dose response signal detection under model uncertainty we investigate likelihood ratio contrast tests for dose response signal detection under model uncertainty when several competing regression models are available to describe the dose response relationship the proposed approach uses the complete structure of the regression models but does not require knowledge of the parameters of the competing models standard likelihood ratio test theory is applicable in linear models as well as in nonlinear regression models with identifiable parameters however for many commonly used nonlinear dose response models the regression parameters are not identifiable under the null hypothesis of no dose response and standard arguments cannot be used to obtain critical values we thus derive the asymptotic distribution of likelihood ratio contrast tests in regression models with a lack of identifiability and use this result to simulate the quantiles based on gaussian processes the new method is illustrated with a real data example and compared to existing procedures using theoretical investigations as well as simulations

bayesian isotonic regression and trend analysis in many applications the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor controlling for covariates in such cases interest often focuses on estimating the regression function while also assessing evidence of an association this article proposes a new framework for bayesian isotonic regression and order restricted inference approximating the regression function with a high dimensional piecewise linear model the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses accounting for flat regions and truncated normal densities to borrow information across the intervals and smooth the curve the prior is formulated as a latent autoregressive normal process this structure facilitates efficient posterior computation since the full conditional distributions of the parameters have simple conjugate forms point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single mcmc run generalizations to categorical outcomes and multiple predictors are described and the approach is applied to an epidemiology application

unobserved heterogeneity in auctions under restricted stochastic dominance abstract we study the identification of first price auctions with nonseparable unobserved heterogeneity in particular we extend hu et al 2013 by relaxing the first order stochastic dominance condition instead we assume restricted stochastic dominance relations among value quantile functions and show that the same relations pass to bid quantile functions an ordered tree summarizes these relations and provides a total ordering relying on the proposed restricted stochastic dominance ordering we extend a list of identification results in the empirical auction literature

burkholder s inequalities associated with orlicz functions in rearrangement invariant spaces in this paper we prove martingale inequalities associated with orlicz functions in the framework of rearrangement invariant spaces more precisely let phi be an orlicz function and let x be a rearrangement invariant spaces we establish the new moment burkholder inequalities when the simonenko indices of phi and the boyd indices of x satisfy some natural conditions our approach mainly relies on a new distribution estimate of the davis type decomposition

bayesian local extremum splines we consider shape restricted nonparametric regression on a closed set formula see text where it is reasonable to assume the function has no more than h local extrema interior to formula see text following a bayesian approach we develop a nonparametric prior over a novel class of local extremum splines this approach is shown to be consistent when modeling any continuously differentiable function within the class considered and is used to develop methods for testing hypotheses on the shape of the curve sampling algorithms are developed and the method is applied in simulation studies and data examples where the shape of the curve is of interest

estimating smooth monotone functions many situations call for a smooth strictly monotone function f of arbitrary flexibility the family of functions defined by the differential equation d 2 f w df where w is an unconstrained coefficient function comprises the strictly monotone twice differentiable functions the solution to this equation is f c 0 c 1 d 1 exp d 1 w where c 0 and c 1 are arbitrary constants and d 1 is the partial integration operator a basis for expanding w is suggested that permits explicit integration in the expression of f in fitting data it is also useful to regularize f by penalizing the integral of w 2 since this is a measure of the relative curvature in f applications are discussed to monotone nonparametric regression to the transformation of the dependent variable in non linear regression and to density estimation

nonparametric bayesian bioassay with prior constraints on the shape of the potency curve summary we consider the problem of implementing nonparametric bayesian analysis of bioassay problems when the prior constrains the form of the potency curve for example to be convex concave or ogive sampling based approaches to calculating posterior features of interest are detailed and illustrated extensions to prior constraints on hazard rates are outlined

