generalized hydraulic geometry derivation based on a multiscaling formalism 1 relationships between channel characteristics e g mean depth water surface width mean velocity and discharge known as hydraulic geometry hg have been extensively used by hydrologists and geomorphologists since the seminal work of leopold and maddock 1953 on the basis of recent empirical evidence that the parameters of at site hg depend systematically on the contributing area scale and that the parameters of downstream hg depend on the frequency of discharge we propose a multiscaling formalism within which to model and interpret both at site and downstream hg in a homogeneous region in particular we postulate and test multiscaling models for cross sectional area and discharge and derive generalized hg relationships that explicitly account for scale frequency dependence the multiscaling formalism is tested in several basins in oklahoma and kansas for drainage areas ranging from 2 to 20 000 km2 and shows good agreement with the data to quantify the effects that scale dependence in hg has on the hydrologic response of a basin a geomorphologic nonlinear cascade of reservoirs model has been used to compute attributes of a representative hydrologic response function for various levels of catchment averaged effective rainfall and different basin orders the numerical experiment shows substantial differences in hydrologic response when using classical versus generalized hg finally a preliminary effort is reported to generalize even further the hg relationships such that they can account for deviations from a single power law e g consideration of two different power laws in low and high flow regimes through the introduction of a bivariate mixed multiscaling framework

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

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

short term flood risk prediction a comparison of the cox regression model and a conditional distribution model two models for estimating the risk of a flood exceeding some critical threshold within a few days smith and karr 1986 ettrick et al 1987 which take account of the season and prevailing catchment conditions have recently been published the models are fitted to a 1000 year synthetic data set to compare the results with empirically determined risk estimates after some modifications to the smith and karr method both models demonstrated reasonable accuracy a second comparison is then made using data from a united kingdom catchment the smith and karr model was further modified to allow risk estimates for up to 30 days ahead to be made both models were applied to both data sets for 30 day ahead estimates and the results demonstrate the sensitivity of the risk to prevailing conditions at the beginning of the period the assumptions data requirements and accuracy of the models are compared and discussed

an approach to parameter estimation and stochastic control in water resources with an application to reservoir operation this paper presents an algorithm for the estimation of parameters in state space models that represent hydrologic processes in which the state variables are observed with error the algorithm is based on the maximization of the conditional expectation of the likelihood function of the state equation the estimation algorithm is numerically stable and guarantees local convergence under mild conditions it is also shown that the estimation algorithm can be coupled with an optimal control method to yield a combined control estimation technique that can be easily implemented an application of the theory and methods developed herein is given for flood routing via reservoir operation

when where and how of efficiency estimation improved procedures for stochastic frontier modeling abstractthe issues of functional form distributions of the error components and endogeneity are for the most part still open in stochastic frontier models the same is true when it comes to imposition of restrictions of monotonicity and curvature making efficiency estimation an elusive goal in this paper we attempt to consider these problems simultaneously and offer practical solutions to the problems raised by stone 2002 and addressed in badunenko henderson and kumbhakar 2012 we provide major extensions to smoothly mixing regressions and fractional polynomial approximations for both the functional form of the frontier and the structure of inefficiency endogeneity is handled simultaneously using copulas we provide detailed computational experiments and an application to us banks to explore the posteriors of the new models we rely heavily on sequential monte carlo techniques

alive smc2 bayesian model selection for low count time series models with intractable likelihoods in this article we present a new method for performing bayesian parameter inference and model choice for low count time series models with intractable likelihoods the method involves incorporating an alive particle filter within a sequential monte carlo smc algorithm to create a novel exact approximate algorithm which we refer to as alive smc2 the advantages of this approach over competing methods are that it is naturally adaptive it does not involve between model proposals required in reversible jump markov chain monte carlo and does not rely on potentially rough approximations the algorithm is demonstrated on markov process and integer autoregressive moving average models applied to real biological datasets of hospital acquired pathogen incidence animal health time series and the cumulative number of prion disease cases in mule deer

central limit theorem for sequential monte carlo methods and its application to bayesian inference the term sequential monte carlo methods or equivalently particle filters refers to a general class of iterative algorithms that performs monte carlo approximations of a given sequence of distributions of interest t we establish in this paper a central limit theorem for the monte carlo estimates produced by these computational methods this result holds under minimal assumptions on the distributions t and applies in a general framework which encompasses most of the sequential monte carlo methods that have been considered in the literature including the resample move algorithm of gilks and berzuini j r stat soc ser b stat methodol 63 2001 127 146 and the residual resampling scheme the corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter we study in particular in some typical examples of bayesian applications whether and at which rate these asymptotic variances diverge in time in order to assess the long term reliability of the considered algorithm

