Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Bayesian hierarchical models in manufacturing bulk service queues
2006
In this paper, Queueing Theory and Bayesian statistical tools are used to analyze the congestion of various manufacturing bulk service queues with the same characteristics that are working independently of one another and in equilibrium. Hierarchical models are discussed in order to develop the whole inferential process for the parameters governing the system. Markov Chain Monte Carlo methods and numerical inversion of transforms are addressed to compute the posterior predictive distributions of the usual measures of performance in practice.
Bayesian design in queues: An application to aeronautic maintenance
2007
We exploit Bayesian criteria for designing M/M/c//r queueing systems with spares. For illustration of our approach we use a real problem from aeronautic maintenance, where the numbers of repair crews and spare planes must be sufficiently large to meet the necessary operational capacity. Bayesian guarantees for this to happen can be given using predictive or posterior distributions.
Modelling residuals dependence in dynamic life tables: A geostatistical approach
2008
The problem of modelling dynamic mortality tables is considered. In this context, the influence of age on data graduation needs to be properly assessed through a dynamic model, as mortality progresses over the years. After detrending the raw data, the residuals dependence structure is analysed, by considering them as a realisation of a homogeneous Gaussian random field defined on R × R. This setting allows for the implementation of geostatistical techniques for the estimation of the dependence and further interpolation in the domain of interest. In particular, a complex form of interaction between age and time is considered, by taking into account a zonally anisotropic component embedded in…
On an approximation problem for stochastic integrals where random time nets do not help
2006
Abstract Given a geometric Brownian motion S = ( S t ) t ∈ [ 0 , T ] and a Borel measurable function g : ( 0 , ∞ ) → R such that g ( S T ) ∈ L 2 , we approximate g ( S T ) - E g ( S T ) by ∑ i = 1 n v i - 1 ( S τ i - S τ i - 1 ) where 0 = τ 0 ⩽ ⋯ ⩽ τ n = T is an increasing sequence of stopping times and the v i - 1 are F τ i - 1 -measurable random variables such that E v i - 1 2 ( S τ i - S τ i - 1 ) 2 ∞ ( ( F t ) t ∈ [ 0 , T ] is the augmentation of the natural filtration of the underlying Brownian motion). In case that g is not almost surely linear, we show that one gets a lower bound for the L 2 -approximation rate of 1 / n if one optimizes over all nets consisting of n + 1 stopping time…
Hard-Core Thinnings of Germ‒Grain Models with Power-Law Grain Sizes
2013
Random sets with long-range dependence can be generated using a Boolean model with power-law grain sizes. We study thinnings of such Boolean models which have the hard-core property that no grains overlap in the resulting germ‒grain model. A fundamental question is whether long-range dependence is preserved under such thinnings. To answer this question, we study four natural thinnings of a Poisson germ‒grain model where the grains are spheres with a regularly varying size distribution. We show that a thinning which favors large grains preserves the slow correlation decay of the original model, whereas a thinning which favors small grains does not. Our most interesting finding concerns the c…
Multivariate statistical analysis for exploring road crash-related factors in the Franche-Comté region of France
2021
Understanding and modelling road crash data is crucial in fulfilling safety goals by helping national authorities to take necessary measures to reduce crash frequency and severity. This work aims at giving a multivariate statistical analysis of road crash data from the French region of Franche-Comte with special attention to road crash gravity. The first step for this multivariate analysis was to perform Multiple Correspondence Analysis in order to assess associations between the road crash injury and several important accident-related factors and circumstances. Log-linear models are used next in order to detect associations between road crash severity and related factors such as al-cohol/d…
An approximation to maximum likelihood estimates in reduced models
1990
SUMMARY An approximation to the maximum likelihood estimates of the parameters in a model can be obtained from the corresponding estimates and information matrices in an extended model, i.e. a model with additional parameters. The approximation is close provided that the data are consistent with the first model. Applications are described to log linear models for discrete data, to models for multivariate normal distributions with special covariance matrices and to mixed discrete-continuous models.
Rough nonlocal diffusions
2019
We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with "common" noise. To study the equation we build a self-contained framework of non-linear rough integration theory which we use to study McKean-Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the corresponding Fokker-Planck equation and prove well-posedness.
Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling
2016
ABSTRACTWe introduce a score-type statistic to test for a non-zero regression coefficient when the relevant term involves a nuisance parameter present only under the alternative. Despite the non-regularity and complexity of the problem and unlike the previous approaches, the proposed test statistic does not require the nuisance to be estimated. It is simple to implement by relying on the conventional distributions, such as Normal or t, and it justified in the setting of probabilistic coherence. We focus on testing for the existence of a breakpoint in segmented regression, and illustrate the methodology with an analysis on data of DNA copy number aberrations and gene expression profiles from…
The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing
2016
Abstract This paper refers to the problem stated by Balakrishnan et al. (2002). They proved that maximum likelihood estimator (MLE) of the exponential mean obtained from grouped samples is stochastically ordered provided that the sequence of the successive distances between inspection times is decreasing. In this paper we show that the assumption of monotonicity of the sequence of distances can be dropped.