Related papers: Recent progress on conditional randomness
In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…
We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
A Bernoulli scheme with unequal harmonic success probabilities is investigated, together with some of its natural extensions. The study includes the number of successes over some time window, the times to (between) successive successes and…
This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are…
One-sided confidence intervals are presented for the average of non-identical Bernoulli parameters. These confidence intervals are expressed as analytical functions of the total number of Bernoulli games won, the number of rounds and the…
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…
We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
We explore the recent results announced in "Robust machine learning by median-of-means: theory and practice" by G. Lecu\'e and M. Lerasle. We show that these results are, in fact, almost obvious outcomes of the machinery developed in [4]…
We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a \psi-irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by…
We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The sample PLR converges to the unknown population PLR under mild conditions. The methodology allows for…
Suppose $N$ independent Bernoulli trials are observed sequentially at random times of a mixed binomial process. The task is to maximise, by using a nonanticipating stopping strategy, the probability of stopping at the last success. We focus…
A concentration result for quadratic form of independent subgaussian random variables is derived. If the moments of the random variables satisfy a "Bernstein condition", then the variance term of the Hanson-Wright inequality can be…
It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous…
This work investigates the optimal selection of the $m$th last success in a sequence of $n$ independent Bernoulli trials. We propose a threshold strategy that is $\varepsilon$-optimal under minimal assumptions about the monotonicity of the…
This paper deals with rates of convergence in the strong law of large numbers, in the Baum-Katz form, for partial sums of Banach space valued random variables. The results are then applied to solve similar problems for weighted partial sums…
We consider a type of random processes which satisfies the conditional increment condition and obtain an estimate for the tail probability and a Doob-type inequality of the maximum of the process. The main result is that, for processes…
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…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…