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

on line bayesian estimation of signals in symmetric spl alpha stable noise in this paper we describe on line bayesian filtering methods for time series models with heavy tailed spl alpha stable noise the filtering methodology is based on a scale mixtures of normals smin representation of the spl alpha stable distribution which reexpresses the intractable stable distribution in a conditionally gaussian form we describe how the method can be used for estimation of time varying autoregressive signals buried in symmetric spl alpha stable noise efficiently implemented using an adaptation to an existing rao blackwellized particle filter the methodology is shown to work well with both simulated and real corrupted audio data for which the spl alpha stable noise distribution is found to fit the noise data better than other more standard heavy tailed distributions

estimation of parameters for macroparasite population evolution using approximate bayesian computation we estimate the parameters of a stochastic process model for a macroparasite population within a host using approximate bayesian computation abc the immunity of the host is an unobserved model variable and only mature macroparasites at sacrifice of the host are counted with very limited data process rates are inferred reasonably precisely modeling involves a three variable markov process for which the observed data likelihood is computationally intractable abc methods are particularly useful when the likelihood is analytically or computationally intractable the abc algorithm we present is based on sequential monte carlo is adaptive in nature and overcomes some drawbacks of previous approaches to abc the algorithm is validated on a test example involving simulated data from an autologistic model before being used to infer parameters of the markov process model for experimental data the fitted model explains the observed extra binomial variation in terms of a zero one immunity variable which has a short lived presence in the host

a sequential particle filter method for static models summary particle filter methods are complex inference procedures which combine importance sampling and monte carlo schemes in order to explore consistently a sequence of multiple distributions of interest we show that such methods can also offer an efficient estimation

a group theoretical identification of integrable cases of the lienard type equation x f x x g x 0 i equations having nonmaximal number of lie point symmetries we carry out a detailed lie point symmetry group classification of the lienard type equation x f x x g x 0 where f x and g x are arbitrary smooth functions of x we divide our analysis into two parts in the present first part we isolate equations that admit lesser parameter lie point symmetries namely one two and three parameter symmetries and in the second part we identify equations that admit maximal eight parameter lie point symmetries in the former case the invariant equations form a family of integrable equations and in the latter case they form a class of linearizable equations under point transformations further we prove the integrability of all the equations obtained in the present paper through equivalence transformations either by providing the general solution or by constructing time independent hamiltonians several of these equations are being identified for the first time from the group theoretical analysis

symmetries of linear systems of second order ordinary differential equations in this paper several problems concerning the lie algebra structure of symmetries and variational symmetries of a general linear system of second order ordinary differential equations are studied in particular a necessary and sufficient condition is obtained in terms of the coefficients of the system for the system s symmetry algebra to be of maximal dimension i e n2 4n 3 and isomorphic to sl n 2 r the well known symmetry algebra of the free particle equation x 0 when this condition is satisfied it is proved that the system is lagrangian and that its variational symmetry algebra is isomorphic to a fixed n2 3n 6 2 dimensional lie algebra whose structure levi mal cev decomposition and realization by means of a matrix algebra is determined for the particular case of isotropic systems which includes as far as is known all the examples treated in the literature explicit formulas for the generators of both the symmetry algebra and the variational symmetry algebra are obtained

asymptotically optimal prediction for time varying data generating processes we develop a methodology referred to as kinetic prediction for predicting time series undergoing unknown changes in their data generating distributions based on kolmogorov tikhomirov s varepsilon entropy we propose a concept called varepsilon predictability that quantifies the size of a model class which can be parametric or nonparametric and the maximal number of abrupt structural changes that guarantee the achievability of asymptotically optimal prediction moreover for parametric distribution families we extend the aforementioned kinetic prediction with discretized function spaces to its counterpart with continuous function spaces and propose a sequential monte carlo based implementation we also extend our methodology for predicting smoothly varying data generating distributions under reasonable assumptions we prove that the average predictive performance converges almost surely to the oracle bound which corresponds to the case that the data generating distributions are known in advance the results also shed some light on the so called prediction inference dilemma various examples and numerical results are provided to demonstrate the wide applicability of our methodology

