minimum proper loss estimators for parametric models in this paper we propose a methodology for systematically deriving estimators minimizing proper loss functions defined on parametric statistical models by restricting ourselves to losses taking a functional form which allows for straightforward proofs of key properties proving propriety is tantamount to deriving a pairwise divergence quantity between probability measures admitting a natural interpretation of minimum proper loss estimators as divergence minimizers we show that proper losses of varying complexity can be readily constructed given propriety of losses taking a rudimentary form and that for many important models verifying desired properties in the rudimentary case is immediate as a special case we derive computationally tractable estimators requiring only the first and second moments verify strict propriety properties and empirically confirm their utility though parameter estimation tasks using both controlled simulations and real world meteorological network data sets comparisons against numerous standard estimators show that the proposed estimators are at least competitive with and often markedly superior to all standard references uniformly across tasks data sets and model classes suggesting a strong alternative to standard benchmarks in a wide variety of estimation problems

statistical models for autocorrelated count data a generalized linear mixed model is an increasingly popular choice for the modelling of correlated non normal responses in a regression setting a number of methods are currently available for fitting a generalized linear mixed model including monte carlo markov chain maximum likelihood algorithms approximate maximum likelihood pql iterative bias correction and others of interest in this paper is to compare the parameter estimation of the various methods in the modelling of a count data set the incidence of polio in the usa over the period 1970 1983 using a longlinear generalized linear mixed model with an autoregressive correlation structure despite the fact that all of these methods are considered valid modelling techniques we find that parameter estimates and standard errors differ substantially between analyses particularly in the estimation of the parameters describing the random effects distribution a small simulation study is helpful in understanding some of these differences the methods lead to reasonably similar predictions for future observations with small differences observed in some monthly counts

on testing the validity of sequential probability forecasts events are observed sequentially and at each stage a probability for the next event is assessed we consider the relationship between the sequence of probability forecasts and the sequence of outcomes we argue that the forecasts may be considered empirically valid when both these sequences are consistent with a common joint distribution for the events to aid in assessing validity we introduce various test statistics that measure in a natural way the empirical performance of the probability forecasts in the light of the outcomes obtained it is shown that under the null hypothesis of forecast validity such statistics will after suitable normalization have a standard normal or chi squared distribution virtually irrespective of the common joint distribution supposed to underlie both sequences

multiple probability assessments by dependent experts abstract when two or more information sources experts provide a decision maker with information on two or more random variables the decision maker using bayes s rule has an opportunity to a update a prior about the random variables and b calibrate the experts calibration is the process of adjusting the decision maker s likelihood about the experts assessments this article presents a model for this two way process and specializes to the case in which the experts assessment errors have a multivariate normal density in general we find that variables which the decision maker and the experts regard as independent a priori will be dependent a posteriori because of dependence in the assessment errors formulas for posterior densities are given for the normal model in this model the posterior density of the random variables depends on only a weighted average of the expert s means with weights that depend on the experts assessments of previously known quantities i also present a special case o

strategic manipulation of empirical tests theories can be produced by experts seeking a reputation for having knowledge hence a tester could anticipate that theories may have been strategically produced by uninformed experts who want to pass an empirical test we show that with no restriction on the domain of permissible theories strategic experts cannot be discredited for an arbitrary but given number of periods no matter which test is used provided that the test does not reject the actual data generating process natural ways around this impossibility result include 1 assuming that unbounded data sets are available and 2 restricting the domain of permissible theories opening the possibility that the actual data generating process is rejected out of hand in both cases it is possible to dismiss strategic experts but only to a limited extent these results show significant limits on what data can accomplish when experts produce theories strategically

