Related papers: Free stochastic measures via noncrossing partition…
Systems with many interacting stochastic constituents are fully characterized by their free energy. Computing this quantity is therefore the objective of various approaches, notably perturbative expansions, which are applied in problems…
In this paper we study splittings of a Poisson point process which are equivariant under a conservative transformation. We show that, if the Cartesian powers of this transformation are all ergodic, the only ergodic splitting is the obvious…
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…
Rationally independent free fermions are those where sums of single-particle energies multiplied by arbitrary rational coefficients vanish only if the coefficients are all zero. This property guaranties that they have no degeneracies in the…
We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower…
We introduce real second-order freeness in second-order noncommutative probability spaces. We demonstrate that under this definition, three real models of random matrices, namely real Ginibre matrices, Gaussian orthogonal matrices, and real…
The paper motivates high dimensional smoothing with penalized splines and its numerical calculation in an efficient way. If smoothing is carried out over three or more covariates the classical tensor product spline bases explode in their…
Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
This paper showed that Poisson brackets in quaternion variables can be obtained directly from canonical Poisson brackets on cotangent bundle of $SE(3)$ (or $SO(3)$) endowed by canonical symplectic geometry. Quaternion parameters in our case…
We study the structure of two cointeracting bialgebras on noncrossing partitions appearing in the theory of free probability. The first coproduct is given by separation of the blocks of the partitions into two parts, with respect to the…
Multidimensional record patterns are random sets of lattice points defined by means of a recursive stochastic construction. The patterns thus generated owe their richness to the fact that the construction is not based on a total order,…
We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology…
In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…
This work addresses the question of whether it is possible to define simple pair-wise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how…
The Fisher-Shannon statistical measure of complexity is analyzed for a continuous manifold of quantum observables. It is probed then than calculating it only in the configuration and momentum spaces will not give a complete description for…
Experimental mathematics is an experimental approach to mathematics in which programming and symbolic computation are used to investigate mathematical objects, identify properties and patterns, discover facts and formulas and even…
We consider the theoretical analysis of Multiscale Sampling Methods, which are a new class of gradient-free Markov chain Monte Carlo (MCMC) methods for high dimensional inverse differential equation problems. A detailed presentation of…
Given a multiarrangement of hyperplanes we define a series by sums of the Hilbert series of the derivation modules of the multiarrangement. This series turns out to be a polynomial. Using this polynomial we define the characteristic…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…