Search results for " Statistics"
showing 10 items of 1891 documents
Stochastic model for the epitaxial growth of two-dimensional islands in the submonolayer regime
2016
The diffusion-based growth of islands composed of clusters of metal atoms on a substrate is considered in the aggregation regime. A stochastic approach is proposed to describe the dynamics of island growth based on a Langevin equation with multiplicative noise. The distribution of island sizes, obtained as a solution of the corresponding Fokker-Planck equation, is derived. The time-dependence of island growth on its fractal dimension is analysed. The effect of mobility of the small islands on the growth of large islands is considered. Numerical simulations are in a good agreement with theoretical results.
Componentwise adaptation for high dimensional MCMC
2005
We introduce a new adaptive MCMC algorithm, based on the traditional single component Metropolis-Hastings algorithm and on our earlier adaptive Metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.
Including covariates in a space-time point process with application to seismicity
2020
AbstractThe paper proposes a spatio-temporal process that improves the assessment of events in space and time, considering a contagion model (branching process) within a regression-like framework to take covariates into account. The proposed approach develops the forward likelihood for prediction method for estimating the ETAS model, including covariates in the model specification of the epidemic component. A simulation study is carried out for analysing the misspecification model effect under several scenarios. Also an application to the Italian seismic catalogue is reported, together with the reference to the developed R package.
Elasticity function of a discrete random variable and its properties
2017
ABSTRACTElasticity (or elasticity function) is a new concept that allows us to characterize the probability distribution of any random variable in the same way as characteristic functions and hazard and reverse hazard functions do. Initially defined for continuous variables, it was necessary to extend the definition of elasticity and study its properties in the case of discrete variables. A first attempt to define discrete elasticity is seen in Veres-Ferrer and Pavia (2014a). This paper develops this definition and makes a comparative study of its properties, relating them to the properties shown by discrete hazard and reverse hazard, as both defined in Chechile (2011). Similar to continuou…
Criteria for Bayesian model choice with application to variable selection
2012
In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the problem of variable selection in normal linear models. This results in a new model selection objective prior with a number of compelling properties.
A gradient-based deletion diagnostic measure for generalized linear mixed models
2016
ABSTRACTA gradient-statistic-based diagnostic measure is developed in the context of the generalized linear mixed models. Its performance is assessed by some real examples and simulation studies, in terms of ability in detecting influential data structures and of concordance with the most used influence measures.
Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter
2013
Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally difficult to find. One way to solve this problem is to use adaptive MCMC algorithms which automatically tune the statistics of a proposal distribution during the MCMC run. A new adaptive MCMC algorithm, called the variational Bayesian adaptive Metropolis (VBAM) algorithm, is developed. The VBAM algorithm updates the proposal covariance matrix using the variational Bayesian adaptive Kalman filter (VB-AKF). A strong law of large numbers for the VBAM algorithm is…
Quantile regression via iterative least squares computations
2012
We present an estimating framework for quantile regression where the usual L 1-norm objective function is replaced by its smooth parametric approximation. An exact path-following algorithm is derived, leading to the well-known ‘basic’ solutions interpolating exactly a number of observations equal to the number of parameters being estimated. We discuss briefly possible practical implications of the proposed approach, such as early stopping for large data sets, confidence intervals, and additional topics for future research.
Forward likelihood-based predictive approach for space-time point processes
2011
Dealing with data from a space–time point process, the estimation of the conditional intensity function is a crucial issue even if a complete definition of a parametric model is not available. In particular, in case of exploratory contexts or if we want to assess the adequacy of a specific parametric model, some kind of nonparametric estimation procedure could be useful. Often, for these purposes kernel estimators are used and the estimation of the intensity function depends on the estimation of bandwidth parameters. In some fields, like for instance the seismological one, predictive properties of the estimated intensity function are pursued. Since a direct ML approach cannot be used, we pr…
Equivalence Testing With Particle Size Distribution Data: Methods and Applications in the Development of Inhalative Drugs
2017
ABSTRACTKey criteria of the quality of inhalative drugs are assessed in experiments generating so-called particle size distributions as data. Many experiments of that kind are carried out to demonstrate that necessary modifications to whatever part of the manufacturing process do not substantially change basic characteristics of an inhalable drug product. The equivalence testing procedures we derive for that purpose rely on different models accommodating the specific structure of such data and on different ways of specifying the region of nonrelevant differences. For each hypotheses formulation, three different tests are derived (two parametric and one asymptotically distribution-free proce…