the estimation of age period and cohort effects for vital rates in models for vital rates which include effects due to age period and cohort there is aliasing due to a linear dependence among these three factors this dependence arises both when age and period intervals are equal and when they are not one solution to the dependence is to set an arbitrary constraint on the parameters estimable functions of the parameters are invariant to the particular constraint applied for evenly spaced intervals deviations from linearity are estimable but only a linear function of the three slopes is estimable when age and period intervals have different widths further aliasing occurs it is assumed that the number of deaths in the numerator of the rate equation has a poisson distribution the calculations are illustrated with data on mortality from prostate cancer among nonwhites in the u s

homogeneous averaging operators on simple finite conformal lie algebras we describe all homogeneous averaging operators on finite simple conformal lie algebras in the case of current algebras these operators are closely related to rational solutions of the classical yang baxter equation

simple finite dimensional double algebras abstract a double algebra is a linear space v equipped with linear map v v v v additional conditions on this map lead to the notions of lie and associative double algebras we prove that simple finite dimensional lie double algebras do not exist over an arbitrary field and all simple finite dimensional associative double algebras over an algebraically closed field are trivial over an arbitrary field every simple finite dimensional associative double algebra is commutative a double algebra structure on a finite dimensional space v is naturally described by a linear operator r on the algebra end v of linear transformations of v double lie algebras correspond in this sense to skew symmetric rota baxter operators double associative algebra structures to left averaging operators

double poisson algebras in this paper we develop poisson geometry for non commutative algebras this generalizes the bi symplectic geometry which was recently and independently introduced by crawley boevey etingof and ginzburg our quasi poisson brackets induce classical quasi poisson brackets on representation spaces as an application we show that the moduli spaces of representations associated to the deformed multiplicative preprojective algebras recently introduced by crawley boevey and shaw carry a natural poisson structure

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

bayesian estimation and experimental design in linear regression models estimation and design as a bayesian decision problem choice of a prior distribution conjugate prior distributions bayes estimation of the regression parameter optimality and robustness of the bayes estimator bayesian interpretation of estimators using non bayesian prior knowledge bayes estimation in case of prior ignorance further problems the design problem for the linear bayes estimator characterization of optimal designs construction of optimal continuous designs construction of exact optimal designs

a score regression approach to assess calibration of continuous probabilistic predictions calibration the statistical consistency of forecast distributions and the observations is a central requirement for probabilistic predictions calibration of continuous forecasts is typically assessed using the probability integral transform histogram in this article we propose significance tests based on scoring rules to assess calibration of continuous predictive distributions for an ideal normal forecast we derive the first two moments of two commonly used scoring rules the logarithmic and the continuous ranked probability score this naturally leads to the construction of two unconditional tests for normal predictions more generally we propose a novel score regression approach where the individual scores are regressed on suitable functions of the predictive variance this conditional approach is applicable even for certain nonnormal predictions based on the dawid sebastiani score two case studies illustrate that the score regression approach has typically more power in detecting miscalibrated forecasts than the other approaches considered including a recently proposed technique based on conditional exceedance probability curves

predictive model assessment for count data we discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for count data our proposals include a nonrandomized version of the probability integral transform marginal calibration diagrams and proper scoring rules such as the predictive deviance in case studies we critique count regression models for patent data and assess the predictive performance of bayesian age period cohort models for larynx cancer counts in germany the toolbox applies in bayesian or classical and parametric or nonparametric settings and to any type of ordered discrete outcomes

making and evaluating point forecasts typically point forecasting methods are compared and assessed by means of an error measure or scoring function with the absolute error and the squared error being key examples the individual scores are averaged over forecast cases to result in a summary measure of the predictive performance such as the mean absolute error or the mean squared error i demonstrate that this common practice can lead to grossly misguided inferences unless the scoring function and the forecasting task are carefully matched effective point forecasting requires that the scoring function be specified ex ante or that the forecaster receives a directive in the form of a statistical functional such as the mean or a quantile of the predictive distribution if the scoring function is specified ex ante the forecaster can issue the optimal point forecast namely the bayes rule if the forecaster receives a directive in the form of a functional it is critical that the scoring function be consistent for it in the sense that t