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

a particle algorithm for sequential bayesian parameter estimation and model selection we describe a particle algorithm for the sequential bayesian estimation of unknown static parameters the algorithm combines sequential importance sampling sis and markov chain monte carlo mcmc to achieve computational efficiency and stability in its most general form the algorithm has three components i sis ii a rejuvenation test and iii mcmc measurements are processed sequentially with an artificial time line if there is no natural one associated with the measurements by sis which is computationally inexpensive after each measurement is processed the rejuvenation test checks whether the resulting sis particles have to be rejuvenated when indicated by the test the particles are completely rejuvenated by mcmc which removes errors that accumulate from sis due to the finite number of particles thus ensuring stability whenever possible the sis particles can be used to advantage in the mcmc there is flexibility in the choice of the rejuvenation test as well as the mcmc method with potential to increase the usefulness of the algorithm in particular by using reversible jump mcnic with multiple models the algorithm can perform simultaneous model selection and parameter estimation in this paper we use a rejuvenation test based on a kullback leibler distance that is easy to compute and our choice of mcnic is independent metropolis hastings with a gaussian proposal density with these choices we illustrate the use of the algorithm in two signal processing applications passive source localization with angle of arrival and simultaneous weak signal detection and parameter estimation involving both simulated and real data the results demonstrate the algorithm s stability its built in protection against model overfitting and tolerance to model mismatch

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

sequential quasi monte carlo this is a written discussion of the paper sequential quasi monte carlo sampling by m gerber and n chopin following the presentation given before the royal statistical society in london on december 10th 2014

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 bayesian information criterion for singular models summary we consider approximate bayesian model choice for model selection problems that involve models whose fisher information matrices may fail to be invertible along other competing submodels such singular models do not obey the regularity conditions underlying the derivation of schwarz s bayesian information criterion bic and the penalty structure in bic generally does not reflect the frequentist large sample behaviour of the marginal likelihood although large sample theory for the marginal likelihood of singular models has been developed recently the resulting approximations depend on the true parameter value and lead to a paradox of circular reasoning guided by examples such as determining the number of components in mixture models the number of factors in latent factor models or the rank in reduced rank regression we propose a resolution to this paradox and give a practical extension of bic for singular model selection problems

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

bayesian inference and state number determination for hidden markov models an application to the information content of the yield curve about inflation this paper is concerned with bayesian inference in hidden markov models focusing on switching regression models we propose a new methodology that delivers a joint estimation of the parameters and the number of regimes that have actually appeared in the studied sample the only prior information that is required on the latter quantity is an upper bound we implement a particle filter algorithm to compute the corresponding estimates applying this methodology to the information content of the yield curve regarding future inflation in four oecd countries we show that the predictive content for given country and combination of maturities is subject to regime switching

monte carlo approximation of bayes factors via mixing with surrogate distributions by mixing the target posterior distribution with a surrogate distribution of which the normalizing constant is tractable we propose a method for estimating the marginal likelihood using the wang

sequentially interacting markov chain monte carlo methods we introduce a novel methodology for sampling from a sequence of probability distributions of increasing dimension and estimating their normalizing constants these problems are usually addressed using sequential monte carlo smc methods the alternative sequentially interacting markov chain monte carlo simcmc scheme proposed here works by generating interacting non markovian sequences which behave asymptotically like independent metropolis hastings mh markov chains with the desired limiting distributions contrary to smc methods this scheme allows us to iteratively improve our estimates in an mcmc like fashion we establish convergence of the algorithm under realistic verifiable assumptions and demonstrate its performance on several examples arising in bayesian time series analysis

sl 3 r realisations and the damped harmonic oscillator the point and contact lie groups for the damped harmonic oscillator are found and several realisations of the sl 3 r lie group are analysed the non critical and critical cases are studied separately and a sort of limiting procedure is defined which leaves the lie algebra structure unchanged some physical applications of these results are also pointed out

