Related papers: Generalized Beta Divergence
Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…
The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
We define an integral, the distributional integral of functions of one real variable, that is more general than the Lebesgue and the Denjoy-Perron-Henstock-Kurzweil integrals, and which allows the integration of functions with…
We construct and propose the "Bayesian Validation Metric" (BVM) as a general model validation and testing tool. We find the BVM to be capable of representing all of the standard validation metrics (square error, reliability, probability of…
Generalized integral formulas involving the generalized modified k-Bessel function $J_{k,\nu }^{c,\gamma ,\lambda }\left( z\right) $ of first kind are expressed in terms generalized $k-$Wright functions. Some interesting special cases of…
The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function phi(x). It is…
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…
We generalize the { ${\rm M}$-estimator} put forward by Catoni in his seminal paper [C12] to the case in which samples can have finite $\alpha$-th moment with $\alpha \in (1,2)$ rather than finite variance, our approach is by slightly…
The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a…
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…
We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…
We study how generalized Jones $\beta$-numbers relate to harmonic measure. Firstly, we generalize a result of Garnett, Mourgoglou and Tolsa by showing that domains in $\mathbb{R}^{d+1}$ whose boundaries are lower $d$-content regular admit…
We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…
We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…
In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional…
In this paper, we introduce and investigate a new extension of the beta function by means of an integral operator involving a product of Bessel-Struve kernel functions. We also define a new extension of the well-known beta distribution, the…
Information measures can be constructed from R\'enyi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson $\alpha$-mutual information and has received renewed attention…
We give necessary and sufficient conditions for the existence of a generalization of R\'enyi divergence, which is defined in terms of a deformed exponential function. If the underlying measure $\mu$ is non-atomic, we found that not all…