on optimal sequential prediction for general processes this paper considers several aspects of the sequential prediction problem for unbounded nonstationary processes under pth power loss spl lscr sub p u v u v sup p 1 p spl infin in the first part it is shown that bayes prediction schemes are cesaro optimal under general conditions that cesaro optimal prediction schemes are unique in a natural sense and that cesaro optimality is equivalent to a form of weak calibration connections between calibration and stronger forms of optimality are considered extensions of the existence and uniqueness results to generalized prediction and prediction from observations with additive noise are established for binary processes it is shown that thresholding an optimal prediction scheme for the squared loss yields an optimal binary prediction scheme for the hamming loss in the second part of the paper it is shown how to construct from a countable family of prediction schemes a single composite scheme whose asymptotic performance on any suitable process dominates the performance of each member of the family the construction is based on aggregating methods for individual binary sequences using the construction some results of algoet 1994 1995 on the existence of cesaro optimal schemes for families of ergodic processes are rederived in a direct way and extended to unbounded processes

auxiliary mixture sampling for parameter driven models of time series of counts with applications to state space modelling we consider parameter driven models of time series of counts where the observations are assumed to arise from a poisson distribution with a mean changing over time according to a latent process estimation of these models is carried out within a bayesian framework using data augmentation and markov chain monte carlo methods we suggest a new auxiliary mixture sampler which possesses a gibbsian transition kernel where we draw from full conditional distributions belonging to standard distribution families only emphasis lies on application to state space modelling of time series of counts but we show that auxiliary mixture sampling may be applied to a wider range of parameter driven models including random effects models and panel data models based on the poisson distribution

the well calibrated bayesian abstract suppose that a forecaster sequentially assigns probabilities to events he is well calibrated if for example of those events to which he assigns a probability 30 percent the long run proportion that actually occurs turns out to be 30 percent we prove a theorem to the effect that a coherent bayesian expects to be well calibrated and consider its destructive implications for the theory of coherence

noncommutative geometry and quiver algebras abstract we develop a new framework for noncommutative differential geometry based on double derivations this leads to the notion of moment map and of hamiltonian reduction in noncommutative symplectic geometry for any smooth associative algebra b we define its noncommutative cotangent bundle t b which is a basic example of noncommutative symplectic manifold applying hamiltonian reduction to noncommutative cotangent bundles gives an interesting class of associative algebras b that includes preprojective algebras associated with quivers our formalism of noncommutative hamiltonian reduction provides the space with a lie algebra structure analogous to the poisson bracket on the zero fiber of the moment map in the special case where is the preprojective algebra associated with a quiver of non dynkin type we give a complete description of the gerstenhaber algebra structure on the hochschild cohomology of in terms of the lie algebra

non stochastic infinite and finite sequences abstract combining outcomes of coin tossing and transducer algorithms it is possible to generate with probability close to 1 very pathological sequences for which computable probabilistic forecasting is impossible these sequences are not random with respect to any reasonable probability distribution a natural consequence from the definition of such sequences is that each simple measure of the set of all such sequences is equal to 0 it was kolmogorov s and levin s idea to estimate the probability of generating of such sequences in the combinations of probabilistic and algorithmic processes 8 14 21 we collect several results in this direction for infinite sequences and asymptotic results for finite sequences including estimation of space and time of losing randomness for time bounded forecasting systems a correction to 22

some stochastic properties of memoryless individual sequences an individual sequence of real numbers is memoryless if no continuous markov prediction scheme of finite order can outperform the best constant predictor under the squared loss it is established that memoryless sequences satisfy an elementary law of large numbers and sliding block versions of hoeffding s inequality and the central limit theorem it is further established that memoryless binary sequences have convergent sample averages of every order and that their limiting distributions are bernoulli several examples and sources of memoryless sequences are given and it is shown how memoryless binary sequences may be constructed from aggregating methods for sequential prediction

the lerch transcendent from the point of view of fourier analysis we obtain some well known expansions for the lerch tran scendent and the hurwitz zeta function using elementary fourier ana lytic methods these fourier series can be used to analytically continue the functions and prove the classical functional equations which arise from the relations satised by the fourier conjugate and at fourier se ries in particular the functional equation for the riemann zeta function can be obtained in this way without contour integrals the conjugate series for special values of the parameters yields analogous results for the bernoulli and apostol bernoulli polynomials finally we give some consequences derived from the fourier series