smc 2 an efficient algorithm for sequential analysis of state space models we consider the generic problem of performing sequential bayesian inference in a state space model with observation process y state process x and fixed parameter theta an idealized approach would be to apply the iterated batch importance sampling ibis algorithm of chopin 2002 this is a sequential monte carlo algorithm in the theta dimension that samples values of theta reweights iteratively these values using the likelihood increments p y t y 1 t 1 theta and rejuvenates the theta particles through a resampling step and a mcmc update step in state space models these likelihood increments are intractable in most cases but they may be unbiasedly estimated by a particle filter in the x dimension for any fixed theta this motivates the smc 2 algorithm proposed in this article a sequential monte carlo algorithm defined in the theta dimension which propagates and resamples many particle filters in the x dimension the filters in the x dimension are an example of the random weight particle filter as in fearnhead et al 2010 on the other hand the particle markov chain monte carlo pmcmc framework developed in andrieu et al 2010 allows us to design appropriate mcmc rejuvenation steps thus the theta particles target the correct posterior distribution at each iteration t despite the intractability of the likelihood increments we explore the applicability of our algorithm in both sequential and non sequential applications and consider various degrees of freedom as for example increasing dynamically the number of x particles we contrast our approach to various competing methods both conceptually and empirically through a detailed simulation study included here and in a supplement and based on particularly challenging examples

multilevel sequential importance sampling for rare event estimation the estimation of the probability of rare events is an important task in reliability and risk assessment we consider failure events that are expressed in terms of a limit state function which dep

a new method for the real time operation of reservoir systems this paper introduces a new method for the real time operation of reservoir systems the system is represented by a set of stochastic differential equations describing the reservoir and river dynamics in state space form the formulated reservoir operation problem calls for finding policies which maximize the expected benefits of one system s objective while satisfying the remaining objectives at prespecified reliability levels the solution is obtained by a new method named extended linear quadratic gaussian elqg controller elqg draws on and extends stochastic control theory results and it is well suited for the optimization of constrained dynamical systems it is a trajectory iteration algorithm theoretically expected to exhibit reliability and computational efficiency the new method is tested and evaluated in a real world case study

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

dimension independent likelihood informed mcmc many bayesian inference problems require exploring the posterior distribution of high dimensional parameters that represent the discretization of an underlying function this work introduces a family of markov chain monte carlo mcmc samplers that can adapt to the particular structure of a posterior distribution over functions two distinct lines of research intersect in the methods developed here first we introduce a general class of operator weighted proposal distributions that are well defined on function space such that the performance of the resulting mcmc samplers is independent of the discretization of the function second by exploiting local hessian information and any associated low dimensional structure in the change from prior to posterior distributions we develop an inhomogeneous discretization scheme for the langevin stochastic differential equation that yields operator weighted proposals adapted to the non gaussian structure of the posterior the resulting dimension independent and likelihood informed dili mcmc samplers may be useful for a large class of high dimensional problems where the target probability measure has a density with respect to a gaussian reference measure two nonlinear inverse problems are used to demonstrate the efficiency of these dili samplers an elliptic pde coefficient inverse problem and path reconstruction in a conditioned diffusion

a time series analysis of binary data abstract binary data d 1 d 2 dn are assumed to be generated by an underlying real valued strictly stationary process xk and a response function f for a given monotone nondecreasing function f from r to 0 1 dk takes on 1 with probability f xk and 0 with probability 1 f xk where xk xk it is shown that all strictly stationary binary processes are characterized by such a procedure several approximations to the n dimensional joint probabilities of dk are developed when xk is a gaussian first order autoregressive process model building procedures and methods by which to estimate parameters of a given model are discussed the predictor of d n 1 that minimizes probability of error among all randomized rules is determined and for certain cases a bound for this probability is found

the inverse problem for confined aquifer flow identification and estimation with extensions the contributions of this work are twofold first a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed the estimation techniques for the distributed parameter inverse problem pertain to linear least squares and generalized least squares methods the linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions the estimation techniques namely two stage least squares and three stage least squares are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator the three stage estimator provides the closer approximation to the actual parameter values but it also shows relatively large standard errors as compared to the ordinary and two stage estimators the estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation second a nonlinear maximum likelihood estimation approach to the inverse problem is presented the statistical properties of maximum likelihood estimators are derived and a procedure to construct confidence intervals and do hypothesis testing is given the relative merits of the linear and maximum likelihood estimators are analyzed other topics relevant to the identification and estimation methodologies i e a continuous time solution to the flow equation coping with noise corrupted head measurements and extension of the developed theory to nonlinear cases are also discussed a simulation study is used to evaluate the methods developed in this study

