Related papers: Nonparametric inference under shape constraints: p…

A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations…

The usual concept of shape invariance is discussed and one extension of this concept is suggested.

Discussions on indeterminism in physics focus on the possibility of an open future, i.e. the possibility of having potential alternative future events, the realisation of one of which is not fully determined by the present state of affairs.…

Causal inference is a science with multi-disciplinary evolution and applications. On the one hand, it measures effects of treatments in observational data based on experimental designs and rigorous statistical inference to draw causal…

Prediction of future observations is a fundamental problem in statistics. Here we present a general approach based on the recently developed inferential model (IM) framework. We employ an IM-based technique to marginalize out the unknown…

In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results.

We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the…

Understanding how anatomical shapes evolve in response to developmental covariates and quantifying their spatially varying uncertainties is critical in healthcare research. Existing approaches typically rely on global time-warping…

We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…

We consider the problem of shape restricted nonparametric regression on a closed set X ?\in R; where it is reasonable to assume the function has no more than H local extrema interior to X: Following a Bayesian approach we develop a…

Invariants underlying shape inference are elusive: a variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: it has both image salience, in…

Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…

These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an inter-disciplinary area of research with theoretical…

It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a…

Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…

The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual…

We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…

This extended preface [to the Book `Bayesian Nonparametrics', Cambridge University Press, 2010, by NL Hjort, CC Holmes, P Mueller, SG Walker] is meant to explain why you are right to be curious about Bayesian nonparametrics -- why you may…

We discuss non-parametric density estimation and regression for astrophysics problems. In particular, we show how to compute non-parametric confidence intervals for the location and size of peaks of a function. We illustrate these ideas…

There are many situations where comparison of different groups is of great interest. Considering the ordering of the efficiency of some treatments is an example. We present nonparametric predictive inference (NPI) for the ordering of…