Related papers: Numerical implementation of some reweighted path i…
I define and characterize the reweighted methods, which are techniques used in conjunction with the random series implementation of the Feynman-Kac formula. I prove several convergence results valid for all series representations and then I…
We perform a thorough analysis of the relationship between discrete and series representation path integral methods, which are the main numerical techniques used in connection with the Feynman-Kac formula. First, a new interpretation of the…
By means of the Ito-Nisio theorem, we introduce and discuss a general approach to series representations of path integrals. We then argue that the optimal basis for both ``primitive'' and partial averaged approaches is the Wiener…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
We study the asymptotic convergence of the partial averaging method, a technique used in conjunction with the random series implementation of the Feynman-Kac formula. We prove asymptotic bounds valid for most series representations in the…
We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
We discuss measures on spaces of unparametrized paths related to the Wiener measure. These measures arise naturally in the study of one-dimensional gravity coupled to scalar fields. Two kinds of discrete approximations are defined, the…
Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we…
In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…
The "weighted ensemble" method, introduced by Huber and Kim, [G. A. Huber and S. Kim, Biophys. J. 70, 97 (1996)], is one of a handful of rigorous approaches to path sampling of rare events. Expanding earlier discussions, we show that the…
Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step…
The comparative study of two globally convergent numerical methods for acoustic tomography is carried out in two dimensions. These are the boundary control method and the quasi-reversibility method. The novelty is that in the latter a…
Depending on initial conditions, individual finite time trajectories of dynamical systems can have very different chaotic properties. Here we present a numerical method to identify trajectories with atypical chaoticity, pathways that are…
We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process…
The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each…
Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum…
We present a new method for recovering the cosmological density, velocity, and potential fields from all-sky redshift catalogues. The method is based on an expansion of the fields in orthogonal radial (Bessel) and angular (spherical…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…