bayesian model comparison with the hyvarinen score computation and consistency the bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out of sample predictive scores under the logarithmic scoring rule however when some of the ca

specification tests based on mcmc output abstract two test statistics are proposed to determine model specification after a model is estimated by an mcmc method the first test is the mcmc version of ios a test and its asymptotic null distribution is normal the second test is motivated from the power enhancement technique of fan et al 2015 it combines a component j 1 that tests a null point hypothesis in an expanded model and a power enhancement component j 0 obtained from the first test it is shown that j 0 converges to zero when the null model is correctly specified and diverges when the null model is misspecified also shown is that j 1 is asymptotically 2 distributed suggesting that the second test is asymptotically pivotal when the null model is correctly specified the main feature of the first test is that no alternative model is needed the second test has several properties first its size distortion is small and hence bootstrap methods can be avoided second it is easy to compute from mcmc output and hence is applicable to a wide range of models including latent variable models for which frequentist methods are difficult to use third when the test statistic rejects the null model and j 1 takes a large value the test suggests the source of misspecification the finite sample performance is investigated using simulated data the method is illustrated in a linear regression model a linear state space model and a stochastic volatility model using real data

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

real time forecasting and daily operation of a multireservoir system during floods by linear quadratic gaussian control the problem of short term daily operation of a multireservoir system during floods is examined the problem is how to use all available real time information to solve the tactical problem of regulating reservoirs to minimize the expected value of flood damage during a relatively short operating horizon and to do so consistently with the long term operating strategy a state space mathematical model is presented for short term forecasting of river flows and description of the dynamics of a multireservoir system the model includes reduced order state space unit hydrographs to forecast storm runoff from effective rainfall and state space representations of linear flood routing the optimization problem is solved in the framework of discrete time linear quadratic gaussian lqg control lqg control is a computationally efficient and flexible method of solving the large dimensional optimization problems associated with the solution of the tactical problem of short term operation of reservoirs for application of the lqg control methodology the system must be represented in state space form with quadratic cost functions subject to linear equality constraints given by the state transition equations the scheme was found to be suitable for operation under moderate flood conditions when capacity constraints are not likely to become binding the methodology has been applied and tested in a real world case

independent particle filters sequential monte carlo methods especially the particle filter pf and its various modifications have been used effectively in dealing with stochastic dynamic systems the standard pf samples the current state through the underlying state dynamics then uses the current observation to evaluate the sample s importance weight however there is a set of problems in which the current observation provides significant information about the current state but the state dynamics are weak and thus sampling using the current observation often produces more efficient samples than sampling using the state dynamics in this article we propose a new variant of the pf the independent particle filter ipf to deal with these problems the ipf generates exchangeable samples of the current state from a sampling distribution that is conditionally independent of the previous states a special case of which uses only the current observation each sample can then be matched with multiple samples of the previous states in

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

scalable bayesian model averaging through local information propagation this article shows that a probabilistic version of the classical forward stepwise variable inclusion procedure can serve as a general data augmentation scheme for model space distributions in generalized linear models this latent variable representation takes the form of a markov process thereby allowing information propagation algorithms to be applied for sampling from model space posteriors in particular we propose a sequential monte carlo method for achieving effective unbiased bayesian model averaging in high dimensional problems using proposal distributions constructed using local information propagation the method called lips for local information propagation based sampling is illustrated using real and simulated examples with dimensionality ranging from 15 to 1000 and its performance in estimating posterior inclusion probabilities and in out of sample prediction is compared to those of several other methods namely mcmc bas ibma and lasso in addition it is shown that the latent variab

approximating hidden gaussian markov random fields summary gaussian markov random field gmrf models are frequently used in a wide variety of applications in most cases parts of the gmrf are observed through mutually independent data hence the full conditional of the gmrf a hidden gmrf hgmrf is of interest we are concerned with the case where the likelihood is non gaussian leading to non gaussian hgmrf models several researchers have constructed block sampling markov chain monte carlo schemes based on approximations of the hgmrf by a gmrf using a second order expansion of the log density at or near the mode this is possible as the gmrf approximation can be sampled exactly with a known normalizing constant the markov property of the gmrf approximation yields computational efficiency the main contribution in the paper is to go beyond the gmrf approximation and to construct a class of non gaussian approximations which adapt automatically to the particular hgmrf that is under study the accuracy can be tuned by intuitive parameters to nearly any precision these non gaussian approximations share the same computational complexity as those which are based on gmrfs and can be sampled exactly with computable normalizing constants we apply our approximations in spatial disease mapping and model based geostatistical models with different likelihoods obtain procedures for block updating and construct metropolized independence samplers

