Related papers: Finite Sample Smeariness on Spheres
We present a unified view of finite-size scaling (FSS) in dimension d above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of…
Random column sampling is not guaranteed to yield data sketches that preserve the underlying structures of the data and may not sample sufficiently from less-populated data clusters. Also, adaptive sampling can often provide accurate low…
A finite size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E {\bf 92}, 062126 (2015)], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities…
A uniform shrinkage prior (USP) distribution on the unknown variance component of a random-effects model is known to produce good frequency properties. The USP has a parameter that determines the shape of its density function, but it has…
The Mat{\'e}rn family of isotropic covariance functions has been central to the theoretical development and application of statistical models for geospatial data. For global data defined over the whole sphere representing planet Earth, the…
This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic…
Sampling from probability distributions is an important problem in statistics and machine learning, specially in Bayesian inference when integration with respect to posterior distribution is intractable and sampling from the posterior is…
The recently developed concept of spreadability, $\mathcal{S}(t)$, provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales. We explicitly compute $\mathcal{S}(t)$ for…
We study a generalization of the Fr\'echet mean on metric spaces, which we call $\phi$-means. Our generalization is indexed by a convex function $\phi$. We find necessary and sufficient conditions for $\phi$-means to be finite and provide a…
We propose new small-sphere distributional families for modeling multivariate directional data on $(\mathbb{S}^{p-1})^K$ for $p \ge 3$ and $K \ge 1$. In a special case of univariate directions in $\Re^3$, the new densities model random…
We introduce and analyse a new nonparametric estimator of a multi-dimensional density. Our smooth projection estimator (SPE) is defined by a least squares projection of the sample onto an infinite dimensional mixture class via an…
The von Mises-Fisher (vMF) distribution has long been a mainstay for inference with data on the unit hypersphere in directional statistics. The performance of statistical inference based on the vMF distribution, however, may suffer when…
Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Lo\`{e}ve expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of…
An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field…
Randomization tests deliver exact finite-sample Type 1 error control when the null satisfies the randomization hypothesis. In practice, achieving these guarantees often requires stronger conditions than the null hypothesis of primary…
A different general philosophy, to be called Full Randomness (FR), for the analysis of random effects models is presented, involving a notion of reducing or preferably eliminating fixed effects, at least formally. For example, under FR…
Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D topological system can transform under symmetry in a fractional way. For example in fractional quantum Hall systems, excitations can carry fractional…
We establish finite sample certificates on the quality of solutions produced by data-based forward-backward (FB) operator splitting schemes. As frequently happens in stochastic regimes, we consider the problem of finding a zero of the sum…
The mean of an unknown variance-$\sigma^2$ distribution $f$ can be estimated from $n$ samples with variance $\frac{\sigma^2}{n}$ and nearly corresponding subgaussian rate. When $f$ is known up to translation, this can be improved…
The consistency of Fr\'echet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies…