Related papers: On Gibbsianness of Random Fields
We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a dynamical notion of randomness: typicality. Roughly, a point is typical for some dynamic, if it follows the…
Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate) tests of hypotheses on an unknown value of the parameter…
This paper proposes a morpho-statistical characterisation of the galaxy distribution through spatial statistical modelling based on inhomogeneous Gibbs point processes. The galaxy distribution is supposed to exhibit two components. The…
In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The…
If the gradient of a probability distribution on a landscape of vacua aligns with the variation of some fundamental parameter, the parameter may be likely to take some non-generic value. Such non-generic values can be associated to critical…
We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…
Critical points mark locations in the domain where the level-set topology of a scalar function undergoes fundamental changes and thus indicate potentially interesting features in the data. Established methods exist to locate and relate such…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
An explicit optimal linear spatial predictor is derived. The spatial correlations are imposed by means of Gibbs energy functionals with explicit coupling coefficients instead of covariance matrices. The model inference process is based on…
We study the typical profiles of a one dimensional random field Kac model, for values of the temperature and magnitude of the field in the region of the two absolute minima for the free energy of the corresponding random field Curie Weiss…
It is often of interest to condition on a singular event given by a random variable, e.g. $\{Y=y\}$ for a continuous random variable $Y$. Conditional measures with respect to this event are usually derived as a special case of the…
Higgs fields on gauge-natural prolongations of principal bundles are defined by invariant variational problems and related canonical conservation laws along the kernel of a gauge-natural Jacobi morphism.
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…
In recent years, there has been a growing interest in statistical methods that exhibit robust performance under distribution changes between training and test data. While most of the related research focuses on point predictions with the…
Gaussian conditional random fields (GCRF) are a well-known used structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which…
In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures. This role has two main aspects, the distinction between which has not always been fully clear: 1) {\em From}…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
In this paper we present a conditional principle of Gibbs type for independent nonidentically distributed random vectors. We obtain this result by performing Edgeworth expansions for densities of sums of independent random vectors.
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…