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

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

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

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

understanding cox s regression model a martingale approach abstract an informal discussion is given of how martingale techniques can be used to extend cox s regression model and to derive its large sample properties

contact symmetries of the harmonic oscillator the symmetry group of contact transformations for the one dimensional harmonic oscillator is determined its generators contain two arbitrary functions i e it is an infinite parameter lie group

error analysis of conventional discrete and gradient dynamic programming an asymptotic error analysis of the conventional discrete dynamic programming ddp method is presented and upper bounds of the error in the control policy i e the difference of the estimated and true optimal control at each operation period are computed this error is shown to be of the order of the state discretization interval as a result with significant implications in the optimization of multistate systems where the curse of dimensionality restricts the number of states to a relatively small number the error in the optimal cost varies with as 2 the analysis provides useful insights into the effects of state discretization on calculated control and cost functions the comparability of results from different discretizations and criteria about the required number of nodes in an effort to reduce the discretization error in the case of smooth cost functions a new discrete dynamic programming method termed gradient dynamic programming gdp is proposed gdp uses a piecewise hermite interpolation of the cost to go function at each stage which preserves the values of the cost to go function and of its first derivatives at the discretization nodes the error in the control policy is shown to be of the order of as 3 and the error in the cost to vary with as thus as as decreases gdp converges to the true optimum much more rapidly than ddp another major advantage of the new methodology is that it facilitates the use of newton type iterative methods in the solution of the nonlinear optimization problems at each stage the linear convergence of ddp and the superlinear convergence of gdp are illustrated in an example

extended linear quadratic gaussian control further extensions the extended linear quadratic gaussian elqg control method georgakakos and marks 1987 is a stochastic control algorithm for the optimal operation of multiobjective reservoirs mathematically this method optimizes a general functional of a stochastic system in state space form with upper and lower release constraints and probabilistic storage bounds elqg is a sequential algorithm which accounts for stochastic effects by preserving the first two statistical moments of the system s inputs and storages in this paper the method is first extended to handle nongaussian features which frequently characterize reservoir inputs second elqg s efficiency with respect to reliability storage constraints is discussed and a new barrier function method is researched these modifications are tested in case studies with the savannah river system

contact symmetries of general linear second order ordinary differential equations using 1 1 mappings the complete symmetry groups of contact transformations of general linear second order ordinary differential equations are determined from two independent solutions of those equations and applied to the harmonic oscillator with and without damping

bayesian optimal design via interacting particle systems we propose a new stochastic algorithm for bayesian optimal design in nonlinear and high dimensional contexts following peter muller we solve an optimization problem by exploring the expected utility surface through markov chain monte carlo simulations the optimal design is the mode of this surface considered a probability distribution our algorithm relies on a particle method to efficiently explore high dimensional multimodal surfaces with simulated annealing to concentrate the samples near the modes we first test the method on an optimal allocation problem for which the explicit solution is available to compare its efficiency with a simpler algorithm we then apply our method to a challenging medical case study in which an optimal protocol treatment needs to be determined for this case we propose a formalization of the problem in the framework of bayesian decision theory taking into account physicians knowledge and motivations we also briefly review further improvements and alternatives

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

ermakov and non ermakov systems in quantum dissipative models via the hydrodynamical formulation of quantum mechanics a unified protocol to treat the quantum time dependent harmonic oscillator with friction is presented described by two different models an explicitly time dependent linear schrodinger equation caldirola kanai model and a logarithmic nonlinear schrodinger equation kostin model for the former model an ermakov system that makes it possible to obtain an invariant of ermakov lewis type is derived for the latter model a non ermakov system is derived instead and it is shown that neither an exact nor an approximate invariant of ermakov lewis type exists

