47,315 research outputs found
Copula Theory and Regression Analysis
Researchers are often interested to study in the relationships between one variable and several other variables. Regression analysis is the statistical method for investigating such relationship and it is one of the most commonly used statistical Methods in many scientific fields such as financial data analysis, medicine, biology, agriculture, economics, engineering, sociology, geology, etc. But basic form of the regression analysis, ordinary least squares is not suitable for actuarial applications because the relationships are often nonlinear and the probability distribution of the response variable may be non-Gaussian distribution. One of the method that has been successful in overcoming these challenges is the generalized linear model (GLM), which requires that the response variable have a distribution from the exponential family. In this research work, we study copula regression as an alternative method to OLS and GLM. The major advantage of a copula regression is that there are no restrictions on the probability distributions that can be used. First part of this study, we will briefly discuss about copula regression by using several variety of marginal copula functions and copula regression is the most appropriate method in non Gaussian variable(violated normality assumption) regression model fitting. Also we validated our results by using real world example data and random generated (50000 observations) data. Second part of this study, we discussed about multiple regression model based on copula theory, and also we derived multiple regression line equation for Multivariate Non-Exchangeable Generalized Farlie-Gumbel-Morgenstern (FGM) copula function
A Laplace Transform Method for Molecular Mass Distribution Calculation from Rheometric Data
Polydisperse linear polymer melts can be microscopically described by the
tube model and fractal reptation dynamics, while on the macroscopic side the
generalized Maxwell model is capable of correctly displaying most of the
rheological behavior. In this paper, a Laplace transform method is derived and
different macroscopic starting points for molecular mass distribution
calculation are compared to a classical light scattering evaluation. The
underlying assumptions comprise the modern understanding on polymer dynamics in
entangled systems but can be stated in a mathematically generalized way. The
resulting method is very easy to use due to its mathematical structure and it
is capable of calculating multimodal molecular mass distributions of linear
polymer melts
Direct estimation of kinetic parametric images for dynamic PET.
Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed
Bayesian uncertainty quantification in linear models for diffusion MRI
Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue
microstructure. By fitting a model to the dMRI signal it is possible to derive
various quantitative features. Several of the most popular dMRI signal models
are expansions in an appropriately chosen basis, where the coefficients are
determined using some variation of least-squares. However, such approaches lack
any notion of uncertainty, which could be valuable in e.g. group analyses. In
this work, we use a probabilistic interpretation of linear least-squares
methods to recast popular dMRI models as Bayesian ones. This makes it possible
to quantify the uncertainty of any derived quantity. In particular, for
quantities that are affine functions of the coefficients, the posterior
distribution can be expressed in closed-form. We simulated measurements from
single- and double-tensor models where the correct values of several quantities
are known, to validate that the theoretically derived quantiles agree with
those observed empirically. We included results from residual bootstrap for
comparison and found good agreement. The validation employed several different
models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI)
and Constrained Spherical Deconvolution (CSD). We also used in vivo data to
visualize maps of quantitative features and corresponding uncertainties, and to
show how our approach can be used in a group analysis to downweight subjects
with high uncertainty. In summary, we convert successful linear models for dMRI
signal estimation to probabilistic models, capable of accurate uncertainty
quantification.Comment: Added results from a group analysis and a comparison with residual
bootstra
Fitting Linear Mixed-Effects Models using lme4
Maximum likelihood or restricted maximum likelihood (REML) estimates of the
parameters in linear mixed-effects models can be determined using the lmer
function in the lme4 package for R. As for most model-fitting functions in R,
the model is described in an lmer call by a formula, in this case including
both fixed- and random-effects terms. The formula and data together determine a
numerical representation of the model from which the profiled deviance or the
profiled REML criterion can be evaluated as a function of some of the model
parameters. The appropriate criterion is optimized, using one of the
constrained optimization functions in R, to provide the parameter estimates. We
describe the structure of the model, the steps in evaluating the profiled
deviance or REML criterion, and the structure of classes or types that
represents such a model. Sufficient detail is included to allow specialization
of these structures by users who wish to write functions to fit specialized
linear mixed models, such as models incorporating pedigrees or smoothing
splines, that are not easily expressible in the formula language used by lmer.Comment: 51 pages, including R code, and an appendi
Efficient computation of capillary-gravity generalized solitary waves
This paper is devoted to the computation of capillary-gravity solitary waves
of the irrotational incompressible Euler equations with free surface. The
numerical study is a continuation of a previous work in several points: an
alternative formulation of the Babenko-type equation for the wave profiles, a
detailed description of both the numerical resolution and the analysis of the
internal flow structure under a solitary wave. The numerical code used in this
study is provided in open source for those interested readers.Comment: 26 pages, 21 figures, 2 tables, 43 references. Other author's papers
can be downloaded at http://www.denys-dutykh.com/. arXiv admin note:
substantial text overlap with arXiv:1411.551
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