Related papers: Strong Consistency of the Good-Turing Estimator
Turing's estimator allows one to estimate the probabilities of outcomes that either do not appear or only rarely appear in a given random sample. We perform a simulation study to understand the finite sample performance of several related…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…
The problem of guessing subject to distortion is considered, and the performance of randomized guessing strategies is investigated. A one-shot achievability bound on the guessing moment (i.e., moment of the number of required queries) is…
We study the probability of Boolean functions with small max influence to become constant under random restrictions. Let $f$ be a Boolean function such that the variance of $f$ is $\Omega(1)$ and all its individual influences are bounded by…
We present a general approach to the problem of determining the asymptotic order of the variance of the optimal score between two independent random sequences defined over an arbitrary finite alphabet. Our general approach is based on…
Consider two random strings having the same length and generated by an iid sequence taking its values uniformly in a fixed finite alphabet. Artificially place a long constant block into one of the strings, where a constant block is a…
We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…
The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the…
We consider randomized dynamics over the $n$-simplex, where at each step a random set, or block, of coordinates is evenly averaged. When all blocks have size 2, this reduces to the repeated averages studied in [CDSZ22], a version of the…
Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…
The random percolation model can be viewed as the dual of a well defined confining gauge theory; since this theory, having no Monte Carlo dynamics at all, is simple to simulate, it is possible to study the properties of the flux tube with…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…
In multiple classification, one aims to determine whether a testing sequence is generated from the same distribution as one of the M training sequences or not. Unlike most of existing studies that focus on discrete-valued sequences with…
Given a random process $x(\tau)$ which undergoes stochastic resetting at a constant rate $r$ to a position drawn from a distribution ${\cal P}(x)$, we consider a sequence of dynamical observables $A_1, \dots, A_n$ associated to the…
In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution.…
The Gumbel-Softmax probability distribution allows learning discrete tokens in generative learning, while the Gumbel-Argmax probability distribution is useful in learning discrete structures in discriminative learning. Despite the efforts…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…