a class of adaptive importance sampling weighted em algorithms for efficient and robust posterior and predictive simulation abstract a class of adaptive sampling methods is introduced for efficient posterior and predictive simulation the proposed methods are robust in the sense that they can handle target distributions that exhibit non elliptical shapes such as multimodality and skewness the basic method makes use of sequences of importance weighted expectation maximization steps in order to efficiently construct a mixture of student t densities that approximates accurately the target distribution typically a posterior distribution of which we only require a kernel in the sense that the kullback leibler divergence between target and mixture is minimized we label this approach mixture of t by importance sampling weighted expectation maximization mitisem the constructed mixture is used as a candidate density for quick and reliable application of either importance sampling is or the metropolis hastings mh method we also introduce three extensions of the basic mitisem approach first we propose a method for applying mitisem in a sequential manner so that the candidate distribution for posterior simulation is cleverly updated when new data become available our results show that the computational effort reduces enormously while the quality of the approximation remains almost unchanged this sequential approach can be combined with a tempering approach which facilitates the simulation from densities with multiple modes that are far apart second we introduce a permutation augmented mitisem approach this is useful for importance or metropolis hastings sampling from posterior distributions in mixture models without the requirement of imposing identification restrictions on the model s mixture regimes parameters third we propose a partial mitisem approach which aims at approximating the joint distribution by estimating a product of marginal and conditional distributions this division can substantially reduce the dimension of the approximation problem which facilitates the application of adaptive importance sampling for posterior simulation in more complex models with larger numbers of parameters our results indicate that the proposed methods can substantially reduce the computational burden in econometric models like dcc or mixture garch models and a mixture instrumental variables model

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

maximum likelihood estimates for the parameters of mixture distributions maximum likelihood estimates for the parameters of a mixture of two normal distributions are presented in terms of an expectation maximization algorithm small sample properties of the parameter estimates are explored using monte carlo simulation although parameters estimated from unclassified data are inaccurate quantiles derived from the fitted distributions are only slightly less accurate than quantiles estimated from classified data

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

the truncated stieltjes moment problem solved by using kernel density functions in this work the problem of the approximate numerical determination of a semi infinite supported continuous probability density function pdf from a finite number of its moments is addressed the target space is carefully defined and an approximation theorem is proved establishing that the set of all convex superpositions of appropriate kernel density functions kdfs is dense in this space a solution algorithm is provided based on the established approximate representation of the target pdf and the exploitation of some theoretical results concerning moment sequence asymptotics the solution algorithm also permits us to recover the tail behavior of the target pdf and incorporate this information in our solution a parsimonious formulation of the proposed solution procedure based on a novel sequentially adaptive scheme is developed enabling a very efficient moment data inversion the whole methodology is fully illustrated by numerical examples

following a moving target monte carlo inference for dynamic bayesian models markov chain monte carlo mcmc sampling is a numerically intensive simulation technique which has greatly improved the practicality of bayesian inference and prediction however mcmc sampling is too slow to be of practical use in problems involving a large number of posterior target distributions as in dynamic modelling and predictive model selection alternative simulation techniques for tracking moving target distributions known as particle filters which combine importance sampling importance resampling and mcmc sampling tend to suffer from a progressive degeneration as the target sequence evolves we propose a new technique based on these same simulation methodologies which does not suffer from this progressive degeneration

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

computational and inferential difficulties with mixture posterior distributions abstract this article deals with both exploration and interpretation problems related to posterior distributions for mixture models the specification of mixture posterior distributions means that the presence of k modes is known immediately standard markov chain monte carlo mcmc techniques usually have difficulties with well separated modes such as occur here the mcmc sampler stays within a neighborhood of a local mode and fails to visit other equally important modes we show that exploration of these modes can be imposed using tempered transitions however if the prior distribution does not distinguish between the different components then the posterior mixture distribution is symmetric and standard estimators such as posterior means cannot be used we propose alternatives for bayesian inference for permutation invariant posteriors including a clustering device and alternative appropriate loss functions

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

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

x tmcmc adaptive kriging for bayesian inverse modeling abstract the bayesian inference of models associated with large scale simulations is prohibitively expensive even for massively parallel architectures we demonstrate that we can drastically reduce this cost by combining adaptive kriging with the population based transitional markov chain monte carlo tmcmc techniques for uni modal posterior probability distribution functions pdf the proposed hybrid method can reduce the computational cost by an order of magnitude with the same computational resources for complex posterior pdf landscapes we show that it is necessary to further extend the tmcmc by langevin adjusted proposals the proposed hybrid method exhibits high parallel efficiency we demonstrate the capabilities of our method on test bed problems and on high fidelity simulations in structural dynamics

quantitative approximations of evolving probability measures and sequential markov chain monte carlo methods we study approximations of evolving probability measures by an interacting particle system the particle system dynamics is a combination of independent markov chain moves and importance sampling resampling steps under global regularity conditions we derive non asymptotic error bounds for the particle system approximation in a few simple examples including high dimensional product measures bounds with explicit constants of feasible size are obtained our main motivation are applications to sequential mcmc methods for monte carlo integral estimation

