Nonparametric Conditional Inference for Regression Coefficients with Application to Configural Polysampling

We consider inference procedures, conditional on an observed ancillary statistic, for regression coefficients under a linear regression setup where the unknown error distribution is specified nonparametrically. We establish conditional asymptotic normality of the regression coefficient estimators under regularity conditions, and formally justify the approach of plugging in kernel-type density estimators in conditional inference procedures. Simulation results show that the approach yields accurate conditional coverage probabilities when used for constructing confidence intervals. The plug-in approach can be applied in conjunction with configural polysampling to derive robust conditional estimators adaptive to a confrontation of contrasting scenarios. We demonstrate this by investigating the conditional mean squared error of location estimators under various confrontations in a simulation study, which successfully extends configural polysampling to a nonparametric context

Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics

Given a sample of size $n$ from a population of individuals belonging to different species with unknown proportions, a popular problem of practical interest consists in making inference on the probability $D_{n}(l)$ that the $(n+1)$-th draw coincides with a species with frequency $l$ in the sample, for any $l=0,1,\ldots,n$. This paper contributes to the methodology of Bayesian nonparametric inference for $D_{n}(l)$. Specifically, under the general framework of Gibbs-type priors we show how to derive credible intervals for a Bayesian nonparametric estimation of $D_{n}(l)$, and we investigate the large $n$ asymptotic behaviour of such an estimator. Of particular interest are special cases of our results obtained under the specification of the two parameter Poisson--Dirichlet prior and the normalized generalized Gamma prior, which are two of the most commonly used Gibbs-type priors. With respect to these two prior specifications, the proposed results are illustrated through a simulation study and a benchmark Expressed Sequence Tags dataset. To the best our knowledge, this illustration provides the first comparative study between the two parameter Poisson--Dirichlet prior and the normalized generalized Gamma prior in the context of Bayesian nonparemetric inference for $D_{n}(l)$

Bartlett-type Adjustments for Empirical Discrepancy Test Statistics

This paper derives two Bartlett-type adjustments that can be used to obtain higher-order improvements to the distribution of the class of empirical discrepancy test statistics recently introduced by Corcoran (1998) as a generalisation of Owen's (1988)empirical likelihood. The corrections are illustrated in the context of the so-called Cressie-Read goodness-of-fit statistic Baggerly, and their effectiveness in finite samples is evaluated using simulations.asymptotic expansions; Bartlett and Bartlett-type corrections; empirical likelihood; nonparametric likelihood inference

A Bi-Directional Refinement Algorithm for the Calculus of (Co)Inductive Constructions

The paper describes the refinement algorithm for the Calculus of (Co)Inductive Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement algorithm is in charge of giving a meaning to the terms, types and proof terms directly written by the user or generated by using tactics, decision procedures or general automation. The terms are written in an "external syntax" meant to be user friendly that allows omission of information, untyped binders and a certain liberal use of user defined sub-typing. The refiner modifies the terms to obtain related well typed terms in the internal syntax understood by the kernel of the ITP. In particular, it acts as a type inference algorithm when all the binders are untyped. The proposed algorithm is bi-directional: given a term in external syntax and a type expected for the term, it propagates as much typing information as possible towards the leaves of the term. Traditional mono-directional algorithms, instead, proceed in a bottom-up way by inferring the type of a sub-term and comparing (unifying) it with the type expected by its context only at the end. We propose some novel bi-directional rules for CIC that are particularly effective. Among the benefits of bi-directionality we have better error message reporting and better inference of dependent types. Moreover, thanks to bi-directionality, the coercion system for sub-typing is more effective and type inference generates simpler unification problems that are more likely to be solved by the inherently incomplete higher order unification algorithms implemented. Finally we introduce in the external syntax the notion of vector of placeholders that enables to omit at once an arbitrary number of arguments. Vectors of placeholders allow a trivial implementation of implicit arguments and greatly simplify the implementation of primitive and simple tactics

Service-oriented Context-aware Framework

Location- and context-aware services are emerging technologies in mobile and desktop environments, however, most of them are difficult to use and do not seem to be beneficial enough. Our research focuses on designing and creating a service-oriented framework that helps location- and context-aware, client-service type application development and use. Location information is combined with other contexts such as the users' history, preferences and disabilities. The framework also handles the spatial model of the environment (e.g. map of a room or a building) as a context. The framework is built on a semantic backend where the ontologies are represented using the OWL description language. The use of ontologies enables the framework to run inference tasks and to easily adapt to new context types. The framework contains a compatibility layer for positioning devices, which hides the technical differences of positioning technologies and enables the combination of location data of various sources