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The problem of generating random samples of high-dimensional posterior distributions is considered. The main results consist of non-asymptotic computational guarantees for Langevin-type MCMC algorithms which scale polynomially in key…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
As medical devices become more complex, they routinely collect extensive and complicated data. While classical regressions typically examine the relationship between an outcome and a vector of predictors, it becomes imperative to identify…
We investigate random compact sets with random functions defined thereon, such as polynomials, rational functions, the pluricomplex Green function and the Siciak extremal function. One surprising consequence of our study is that randomness…
We construct long-term prediction intervals for time-aggregated future values of univariate economic time series. We propose computational adjustments of the existing methods to improve coverage probability under a small sample constraint.…
In this paper we obtain several extensions to the quaternionic setting of some results concerning the approximation by polynomials of functions continuous on a compact set and holomorphic in its interior. The results include approximation…
A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…
Time series forecasting is a critical task in various domains, where accurate predictions can drive informed decision-making. Traditional forecasting methods often rely on current observations of variables to predict future outcomes,…
We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper…
We introduce a new class of forward performance processes that are endogenous and predictable with regards to an underlying market information set and, furthermore, are updated at discrete times. We analyze in detail a binomial model whose…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
Model based signal processing or signal analysis or signal representation has a rather different point of view from the more traditional filtering and algorithm based approaches. However, in all of these, the names of Prony, Pad\'e, and…
We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof is based on the alternate applications of projection…
Random field models have been widely employed to develop a predictor of an expensive function based on observations from an experiment. The traditional framework for developing a predictor with random field models can fail due to the…
The period of a Morse oscillator and mathematical pendulum system are obtained, accurate to 100 significant digits, by forward period analysis (FPA). From these results, the long-term [0, 10^60] (time unit) solutions, which overlap from the…
A generalized matrix-pencil approach is proposed for the estimation of complex exponential components with segmented signal samples, which is very efficient and provides super-resolution estimations. It is applicable to the signals sampled…
Given any postsingularly finite exponential function $p_\lambda(z) = \lambda \exp(z)$ where $\lambda \in \C^*$, we construct a sequence of postcritically finite unicritical polynomials $p_{d,\lambda_d}(z) = \lambda_d(1+\frac{z}{d})^d$ that…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local $X$-Whittle estimators -- as generalizations of their univariate counterparts. As the…
Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs…