Related papers: Approximating a sequence of observations by a simp…
We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…
Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…
Mathematicians tend to use the phrase "arbitrarily close" to mean something along the lines of "every neighborhood of a point intersects a set". Taking the latter statement as a technical definition for arbitrarily close leads to an…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
Non-parametric methods avoid the problem of having to specify a particular data generating mechanism, but can be computationally intensive, reducing their accessibility for large data problems. Empirical likelihood, a non-parametric…
The Levenshtein distance is an important tool for the comparison of symbolic sequences, with many appearances in genome research, linguistics and other areas. For efficient applications, an approximation by a distance of smaller…
The frequentist interpretation of measurement results requires the specification of an ensemble of independent replications of the same experiment. For complex calculations of bias, coverage, significance, etc., this ensemble is often…
In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an…
A supersequence over a finite set is a sequence that contains as subsequence all permutations of the set. This paper defines an infinite array of methods to create supersequences of decreasing lengths. This yields the shortest known…
A very simple event frequency approximation algorithm that is sensitive to event timeliness is suggested. The algorithm iteratively updates categorical click-distribution, producing (path of) a random walk on a standard $n$-dimensional…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
Within the context of the binomial model, we analyse sequences of values that are almost-uniform and we discuss a prediction method called the frequent outcome approach, in which the outcome that has occurred the most in the observed trials…
The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The…
In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…
We describe a simple and efficient procedure for approximating the L\'evy measure of a $\text{Gamma}(\alpha,1)$ random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's…
How do we estimate the probability of an abundant objects' formation, with minimal context or assumption about is origin? To explore this we have previously introduced the concept of pathway assembly (as pathway complexity), in a graph…
This work proposes a decision-making framework for partially observable systems in continuous time with discrete state and action spaces. As optimal decision-making becomes intractable for large state spaces we employ approximation methods…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.