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

fuzzy set theory observer bias and probability theory abstract it is known that given certain seemingly implausible assumption probability functions act like fuzzy set membership functions this paper shows that these seemingly implausible assumptions are satisfied in probabilistic situations where the sole uncertainty arises from unknown but systematic observer bias now such situations could be considered as on the borderline between the domain of applicability of probability functions and the domain of fuzzy set membership functions hence the convergence between the rules for combining probabilistic functions and those for combining fuzzy set membership functions in these borderline instances is intuitively quite satisfying this convergence also suggests a number of other ways in which possibility theory and probability theory are interrelated

econometric models for count data with an application to the patents r d relationship this paper focuses on developing and adapting statistical models of counts nonnegative integers in the context of panel data and using them to analyze the relationship between patents and r d expenditures since a variety of other economic data come in the form of repeated counts of some individual actions or events the methodology should have wide applications the statistical models we develop are applications and generalizations of the poisson distribution two important issues are i given the panel nature of our data how can we allow for separate persistent individual fixed or random effects ii how does one introduce the equivalent of disturbances in the equation into the analysis of poisson and other discrete probability functions the first problem is solved by conditioning on the total sum of outcomes over the observed years while the second problem is solved by introducing an additional source of randomness allowing the poisson parameter to be itself randomly distributed and compounding the two distributions lastly we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models

predictive likelihood inference with applications summary conditional and marginal predictive likelihood are defined and used in predicting un observed or missing data a distinction is made between predictive and estimative goals of a data analysis such methodology and distinctions are illustrated in the context of outlier theory and mixed model ano va the prediction of unobserved or missing data is considered from a likelihood perspective a general predictive likelihood is proposed for such purposes and contrasted with parametric likelihood the resulting maximum likelihood predictor is also compared with the limiting imputation from the em algorithm the new methodology is illustrated and contrasted with estimative likelihood analysis in the context of outlier theory and mixed model ano va predictions are proposed that are based on conditional and marginal predictive likelihoods for the unobserved data which are predictive adaptations of the methods developed by kalbfleisch and sprott 1970 1973 these authors were concerned with the elimination of nuisance parameters in order to make inference about another set of structural parameters prediction in the frame work of parametric distributions involves the elimination of all parameters in such a way that inference about the unobserved data is possible therefore in the predictive setting all para meters are nuisance parameters and the unobserved data now play a role similar to that of the structural parameters various predictive approaches to statistical inference have been advocated principally by geisser 1971 1975 stone 1974 aitchison and dunsmore 1975 and guttman 1970 a survey is provided by geisser 1980 and a brief overview in a parametric setting is presented in the next section following this a conditional likelihood approach is developed and shown to be closely related to the lauritzen 1974 hinkley 1979 likelihood method but specified in a manner allowing for a wider range of applicability a marginal predictive likelihood procedure is also specified which when applicable essentially agrees with the conditional likelihood procedure for the examples considered for a general account of likelihood based inference see fraser

parameter neutral optimum design for non linear models some bayesian approaches to d optimum design of experiments are considered from the viewpoint of invariance under reparameterization of the underlying statistical model an invariant criterion is proposed which does not require the detailed specification of a prior and which is shown to be equivalent to g optimality under a jeffreys prior the methods are applied and discussed in the contexts of exponential decay and quantal response models

a new goodness of fit test for event forecasting and its application to credit defaults we develop a new goodness of fit test for validating the performance of probability forecasts our test statistic is particularly powerful under sparseness and dependence in the observed data to build our test statistic we start from a formal definition of calibrated forecasts which we operationalize by introducing two components the first component tests the level of the estimated probabilities the second validates the shape measuring the differentiation between high and low probability events after constructing test statistics for both level and shape we provide a global goodness of fit statistic which is asymptotically 2 distributed in a simulation exercise we find that our approach is correctly sized and more powerful than alternative statistics in particular our shape statistic is significantly more powerful than the kolmogorov smirnov test under independence our global test has significantly greater power than the popular hosmer lemeshow s 2 test moreover even under dependence our global test remains correctly sized and consistent as a timely and important empirical application of our method we study the validation of a forecasting model for credit default events this paper was accepted by wei xiong finance

a bayesian generalized age period cohort power model for cancer projections age period cohort apc models are the state of art in cancer projections assessing past and recent trends and extrapolating mortality or incidence data into the future nordpred is a well established software assuming a poisson distribution for the counts and a log link or power link function with fixed power however its predictive performance is poor for sparse data bayesian models with log link function have been applied but they can lead to extreme estimates in this paper we address criticisms of the aforementioned models by providing bayesian formulations based on a power link and develop a generalized apc power link model which assumes a random rather than fixed power parameter in addition a power model with a fixed power parameter of five was formulated in the bayesian framework the predictive performance of the new models was evaluated on swiss lung cancer mortality data using model based estimates of observed periods results indicated that the generalized apc power link model provides best estimates for male and female lung cancer mortality the gender specific models were further applied to project lung cancer mortality in switzerland during the periods 2009 2013 and 2014 2018 copyright 2014 john wiley sons ltd

any inspection is manipulable consider a sequential forecast that may vary with time and history a calibration test see dawid 1982 foster and vohra 1997 and kalai lehrer and smorodinsky 1999 compares the observed empirical frequency over a set of times with the average prediction over the same set of times each test checks different events at different times a forecasting scheme passes a calibration test at a sequence of state realizations if the gap between these two figures diminishes to zero in other words each test defines what is consistent with the observed facts differently a forecast is consistent with the observed facts according to a given test if the empirical frequency of the events checked coincides asymptotically with the average prediction of these events when the forecast and the true distribution according to which the states are selected are the same the forecast passes any calibration test with probability one a calibration test is therefore type i error free the calibration tests treated in the literature are pure after any history it is known what specific event for instance rain foggy is being considered here we introduce mixed calibration tests where after each history a randomly chosen event is checked a mixed test checks whether the average prediction of these randomly chosen events is asymptotically equal to the frequency of their realizations like a deterministic test a mixed calibration test is also type i error free the main result of this paper shows that there is no mixed calibration test that rejects any inaccurate forecast that is for any test of this kind there exists a forecasting scheme that is always consistent with the realized events a constructive method to produce this scheme is provided as well another interpretation of the main result involves a forecaster and an inspector the inspector randomly chooses a calibration test according to a known distribution it is shown that a forecaster without knowing anything regarding the way states are selected can pass almost every test chosen by the inspector independently of the sequence of realizations in other words the forecaster has a forecasting method that is consistent with the observed facts in the meaning induced by almost all tests instead of randomly choosing one test as discussed previously the inspector can employ a set of tests simultaneously the main result implies that if the inspector employs countably many calibration tests for instance all those computable by a turing machine a forecaster can likewise pass them all2 simultaneously it means that a consultant or a scientist e g a weather forecaster who knows the countable set of

a predictive approach to the bayesian design problem with application to normal regression models a predictive decision theoretic approach is developed for the bayesian design problem the loss functions used are fair bayes or proper scoring rules and are quadratic measures of distance between probability measures optimal bayesian designs are those which minimise the preposterior risk for the decision problem such designs typically depend on both the prior distribution and the loss function the results are applied to certain normal regression models where explicit optimal designs are constructed

