Related papers: Recent progress on conditional randomness
A scenario is outlined for quantum measurement, assuming that self-sustaining classicality is the consequence of an attractive gravitational self-interaction acting on massive bodies, and randomness arises already in the classical domain. A…
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a…
In this paper, we propose a new approach for deriving probabilistic inequalities. Our main idea is to exploit the information of underlying distributions by virtue of the monotone likelihood ratio property and Berry-Essen inequality.…
Our aim is to make a step towards clarification of foundations for the notion of entanglement (both physical and mathematical) by representing it in the conditional probability framework. In Schr\"odinger's words, this is entanglement of…
The distribution of the spectral numbers of an isolated hypersurface singularity is studied in terms of the Bernoulli moments. These are certain rational linear combinations of the higher moments of the spectral numbers. They are related to…
In this paper, we establish an identity for Bernoulli's generalized polynomials. We deduce generalizations for many relations involving classical Bernoulli numbers or polynomials. In particular, we generalize a recent Gessel identity.
There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…
Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
We describe some recent approaches to likelihood based inference in the presence of nuisance parameters. Our approach is based on plotting the likelihood function and the $p$-value function, using recently developed third order…
For a general renewal process $N$ (allowing delay, defect and multiple simultaneous arrivals) the independence of the first renewal epochs of the marked processes got from $N$ by Bernoulli $0$/$1$ thinning is characterized. This…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
Recently noticed ability of restart to reduce the expected completion time of first-passage processes allows appealing opportunities for performance improvement in a variety of settings. However, complex stochastic processes often exhibit…
Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior…
The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records…
A result of Chebyshev (1864) and Hoeffding1956}, on bounding an expectation of a given function with respect to a Bernoulli convolution (also called Poisson binomial law, or law of the number of successes in independent trials) with any…