Robust optimal estimation of location from discretely sampled functional data

Estimating Continuous-Time Models with Discretely Sampled Data∗

This lecture surveys the recent literature on estimating continuous-time models using discrete observations. I start with the simplest possible framework and review different possible approaches as I progressively relax the assumptions made, to include different data generating processes (such as multivariate diffusions or jump processes), different observation schemes (such as incorporating ma...

Numerical estimation of volatility values from discretely observed diffusion data

We consider a Black-Scholes type model, but with volatility being a Markov Chain process. Assuming that the stock price is observed at discrete, possibly random times, the goal is to estimate the current volatility value. The model parameters, that is, the possible volatility values and transition probabilities, are estimated using the Multiscale Trend Analysis method of Zaliapin, Gabrielov and...

Optimal Sampled-data Control

Robust extraction of multiple structures from non-uniformly sampled data

The extraction of multiple coherent structures from point clouds is crucial to the problem of scene modeling. While many statistical methods exist for robust estimation from noisy data, they are inadequate for addressing issues of scale, semi-structured clutter, and large point density variation together with the computational restrictions of autonomous navigation. This paper extends an approac...

Deforming and Animating Discretely Sampled Object Representations

A discretely sampled object representation (DSOR) defines a graphical model using data obtained by a sampling process, which takes a collection of samples at discrete positions in space in order to capture certain geometrical and physical properties of one or more objects of interest. Examples of DSORs include images, videos, volume datasets and point datasets. Unlike many commonly used data re...