game theory maximum entropy minimum discrepancy and robust bayesian decision theory we describe and develop a close relationship between two problems that have customarily been regarded as distinct that of maximizing entropy and that of minimizing worst case expected loss using a formulation grounded in the equilibrium theory of zero sum games between decision maker and nature these two problems are shown to be dual to each other the solution to each providing that to the other although topsoe described this connection for the shannon entropy over 20 years ago it does not appear to be widely known even in that important special case we here generalize this theory to apply to arbitrary decision problems and loss functions we indicate how an appropriate generalized definition of entropy can be associated with such a problem and we show that subject to certain regularity conditions the above mentioned duality continues to apply in this extended context this simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust bayes acts we also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions this leads to an extension to arbitrary discrepancies of a well known minimax theorem for the case of kullback leibler divergence the redundancy capacity theorem of information theory for the important case of families of distributions having certain mean values specified we develop simple sufficient conditions and methods for identifying the desired solutions we use this theory to introduce a new concept of generalized exponential family linked to the specific decision problem under consideration and we demonstrate that this shares many of the properties of standard exponential families finally we show that the existence of an equilibrium in our game can be rephrased in terms of a pythagorean property of the related divergence thus generalizing previously announced results for kullback leibler and bregman divergences

model choice a minimum posterior predictive loss approach summary model choice is a fundamental and much discussed activity in the analysis of datasets nonnested hierarchical models introducing random effects may not be handled by classical methods bayesian approaches using predictive distributions can be used though the formal solution which includes bayes factors as a special case can be criticised we propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values we obtain this criterion by minimising posterior loss for a given model and then for models under consideration selecting the one which minimises this criterion for a broad range of losses the criterion emerges as a form partitioned into a goodness of fit term and a penalty term we illustrate its performance with an application to a large dataset involving residential property transactions

validation and updating of predictive logistic regression models a study on sample size and shrinkage a logistic regression model may be used to provide predictions of outcome for individual patients at another centre than where the model was developed when empirical data are available from this centre the validity of predictions can be assessed by comparing observed outcomes and predicted probabilities subsequently the model may be updated to improve predictions for future patients as an example we analysed 30 day mortality after acute myocardial infarction in a large data set gusto i n 40 830 we validated and updated a previously published model from another study timi ii n 3339 in validation samples ranging from small 200 patients 14 deaths to large 10 000 patients 700 deaths updated models were tested on independent patients updating methods included re calibration re estimation of the intercept or slope of the linear predictor and more structural model revisions re estimation of some or all regression coefficients model extension with more predictors we applied heuristic shrinkage approaches in the model revision methods such that regression coefficients were shrunken towards their re calibrated values parsimonious updating methods were found preferable to more extensive model revisions which should only be attempted with relatively large validation samples in combination with shrinkage copyright 2004 john wiley sons ltd

higher order elicitability and osband s principle a statistical functional such as the mean or the median is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score such scoring functions are called strictly consistent for the functional the elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores in this paper we explore the notion of elicitability for multi dimensional functionals and give both necessary and sufficient conditions for strictly consistent scoring functions we cover the case of functionals with elicitable components but we also show that one dimensional functionals that are not elicitable can be a component of a higher order elicitable functional in the case of the variance this is a known result however an important result of this paper is that spectral risk measures with a spectral measure with finite support are jointly elicitable if one adds the correct quantiles a direct consequence of applied interest is that the pair value at risk expected shortfall is jointly elicitable under mild conditions that are usually fulfilled in risk management applications

toward a reconciliation of the bayesian and frequentist approaches to point estimation abstract the bayesian and frequentist approaches to point estimation are reviewed the status of the debate regarding the use of one approach over the other is discussed and its inconclusive character is noted a criterion for comparing bayesian and frequentist estimators within a given experimental framework is proposed the competition between a bayesian and a frequentist is viewed as a contest with the following components a random observable a true prior distribution unknown to both statisticians an operational prior used by the bayesian a fixed frequentist rule used by the frequentist and a fixed loss criterion this competition is studied in the context of exponential families conjugate priors and squared error loss the class of operational priors that yield bayes estimators superior to the best frequentist estimator is characterized the implications of the existence of a threshold separating the space of operational priors into good and bad priors are explored and their relevance in ar

