Search results for " Uncertainty"

Mögliche Aussagen bei Fragen der statistischen Ursachenforschung

1971

Distribucion final de referencia para el problema de Fieller-Creasy

1982

The problem of making inferences about the ratio of two normal populations is usually known as the Fieller-Creasy problem, and it gave rise to a controversy among fiducialists and confidence-intervalists. A Bayesian solution to such a problem when the two normal populations have the same unknown variance was presented by Bernardo (1977) using reference non-informative prior distributions. The solution to the case in which the variances are not assumed equal is obtained here. Some numerical results for artificial populations are given

Selecting the tuning parameter in penalized Gaussian graphical models

2019

Penalized inference of Gaussian graphical models is a way to assess the conditional independence structure in multivariate problems. In this setting, the conditional independence structure, corresponding to a graph, is related to the choice of the tuning parameter, which determines the model complexity or degrees of freedom. There has been little research on the degrees of freedom for penalized Gaussian graphical models. In this paper, we propose an estimator of the degrees of freedom in $$\ell _1$$ -penalized Gaussian graphical models. Specifically, we derive an estimator inspired by the generalized information criterion and propose to use this estimator as the bias term for two informatio…

Clusters of effects curves in quantile regression models

2018

In this paper, we propose a new method for finding similarity of effects based on quantile regression models. Clustering of effects curves (CEC) techniques are applied to quantile regression coefficients, which are one-to-one functions of the order of the quantile. We adopt the quantile regression coefficients modeling (QRCM) framework to describe the functional form of the coefficient functions by means of parametric models. The proposed method can be utilized to cluster the effect of covariates with a univariate response variable, or to cluster a multivariate outcome. We report simulation results, comparing our approach with the existing techniques. The idea of combining CEC with QRCM per…

Tests and estimates of shape based on spatial signs and ranks

2009

Nonparametric procedures for testing and estimation of the shape matrix in the case of multivariate elliptic distribution are considered. Testing for sphericity is an important special case. The tests and estimates are based on the spatial sign and rank covariance matrices. The estimates based on the spatial sign covariance matrix and symmetrized spatial sign covariance matrix are Tyler's [A distribution-free M-estimator of multivariate scatter, Ann. Statist. 15 (1987), pp. 234–251] shape matrix and and Dümbgen's [On Tyler's M-functional of scatter in high dimension, Ann. Inst. Statist. Math. 50 (1998), pp. 471–491] shape matrix, respectively. The test based on the spatial sign covariance m…

On the relationship between the reversed hazard rate and elasticity

2012

Despite hazard and reversed hazard rates sharing a number of similar aspects, reversed hazard functions are far less frequently used. Understanding their meaning is not a simple task. The aim of this paper is to expand the usefulness of the reversed hazard function by relating it to other well-known concepts broadly used in economics: (linear or cumulative) rates of increase and elasticity. This will make it possible (i) to improve our understanding of the consequences of using a particular distribution and, in certain cases, (ii) to introduce our hypotheses and knowledge about the random process in a more meaningful and intuitive way, thus providing a means to achieving distributions that …

Building up adjusted indicators of students' evaluation of university courses using generalized item response models

2012

This article advances a proposal for building up adjusted composite indicators of the quality of university courses from students’ assessments. The flexible framework of Generalized Item Response Models is adopted here for controlling the sources of heterogeneity in the data structure that make evaluations across courses not directly comparable. Specifically, it allows us to: jointly model students’ ratings to the set of items which define the quality of university courses; explicitly consider the dimensionality of the items composing the evaluation form; evaluate and remove the effect of potential confounding factors which may affect students’ evaluation; model the intra-cluster variabilit…

Quantitative ergodicity for some switched dynamical systems

2012

International audience; We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.

Gossip: The Architecture of SpreadPlots

2003

A spreadplot is a visualization that simultaneously shows several different views of a dataset or model. The individual views can be dynamic, can support high-interaction direct manipulation, and can be algebraically linked with each other, possibly via an underlying statistical model. Thus, when a data analyst changes the information shown in one view of a statistical model, the changes can be processed by the model and instantly represented in the other views. Spreadplots simplify the analyst's task when many different plots are relevant to the analysis at hand, as is the case in regression analysis, where there are many plots that can be used for model building and diagnosis. On the othe…

Bayesian Design of “Successful” Replications

2002

Replication of experiments is commonin applied research. However, systematic studies of the goals and motivations of a “replication” are rare. As a consequence, there does not seem to be a precise notion of what a “success” when replicating means. This article discusses some of the possible goals for replication; this leads to different (but precise) notions of “success” when replicating. Bayesian hierarchical models allow for a flexible and explicit incorporation of the assumed relationship among the experiments. Bayesian predictive distributions are a natural tool to compute the probability of the replication being successful, and hence to design the replication so that the probability of…