combining multiple comparisons and modeling techniques in dose response studies the analysis of data from dose response studies has long been divided according to two major strategies multiple comparison procedures and model based approaches model based approaches assume a functional relationship between the response and the dose taken as a quantitative factor according to a prespecified parametric model the fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose response model multiple comparison procedures regard the dose as a qualitative factor and make very few if any assumptions about the underlying dose response model the primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect one approach is to evaluate the significance of contrasts between different dose levels while preserving the family wise error rate such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation we describe a unified strategy to the analysis of data from dose response studies which combines multiple comparison and modeling techniques we assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose response curve while preserving the family wise error rate the selected model is then used to provide inference on adequate doses

monotonic smoothing splines fitted by cross validation a practical method for calculating monotonic cubic smoothing splines is given linear sufficient conditions for monotonicity are employed and the spline coefficients are obtained using quadratic p

bayesian isotonic density regression density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions and are well supported in many applications a rich variety of bayesian methods have been proposed for density regression but it is not clear whether such priors have full support so that any true data generating model can be accurately approximated this article develops a new class of density regression models that incorporate stochastic ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor theory is developed showing large support methods are developed for hypothesis testing with posterior computation relying on a simple gibbs sampler frequentist properties are illustrated in a simulation study and an epidemiology application is considered

bayesian nonparametric estimation of continuous monotone functions with applications to dose response analysis in this article we consider monotone nonparametric regression in a bayesian framework the monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions and a general random probability measure is assumed as the prior for the mixing distribution we investigate the choice of the underlying parametric distribution function and find that the two sided power distribution function is well suited both from a computational and mathematical point of view the model is motivated by traditional nonlinear models for dose response analysis and provides possibilities to elicitate informative prior distributions on different aspects of the curve the method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose response analysis

bayesian nonparametric modeling using mixtures of triangular distributions nonparametric modeling is an indispensable tool in many applications and its formulation in an hierarchical bayesian context using the entire posterior distribution rather than particular expectations increases its flexibility in this article the focus is on nonparametric estimation through a mixture of triangular distributions the optimality of this methodology is addressed and bounds on the accuracy of this approximation are derived although our approach is more widely applicable we focus for simplicity on estimation of a monotone nondecreasing regression on 0 1 with additive error effectively approximating the function of interest by a function having a piecewise linear derivative computationally accessible methods of estimation are described through an amalgamation of existing markov chain monte carlo algorithms simulations and examples illustrate the approach

optimal designs for dose finding studies with an active control summary dose finding studies often compare several doses of a new compound with a marketed standard treatment as an active control in the past however research has focused mostly on experimental designs for placebo controlled dose finding studies to the best of our knowledge optimal designs for dose finding studies with an active control have not been considered so far as the statistical analysis for an active controlled dose finding study can be formulated in terms of a mixture of two regression models the related design problem is different from what has been investigated before in the literature we present a rigorous approach to the problem of determining optimal designs for estimating the smallest dose achieving the same treatment effect as the active control we determine explicitly the locally optimal designs for a broad class of models employed in such studies we also discuss robust design strategies and determine related bayesian and standardized minimax optimal designs we illustrate the results by investigating alternative designs for a clinical trial which has recently appeared in a consulting project of one of the authors

equivalence of the dynamics of nonholonomic and variational nonholonomic systems for certain initial data in this paper we discuss the necessary and sufficient conditions for the equivalence of the dynamics of nonholonomic mechanics and variational nonholonomic vakonomic dynamics for certain initial conditions we derive a priori results for identifying equivalence and specializing to abelian chaplygin systems prove that equivalence results if and only if the constrained nonholonomic equations are lagrangian we eliminate the need to solve the variational nonholonomic problem when checking equivalence by obtaining explicit formulae for the system s multipliers and then derive conditions under which the multiplier free lagrangian gives equivalence of the dynamics we consider nonholonomic systems possessing invariant measures showing when equivalence and hamiltonization are the same we also derive conditions under which measure preserving systems exhibit equivalence we apply the results to many of the known nonholonomic systems