a two step bayesian approach for propensity score analysis simulations and case study a two step bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous bayesian propensity score approaches the corresponding variance estimators are also provided the two step bayesian propensity score is provided for three methods of implementation propensity score stratification weighting and optimal full matching three simulation studies and one case study are presented to elaborate the proposed two step bayesian propensity score approach results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist based treatment effect a slight advantage is shown for the bayesian approach in small samples results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results however greater precision around the correct treatment effect parameter yields quite good results with slight improvement seen with greater precision in the propensity score equation a comparison of coverage rates for the conventional frequentist approach and proposed bayesian approach is also provided the case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non informative

bayesian prediction of spatial count data using generalized linear mixed models summary spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a bayesian approach and markov chain monte carlo informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling furthermore we demonstrate that so called langevin hastings updates are useful for efficient simulation of the posterior distributions and we discuss computational issues concerning prediction

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

on calibration error of randomized forecasting algorithms it has been recently shown that calibration with an error less than d 0 is almost surely guaranteed with a randomized forecasting algorithm where forecasts are obtained by random rounding the deterministic forecasts up to d we show that this error cannot be improved for a vast majority of sequences we prove that using a probabilistic algorithm we can effectively generate with probability close to one a sequence resistant to any randomized rounding forecasting with an error much smaller than d we also reformulate this result by means of a probabilistic game

efficient probabilistic forecasts for counts summary efficient probabilistic forecasts of integer valued random variables are derived the optimality is achieved by estimating the forecast distribution non parametrically over a given broad model class and proving asymptotic non parametric efficiency in that setting the method is developed within the context of the integer auto regressive class of models which is a suitable class for any count data that can be interpreted as a queue stock birth and death process or branching process the theoretical proofs of asymptotic efficiency are supplemented by simulation results that demonstrate the overall superiority of the non parametric estimator relative to a misspecified parametric alternative in large but finite samples the method is applied to counts of stock market iceberg orders a subsampling method is used to assess sampling variation in the full estimated forecast distribution and a proof of its validity is given

bayesianly justifiable and relevant frequency calculations for the applied statistician a common reaction among applied statisticians is that the bayesian statistician s energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying bayes s theorem to calculate conditional distributions of unknowns given knowns i feel however that the applied bayesian statistician s tool kit should be more extensive and include tools that may be usefully labeled frequency calculations three types of bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician

asymptotic estimates for apostol bernoulli and apostol euler polynomials we analyze the asymptotic behavior of the apostol bernoulli polynomials bn x in detail the starting point is their fourier series on 0 1 which it is shown remains valid as an asymptotic expansion over compact subsets of the complex plane this is used to determine explicit estimates on the constants in the approximation and also to analyze oscillatory phenomena which arise in certain cases these results are transferred to the apostol euler polynomials en x via a simple relation linking them to the apostol bernoulli polynomials

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

coherent dispersion criteria for optimal experimental design we characterize those coherent design criteria which depend only on the dispersion matrix assumed proper and nonsingular of the state of nature which may be a parameter vector or a set of future observables and describe the associated decision problems connections are established with the classical approach to optimal design theory for the normal linear model based on concave functions of the information matrix implications of the theory for more general models are also considered

