Search results for "statistical [methods]"

L\'{e}vy flights in inhomogeneous environments

2009

We study the long time asymptotics of probability density functions (pdfs) of L\'{e}vy flights in different confining potentials. For that we use two models: Langevin - driven and (L\'{e}vy - Schr\"odinger) semigroup - driven dynamics. It turns out that the semigroup modeling provides much stronger confining properties than the standard Langevin one. Since contractive semigroups set a link between L\'{e}vy flights and fractional (pseudo-differential) Hamiltonian systems, we can use the latter to control the long - time asymptotics of the pertinent pdfs. To do so, we need to impose suitable restrictions upon the Hamiltonian and its potential. That provides verifiable criteria for an invarian…

Statistical inference as a decision problem: the choice of sample size

1997

Discord of response

2014

The presence of quantum correlations in a quantum state is related to the state response to local unitary perturbations. Such response is quantified by the distance between the unperturbed and perturbed states, minimized with respect to suitably identified sets of local unitary operations. In order to be a bona fide measure of quantum correlations, the distance function must be chosen among those that are contractive under completely positive and trace preserving maps. The most relevant instances of such physically well behaved metrics include the trace, the Bures, and the Hellinger distance. To each of these metrics one can associate the corresponding discord of response, namely the trace,…

On critical properties of the Berry curvature in the Kitaev honeycomb model

2019

We analyse the Kitaev honeycomb model, by means of the Berry curvature with respect to Hamiltonian parameters. We concentrate on the ground-state vortex-free sector, which allows us to exploit an appropriate Fermionisation technique. The parameter space includes a time-reversal breaking term which provides an analytical headway to study the curvature in phases in which it would otherwise vanish. The curvature is then analysed in the limit in which the time-reversal-symmetry-breaking perturbation vanishes. This provides remarkable information about the topological phase transitions of the model. The Berry curvature in itself exhibits no singularities at criticality, nevertheless it distingui…

n-cluster models in a transverse magnetic field

2017

In this paper we analize a family of one dimensional fully analytically solvable models, named the n-cluster models in a transverse magnetic field, in which a many-body cluster interaction competes with a uniform transverse magnetic field. These models, independently by the cluster size n + 2, exibit a quantum phase transition, that separates a paramagnetic phase from a cluster one, that corresponds to a nematic ordered phase or a symmetry-protected topological ordered phase for even or odd n respectively. Due to the symmetries of the spin correlation functions, we prove that these models have no genuine n+2-partite entanglement. On the contrary, a non vanishing concurrence arises between s…

Value-at-Risk and Tsallis statistics: risk analysis of the aerospace sector

2004

In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is well described by Tsallis distribution. We explore this result and modify the standard Value-at-Risk (VaR), financial risk assessment methodology in order to reflect an asset which obeys Tsallis non-extensive statistics.

Probabilistic small area risk assessment using GIS-based data: a case study on Finnish childhood diabetes

2000

A Bayesian hierarchical spatial model is constructed to describe the regional incidence of insulin dependent diabetes mellitus (IDDM) among the under 15-year-olds in Finland. The model exploits aggregated pixel-wise locations for both the cases and the population at risk. Typically such data arise from combining geographic information systems (GIS) with large databases. The dates of diagnosis and locations of the cases are observed from 1987 to 1996. The population at risk counts are available for every second year during the same period. A hierarchical model is suggested for the pixel wise case counts, including a population model to account for the uncertainty of the population at risk ov…

Using R via PHP for Teaching Purposes: R-php

2006

This paper deals with the R-php statistical software, that is an environment for statistical analysis, freely accessible and attainable through the World Wide Web, based on R. Indeed, this software uses, as "engine" for statistical analyses, R via PHP and its design has been inspired by a paper of de Leeuw (1997). R-php is based on two modules: a base module and a point-and-click module. R-php base allows the simple editing of R code in a form. R-php point-and-click allows some statistical analyses by means of a graphical user interface (GUI): then, to use this module it is not necessary for the user to know the R environment, but all the allowed analyses can be performed by using the compu…

The “ThreePlusOne” Likelihood-Based Test Statistics: Unified Geometrical and Graphical Interpretations

2014

The presentation of the well known Likelihood Ratio, Wald and Score test statistics in textbooks appears to lack a unified graphical and geometrical interpretation. We present two simple graphical representations on a common scale for these three test statistics, and also the recently proposed Gradient test statistic. These unified graphical displays may favour better understanding of the geometrical meaning of the likelihood based statistics and provide useful insights into their connections.

On quantumness in multi-parameter quantum estimation

2019

In this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann Curvature and the Fisher Information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cram\'er-Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium, and explore the quantum compatibility of the model across its phase diagram.