Related papers: Constructive approximations of the $q=1/2$ maximum…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
It is known that the nonextensive statistics was originally formulated for the systems composed of subsystems having same $q$. In this paper, the existence of composite system with different $q$ subsystems is investigated by fitting the…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
Using R\'enyi entropy, a possible thermostatistics for nonextensive systems is discussed. We show that it is possible to get the $q$-exponential distribution function for nonextensive systems having nonadditive energy but additive entropy.…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…
Entropy maximization procedure has been a general practice in many diverse fields of science to obtain the concomitant probability distributions. The consistent use of the maximization procedure on the other hand requires the probability…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
The nonextensive statistics based on the $q$-entropy $S_q=-\frac{\sum_{i=1}^v(p_i-p_i^q)}{1-q}$ has been so far applied to systems in which the $q$ value is uniformly distributed. For the systems containing different $q$'s, the…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
In this paper we extend our recent results [Physica A340 (2004)110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Renyi with the q-deformed version of Khinchin axioms to obtain the…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
A new paradigm is proposed for the robustification of the LQG controller against distributional uncertainties on the noise process. Our controller optimizes the closed-loop performances in the worst possible scenario under the constraint…
We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…
Bayesian optimal experimental design provides a principled framework for selecting experimental settings that maximize obtained information. In this work, we focus on estimating the expected information gain in the setting where the…
We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy…
Probability distributions which emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this paper we unite modeling of such distributions with the model of widespread 1/f noise. We…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
We consider the following frustrated optimization problem: given a prior probability distribution $q$, find the distribution $p$ minimizing the relative entropy with respect to $q$ such that $\textrm{mean}(p)$ is fixed and large. We show…