Interpolation, realization, and reconstruction of noisy, irregularly sampled data

Abstract

Various statistical procedures related to linear prediction and optimal filtering are developed for general, irregularly sampled, data sets. The data set may be a function of time, a spatial sample, or an unordered set. In the case of time series, the underlying process may be low-frequency divergent (weakly nonstationary). Explicit formulas are given for (i) maximum likelihood reconstruction (interpolation) with estimation of uncertainties, (ii) reconstruction by unbiased estimators (Gauss-Markov), (iii) unconstrained Monte Carlo realization of the underlying process, (iv) Monte Carlo realizations constrained by measured data, and (v) simultaneous reconstruction and determination of unknown linear parameters.