Related papers: Exchangeability and randomness for infinite and fi…
For models of concurrent and distributed systems, it is important and also challenging to establish correctness in terms of safety and/or liveness properties. Theories of distributed systems consider equivalences fundamental, since they (1)…
This note continues study of exchangeability martingales, i.e., processes that are martingales under any exchangeable distribution for the observations. Such processes can be used for detecting violations of the IID assumption, which is…
We characterize the identified sets of a wide range of stochastic choice models, including random utility, various models of boundedly-rational behavior, and dynamic discrete choice. In each of these settings, we show two distributions over…
If quantum mechanics is taken for granted the randomness derived from it may be vacuous or even delusional, yet sufficient for many practical purposes. "Random" quantum events are intimately related to the emergence of both space-time as…
The randomness rate of an infinite binary sequence is characterized by the sequence of ratios between the Kolmogorov complexity and the length of the initial segments of the sequence. It is known that there is no uniform effective procedure…
The convergence of simultaneous and marginal predictive classifiers under partition exchangeability in supervised classification is obtained. The result shows the asymptotic convergence of these classifiers under infinite amount of training…
Randomness is viewed through an analogy between a physical quantity, density of gas, and a mathematical construct -- probability density. Boltzmann's deduction of equilibrium distribution of ideal gas placed in an external potential field…
To render a sequence testable, namely capable of identifying and detecting errors, it is necessary to apply a transformation that increases its length by introducing statistical dependence among symbols, as commonly exemplified by the…
Reasoning about unpredicted change consists in explaining observations by events; we propose here an approach for explaining time-stamped observations by surprises, which are simple events consisting in the change of the truth value of a…
Prediction algorithms assign numbers to individuals that are popularly understood as individual "probabilities" -- what is the probability of 5-year survival after cancer diagnosis? -- and which increasingly form the basis for life-altering…
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…
The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…
In this paper, we consider the sublinear expectation on bounded random variables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the notion of…
Structural identifiability is an important property of parametric ODE models. When conducting an experiment and inferring the parameter value from the time-series data, we want to know if the value is globally, locally, or non-identifiable.…
The minimum average number of bits need to describe a random variable is its entropy, assuming knowledge of the underlying statistics On the other hand, universal compression supposes that the distribution of the random variable, while…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same…
A common assumption in causal inference is that random treatment assignment ensures that potential outcomes are independent of treatment, or in one word, unconfoundedness. This paper highlights that randomization and unconfoundedness are…
Many empirical time series are genuinely symbolic: examples range from link activation patterns in network science, DNA coding or firing patterns in neuroscience to cryptography or combinatorics on words. In some other contexts, the…
We present simple randomized and exchangeable improvements of Markov's inequality, as well as Chebyshev's inequality and Chernoff bounds. Our variants are never worse and typically strictly more powerful than the original inequalities. The…