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The German tank problem has an interesting historical background and is an engaging problem of statistical estimation for the classroom. The objective is to estimate the size of a population of tanks inscribed with sequential serial…
To handle with inverse problems, two probabilistic approaches have been proposed: the maximum entropy on the mean (MEM) and the Bayesian estimation (BAYES). The main object of this presentation is to compare these two approaches which are…
Inferring a quantum system from incomplete information is a common problem in many aspects of quantum information science and applications, where the principle of maximum entropy (MaxEnt) plays an important role. The quantum state…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
It is proposed in the literature that in some complicated problems maximum likelihood estimates (MLE) are not suitable or even do not exist. An alternative to MLE for estimation of the parameters is the Bayesian method. The Markov chain…
In this paper we show that the so-called array Fr\'echet problem in Probability/Statistics is (max, +)-linear. The upper bound of Fr\'echet is obtained using simple arguments from residuation theory and lattice distributivity. The lower…
The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction…
The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach…
Recently, the conditional maximum-entropy method (abbreviated as C-MaxEnt) has been proposed for selecting priors in Bayesian statistics in a very simple way. Here, it is examined for extreme-value statistics. For the Weibull type as an…
The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and…
In this article we consider parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable Levy process, which is observed at high frequency. In most cases of practical interest, the likelihood…
An $n$-vertex graph is called $C$-Ramsey if it has no clique or independent set of size $C\log_2 n$ (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge-statistics in Ramsey graphs, in particular obtaining very…
Calculations and mechanistic explanations for the probabilistic movement of objects at the highly relevant cm length scales has been lacking and overlooked due to the complexity of current techniques. Predicting the final-configuration…
Maximum entropy (MAXENT) method has a large number of applications in theoretical and applied machine learning, since it provides a convenient non-parametric tool for estimating unknown probabilities. The method is a major contribution of…
For a wide range of entropy measures, easy calculation of equilibria is possible using a principle of Game Theoretical Equilibrium related to Jaynes Maximum Entropy Principle. This follows previous work of the author and relates to works of…
We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured,…
We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium…
Superstatistics is a generalization of equilibrium statistical mechanics that describes systems in nonequilibrium steady states. Among the possible superstatistical distributions, the $q$-canonical ensemble (also known as Tsallis'…
The microscopic foundation of the generalized equilibrium statistical mechanics based on the Tsallis entropy is given by using the Gibbs idea of statistical ensembles of the classical and quantum mechanics. The equilibrium distribution…
Maxwells Demon is a mythical being, first described by the physicist James Clerk Maxwell (although named Maxwells Demon by Lord Kelvin). Maxwell used it in a thought experiment to potentially violate the Second Law of Thermodynamics by…