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

stochastic daily precipitation models 2 a comparison of distributions of amounts chain dependent and independent exponential gamma and mixed exponential distributions are compared as models for the distribution of daily precipitation parameters for each distribution are estimated by maximum likelihood techniques for 14 day periods the akaike information criterion is used to select the most appropriate distribution for each period and for the entire year for the five u s stations studied the independent mixed exponential distribution was the best on the basis of the akaike information criterion and the independent gamma and chain dependent gamma ranked second and third respectively fourier series are fit to the parameters by least squares to provide starting values for subsequent numerical maximum likelihood estimates of the fourier coefficients according to the akaike information criterion the fourier series description of model parameters for the mixed exponential model is superior to the specification of parameters for each 14 day period

radiological source detection and localisation using bayesian techniques the problem considered in this paper is detection and estimation of multiple radiation sources using a time series of radiation counts from a collection of sensors a bayesian framework is adopted source detection is approached as a model selection problem in which competing models are compared using partial bayes factors given the number of sources the posterior mean is the minimum mean square error estimator of the source parameters exact calculation of the partial bayes factors and the posterior mean is not possible due to the presence of intractable integrals importance sampling using progressive correction is proposed as a computationally efficient method for approximating these integrals previously proposed algorithms have been restricted to one or two sources a simulation analysis shows that the proposed methods can detect and accurately estimate the parameters of four sources with reasonable computational expense

inference and model choice for sequentially ordered hidden markov models summary the system equation of a hidden markov model is rewritten to label the components by order of appearance and to make explicit the random behaviour of the number of components mt we argue that this reformulation is often a good way to achieve identifiability as it facilitates the interpretation of the posterior density and the estimation of the number of components that have appeared in a given sample we develop a sequential monte carlo algorithm for estimating the reformulated model which relies on particle filtering and gibbs sampling our algorithm has a computational cost that is similar to that of a markov chain monte carlo sampler and is much less likely to be affected by label switching i e the possibility of becoming trapped in a local mode of the posterior density the extension to transdimensional priors is also considered the approach is illustrated by two real data examples

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

two dimensional dynamical systems which admit lie and noether symmetries we consider a dynamical system moving in a riemannian space and prove two theorems which relate the lie point symmetries and noether symmetries of the equation of motion with the special projective group and the homothetic group of the space respectively these theorems are used to classify the two dimensional newtonian dynamical systems which admit lie point noether symmetries the results of the study i e expressions of forces potentials lie symmetries noether vectors and noether integrals are presented in the form of tables for easy reference and convenience two cases are considered hamiltonian and non hamiltonian systems the results are used to determine the lie noether symmetries of two different systems the kepler ermakov system which in general is non conservative and the conservative system with potential similar to the henon heiles potential as an additional application we consider the scalar field cosmologies in a frw background with no matter and look for the scalar field potentials for which the resulting cosmological models are integrable it is found that the only integrable scalar field cosmologies are defined by the exponential and the unified dark matter potential it is to be noted that in all aforementioned applications the lie noether symmetry vectors are found by simply reading the appropriate entry in the relevant tables

contact symmetries and integrable non linear dynamical systems the authors present a systematic method of classifying and constructing invariants for lagrangians containing arbitrary polynomial non linear potentials it is based on the assumption that these lagrangians are invariant under contact groups of transformations for a finite number of degrees of freedom they can prove integrability for a large class of polynomial potentials the method can be extended in several directions

parameterization and bayesian modeling progress in statistical computation often leads to advances in statistical modeling for example it is surprisingly common that an existing model is reparameterized solely for computational purposes but then this new configuration motivates a new family of models that is useful in applied statistics one reason why this phenomenon may not have been noticed in statistics is that reparameterizations do not change the likelihood in a bayesian framework however a transformation of parameters typically suggests a new family of prior distributions we discuss examples in censored and truncated data mixture modeling multivariate imputation stochastic processes and multilevel models

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