some new φ moment martingale inequalities associated with concave functions abstract the paper is devoted to study the moment inequalities for martingales where is a concave function we mainly employ the method of atomic decomposition involving moment martingale inequalities

a bayesian approach to the analysis of quantal bioassay studies using nonparametric mixture models we develop a bayesian nonparametric mixture modeling framework for quantal bioassay settings the approach is built upon modeling dose dependent response distributions we adopt a structured nonparametric prior mixture model which induces a monotonicity restriction for the dose response curve particular emphasis is placed on the key risk assessment goal of calibration for the dose level that corresponds to a specified response the proposed methodology yields flexible inference for the dose response relationship as well as for other inferential objectives as illustrated with two data sets from the literature

bayesian spatial monotonic multiple regression we consider monotonic multiple regression for contiguous regions the regression functions vary regionally and may exhibit spatial structure we develop bayesian nonparametric methodology that permits estimation of both continuous and discontinuous functional shapes using marked point process and reversible jump markov chain monte carlo techniques spatial dependence is incorporated by a flexible prior distribution which is tuned using cross validation and bayesian optimization we derive the mean and variance of the prior induced by the marked point process approach asymptotic results show consistency of the estimated functions posterior realizations enable variable selection the detection of discontinuities and prediction in simulations and in an application to a norwegian insurance data set our methodology shows better performance than existing approaches

on some inequalities for doob decompositions in banach function spaces let phi mathbb r to 0 infty be a young function and let f f n n in mathbb z be a martingale such that phi f n in l 1 for all n in mathbb z then the process phi f phi f n n in mathbb z can be uniquely decomposed as phi f n g n h n where g g n n in mathbb z is a martingale and h h n n in mathbb z is a predictable nondecreasing process such that h0 0 almost surely the main results characterize those banach function spaces x such that the inequality h infty x leq c phi mf x is valid and those x such that the inequality h infty x leq c phi sf x is valid where mf and sf denote the maximal function and the square function of f respectively

noncommutative burkholder rosenthal inequalities we investigate martingale inequalities in noncommutative lp spaces associated with a von neumann algebra equipped with a faithful normal state we prove the noncommutative analogue of the classical burkholder inequality on the conditioned or little square function and extend the noncommutative burkholder gundy inequalities from comm math phys 189 1997 667 698 to this nontracial setting we include several related results

monotone nonparametric regression in monotone regression procedures one utilizes only the monotonicity of the regression function in nonparametric regression one utilizes only the assumed smoothness the analytic and asymptotic properties of the estimator are superior in the latter case however monotonicity is not guaranteed we study a hybrid procedure that produces monotone estimators with properties similar to those of nonparametric regression estimators

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

constraints reduction and quantization theorems are proved that establish the unitary equivalence of the extended and reduced phase space quantizations of a constrained classical system with symmetry several examples are presented

bayesian monotone regression using gaussian process projection shape constrained regression analysis has applications in dose response modelling environmental risk assessment disease screening and many other areas incorporating the shape constraints can improve estimation efficiency and avoid implausible results we propose a novel method focusing on monotone curve and surface estimation which uses gaussian process projections our inference is based on projecting posterior samples from the gaussian process we develop theory on continuity of the projection and rates of contraction our approach leads to simple computation with good performance in finite samples the proposed projection method can also be applied to other constrained function estimation problems including those in multivariate settings

quantizing conditionally variational nonholonomic systems in this paper we present a quantization procedure for a class of nonholonomic systems briefly mechanical systems subject to nonintegrable constraints on the velocities whose reduced mechanics is hamiltonian we illustrate the theory developed through several examples one of which demonstrates how the classical nonholonomic constraints are sometimes manifested quantum mechanically as a shift in the ground state energy of the system

nonparametric bayesian bioassay including ordered polytomous response abstract previous attempts at implementing fully bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties we show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features a useful extension is presented which treats the case of ordered polytomous response illustrative examples are provided