Search results for "probability"
showing 10 items of 3417 documents
Fractional calculus approach to the statistical characterization of random variables and vectors
2009
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. A…
Hydrokinetic simulations of nanoscopic precursor films in rough channels
2009
We report on simulations of capillary filling of high-wetting fluids in nano-channels with and without obstacles. We use atomistic (molecular dynamics) and hydrokinetic (lattice-Boltzmann) approaches which point out clear evidence of the formation of thin precursor films, moving ahead of the main capillary front. The dynamics of the precursor films is found to obey a square-root law as the main capillary front, z^2(t) ~ t, although with a larger prefactor, which we find to take the same value for the different geometries (2D-3D) under inspection. The two methods show a quantitative agreement which indicates that the formation and propagation of thin precursors can be handled at a mesoscopic…
Discussion of "Objective Priors: An Introduction for Frequentists" by M. Ghosh
2011
Discussion of "Objective Priors: An Introduction for Frequentists" by M. Ghosh [arXiv:1108.2120]
DRHotNet: An R package for detecting differential risk hotspots on a linear network
2019
One of the most common applications of spatial data analysis is detecting zones, at a certain investigation level, where a point-referenced event under study is especially concentrated. The detection of this kind of zones, which are usually referred to as hotspots, is essential in certain fields such as criminology, epidemiology or traffic safety. Traditionally, hotspot detection procedures have been developed over areal units of analysis. Although working at this spatial scale can be suitable enough for many research or practical purposes, detecting hotspots at a more accurate level (for instance, at the road segment level) may be more convenient sometimes. Furthermore, it is typical that …
Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers
2018
We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential boundedness of potential functions associated with the i-cSMC algorithm provide necessary and sufficient conditions for the uniform ergodicity of the i-cSMC Markov chain, as well as quantitative bounds on its (uniformly geometric) rate of convergence. Furthermore, we show that the i-cSMC Markov chain cannot even be geometrically ergodic if this essential boundedness does not hold in many applications of interest. Our sufficiency and quantitative bounds rely on…
Continuum reconstruction of the pore scale microstructure for Fontainebleau sandstone
2010
Abstract A stochastic geometrical modeling technique is used to reconstruct a laboratory scale Fontainebleau sandstone with a sidelength of 1.5 cm. The model reconstruction is based on crystallite properties and diagenetic parameters determined from two-dimensional images. The three-dimensional pore scale microstructure of the sandstone is represented by a list of quartz crystallites defined geometrically and placed in the continuum. This allows generation of synthetic μ -CT images of the rock model at arbitrary resolutions. Quantitative microstructure comparison based on Minkowski functionals, two-point correlation function and local porosity theory indicates that this modeling technique c…
Model selection in linear mixed-effect models
2019
Linear mixed-effects models are a class of models widely used for analyzing different types of data: longitudinal, clustered and panel data. Many fields, in which a statistical methodology is required, involve the employment of linear mixed models, such as biology, chemistry, medicine, finance and so forth. One of the most important processes, in a statistical analysis, is given by model selection. Hence, since there are a large number of linear mixed model selection procedures available in the literature, a pressing issue is how to identify the best approach to adopt in a specific case. We outline mainly all approaches focusing on the part of the model subject to selection (fixed and/or ra…
Segmented mixed models with random changepoints: a maximum likelihood approach with application to treatment for depression study
2014
We present a simple and effective iterative procedure to estimate segmented mixed models in a likelihood based framework. Random effects and covariates are allowed for each model parameter, including the changepoint. The method is practical and avoids the computational burdens related to estimation of nonlinear mixed effects models. A conventional linear mixed model with proper covariates that account for the changepoints is the key to our estimating algorithm. We illustrate the method via simulations and using data from a randomized clinical trial focused on change in depressive symptoms over time which characteristically show two separate phases of change.
Degree course change and student performance: a mixed-effect approach
2015
This paper focuses on students credits earning speed over time and its determinants, dealing with the huge percentage of students who do not take the degree within the legal duration in the Italian University System. A new indicator for the performance of the student career is proposed on real data, concerning the cohort of students enrolled at a Faculty of the University of Palermo (followed for 7 years). The new indicator highlights a typical zero-inflated distribution and suggests to investigate the effect of the degree course (DC) change on the student career. A mixed-effect model for overdispersed data is considered, with the aim of taking into account the individual variability as wel…
A new measure for the attitude to mobility of Italian students and graduates: a topological data analysis approach
2022
AbstractStudents’ and graduates’ mobility is an interesting topic of discussion especially for the Italian education system and universities. The main reasons for migration and for the so called brain drain, can be found in the socio-economic context and in the famous North–South divide. Measuring mobility and understanding its dynamic over time and space are not trivial tasks. Most of the studies in the related literature focus on the determinants of such phenomenon, in this paper, instead, combining tools coming from graph theory and Topological Data Analysis we propose a new measure for the attitude to mobility. Each mobility trajectory is represented by a graph and the importance of the…