new goodness of fit diagnostics for conditional discrete response models abstract this paper proposes new specification tests for conditional models with discrete responses which are key to apply efficient maximum likelihood methods to obtain consistent estimates of partial effects and to get appropriate predictions of the probability of future events in particular we test the static and dynamic ordered choice model specifications and can cover infinite support distributions for e g count data the traditional approach for specification testing of discrete response models is based on probability integral transforms of a jittered discrete data which leads to continuous uniform i i d series under the true conditional distribution then standard specification testing techniques for continuous variables could be applied to the transformed series but the extra randomness from jitters affects the power properties of these methods we investigate in this paper an alternative transformation based only on original discrete data that avoids any randomization we analyze the asymptotic properties of goodness of fit tests based on this new transformation and explore the properties in finite samples of a bootstrap algorithm to approximate the critical values of test statistics which are model and parameter dependent we show analytically and in simulations that our approach dominates the methods based on randomization in terms of power we apply the new tests to models of the monetary policy conducted by the federal reserve

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

probabilistic forecasts calibration and sharpness summary probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions we propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive distributions subject to calibration calibration refers to the statistical consistency between the distributional forecasts and the observations and is a joint property of the predictions and the events that materialize sharpness refers to the concentration of the predictive distributions and is a property of the forecasts only a simple theoretical framework allows us to distinguish between probabilistic calibration exceedance calibration and marginal calibration we propose and study tools for checking calibration and sharpness among them the probability integral transform histogram marginal calibration plots the sharpness diagram and proper scoring rules the diagnostic approach is illustrated by an assessment and ranking of probabilistic forecasts of wind speed at the stateline wind energy centre in the us pacific northwest in combination with cross validation or in the time series context our proposal provides very general nonparametric alternatives to the use of information criteria for model diagnostics and model selection

internal regret with partial monitoring calibration based optimal algorithms we provide consistent random algorithms for sequential decision under partial monitoring when the decision maker does not observe the outcomes but receives instead random feedback signals those algorithms have no internal regret in the sense that on the set of stages where the decision maker chose his action according to a given law the average payoff could not have been improved in average by using any other fixed law they are based on a generalization of calibration no longer defined in terms of a voronoi diagram but instead of a laguerre diagram a more general concept this allows us to bound for the first time in this general framework the expected average internal as well as the usual external regret at stage n by o n 1 3 which is known to be optimal

deformations and homotopy theory of relative rota baxter lie algebras we determine the l infty algebra that controls deformations of a relative rota baxter lie algebra and show that it is an extension of the dg lie algebra controlling deformations of the underlying mathsf lie mathsf rep pair by the dg lie algebra controlling deformations of the relative rota baxter operator consequently we define the cohomology of relative rota baxter lie algebras and relate it to their infinitesimal deformations a large class of relative rota baxter lie algebras is obtained from triangular lie bialgebras and we construct a map between the corresponding deformation complexes next the notion of a homotopy relative rota baxter lie algebra is introduced we show that a class of homotopy relative rota baxter lie algebras is intimately related to pre lie infty algebras

double poisson vertex algebras and non commutative hamiltonian equations we develop the formalism of double poisson vertex algebras local and non local aimed at the study of non commutative hamiltonian pdes this is a generalization of the theory of double poisson algebras developed by van den bergh which is used in the study of hamiltonian odes we apply our theory of double poisson vertex algebras to non commutative kp and gelfand dickey hierarchies we also construct the related non commutative de rham and variational complexes

on bayesian d optimum design criteria and the equivalence theorem in non linear models the concavity of some bayesian d optimality criteria is investigated and is found in some cases to depend on the prior distribution in the case of a non concave criterion the standard equivalence theorem may fail but a local version continues to apply

evaluating probability forecasts probability forecasts of events are routinely used in climate predictions in forecasting default probabilities on bank loans or in estimating the probability of a patient s positive response to treatment scoring rules have long been used to assess the efficacy of the forecast probabilities after observing the occurrence or nonoccurrence of the predicted events we develop herein a statistical theory for scoring rules and propose an alternative approach to the evaluation of probability forecasts this approach uses loss functions relating the predicted to the actual probabilities of the events and applies martingale theory to exploit the temporal structure between the forecast and the subsequent occurrence or nonoccurrence of the event