields designed as replicates exhibit different hydrological behaviors which yield different model performances for fields with low initial discharge levels at the beginning of events the conceptual stores considered reach their limit of applicability conversely one of the fields yielding more discharge than the others but having larger data gaps allows for greater flexibility in the choice of model structures as a model learning exercise the study points to a leaking of the fields not evident from previous field experiments it is discussed how understanding observational uncertainties and incorporating these into model diagnostics can help appreciate the scale of model structural error

a shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters author s vrugt ja gupta hv bouten w sorooshian s abstract markov chain monte carlo mcmc methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models however mcmc methods require the a priori definition of a proposal or sampling distribution which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the markov chain and its rate of convergence in this paper we present an mcmc sampler entitled the shuffled complex evolution metropolis algorithm scem ua which is well suited to infer the posterior distribution of hydrologic model parameters the scem ua algorithm is a modified version of the original sce ua global optimization algorithm developed by duan et al 1992 the scem ua algorithm operates by merging the strengths of the metropolis algorithm controlled random search competitive evolution and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution three case studies demonstrate that the adaptive capability of the scem ua algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional metropolis hastings samplers

an introduction to stochastic modeling stochastic modeling probability review the major discrete distributions rtant continuous distributions some elementary exercises useful functions integrals and sums conditional probability and conditional expectation the discrete case the dice game craps random sums conditioning on a continuous random variable markov chains introduction definitions transition probability matrices of a markov chain some markov chain models first step analysis some special markov chains functionals of random walks and success runs another look at first step analysis the long run behavior of markov chains regular transition probability matrices examples the classification of states the basic limit theorem of markov chains reducible markov chains sequential decisions and markov chains poisson processes the poisson distribution and the poisson processes the law of rare events distributions associated with the poisson process the uniform distribution and poisson processes spatial poisson processes compound and marked poisson processes continuous time markov chains pure birth processes ptire death processes birth and death processes the limiting behavior of birth and death processes birth and death processes with absorbing states finite state continuous time markov chains set valued processes renewal phenomena definition of a renewal process and related concepts some examples of renewal processes the poisson process viewed as a renewal process the asymptotic 3ehavior as renewal process

an alternative stochastic supervisor in discriminant analysis abstract suggested here is a model for a stochastic supervisor that is an alternative to the model proposed for the 2 group case by krishnan and nandy 6 the model uses a logistic normal distribution for the classification variable and this results in a simple em algorithm for parameter estimation illustrative comparisons are provided and generalisations are discussed

terwilliger algebras of wreath products by quasi thin schemes abstract the structure of terwilliger algebras of wreath products by thin schemes or one class schemes was studied in a hanaki k kim y maekawa terwilliger algebras of direct and wreath products of association schemes j algebra 343 2011 195 200 in this paper we will consider the structure of terwilliger algebras of wreath products by quasi thin schemes this gives a generalization of their result

discriminant analysis with a stochastic supervisor abstract we consider the problem of linear discriminant analysis for two p variate normal distributions with a common covariance matrix where the initial sample classification is done stochastically assuming a beta model for this classification variable and its independence of the observed variable for each group we derive the em algorithm for maximum likelihood estimation of the parameters

efficiency of discriminant analysis when initial samples are classified stochastically abstract we consider the problem of discriminant analysis of two multivariate normal populations having a common dispersion matrix where the initial samples are classified stochastically we assume a beta model for this classification variable and assume it to be independent of the feature vector x given the group we study the efron efficiency of this procedure compared to the situation where the initial classification is done deterministically and correctly we present tables and charts of this efficiency and conclude that stochastic supervision contains a great deal of information on the discriminant function

efficiency of logistic normal stochastic supervision abstract we consider the case of a stochastic supervision scheme in which the logarithm of odds ratio of the supervisor classification has a normal distribution and is independent of the feature vector we consider the two group multinormal case with a common covariance matrix and compute the efron efficiency of this supervision scheme for various values of parameters of the feature distribution and the supervision distribution we interpret these efficiency values to draw conclusions on the worth of stochastic supervision

a comparison of methods for streamflow uncertainty estimation stream ow time series are commonly derived from stage discharge rating curves but theuncertainty of the rating curve and resulting stream ow series are poorly understood while differentmethods to quantify uncertainty in the stage discharge relationship exist there is limited understanding ofhow uncertainty estimates differ between methods due to different assumptions and methodologicalchoices we compared uncertainty estimates and stage discharge rating curves from seven methods at threeriver locations of varying hydraulic complexity comparison of the estimated uncertainties revealed a widerange of estimates particularly for high and low ows at the simplest site on the isere river france fullwidth 95 uncertainties for the different methods ranged from 3 to 17 for median ows in contrast uncertainties were much higher and ranged from 41 to 200 for high ows in an extrapolated section of therating curve at the mahurangi river new zealand and 28 to 101 for low ows at the taf river unitedkingdom where the hydraulic control is unstable at low ows differences between methods result fromdifferences in the sources of uncertainty considered differences in the handling of the time varying nature ofrating curves differences in the extent of hydraulic knowledge assumed and differences in assumptionswhen extrapolating rating curves above or below the observed gaugings ultimately the selection of anuncertainty method requires a match between user requirements and the assumptions made by theuncertainty method given the signi cant differences in uncertainty estimates between methods we suggestthat a clear statement of uncertainty assumptions be presented alongside stream ow uncertainty estimates

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

on quasi thin association schemes abstract an association scheme is called quasi thin if each of its basic relations has valency 1 or 2 a quasi thin scheme is called kleinian if its thin residue is the klein four group with respect to relational multiplication it is proved that any kleinian quasi thin scheme arises from a near pencil on 3 points from an affine plane of order 2 or from a projective plane of order 2 the main result in this paper is that any non kleinian quasi thin scheme is schurian and separable we also construct an infinite family of kleinian quasi thin schemes which is neither schurian nor separable

correlated rating curve error in flood frequency inference an incremental rating curve error model is proposed to describe the systematic error introduced when a rating curve is extended by methods such as slope conveyance log log extrapolation or fitting to indirect discharge estimates extension can introduce a systematic or highly correlated error which is anchored by the more extensively measured part of the rating curve a likelihood function is developed which explicitly accounts for such error and accepts both gauged and binomial censored data a sampling experiment based on the three parameter generalized extreme value distribution was conducted to assess the performance of maximum likelihood quantile estimators this experiment revealed that substantial and in some cases massive degradation in the performance of quantile estimators can occur in the presence of correlated rating curve error rating error comparison of maximum likelihood estimators allowing for and ignoring rating error produced mixed results as rating error impact and or information content increased estimators allowing for rating error tended to perform better and in some cases significantly better than estimators ignoring rating error it is also shown that in the presence of rating error the likelihood surface may have multiple optima that may result in nonunique solutions for hill climbing search methods moreover in the presence of multiple optima and constraints on parameters the likelihood surface may be poorly described by asymptotic approximations

on quasi thin association schemes with odd number of points abstract let x r be an association scheme in the sense of p h zieschang 1996 an algebraic approach to association schemes lecture notes in mathematics vol 1628 springer new york berlin where x is a finite set and r is a partition of x x we say that x r is quasi thin if each element of r has a valency of at most two in this paper we focus on quasi thin association schemes with an odd number of points and obtain that x r has a regular automorphism group when n o r is square free

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise