Search results for "Probability Distribution"
showing 10 items of 263 documents
Pairwise Markov properties for regression graphs
2016
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of conditional distributions, named regressions in joint responses. The involved random variables may be discrete, continuous or of both types. Such a generating process specifies for each response a conditioning set that contains just its regressor variables, and it leads to at least one valid ordering of all nodes in the corresponding regression graph that has three types of edge: one for undirected dependences among context variables, another for undirect…
MCMC methods to approximate conditional predictive distributions
2006
Sampling from conditional distributions is a problem often encountered in statistics when inferences are based on conditional distributions which are not of closed-form. Several Markov chain Monte Carlo (MCMC) algorithms to simulate from them are proposed. Potential problems are pointed out and some suitable modifications are suggested. Approximations based on conditioning sets are also explored. The issues are illustrated within a specific statistical tool for Bayesian model checking, and compared in an example. An example in frequentist conditional testing is also given.
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…
Analysis of resources distribution in economics based on entropy
2002
We propose a new approach to the problem of e0cient resources distribution in di1erent types of economic systems. We also propose to use entropy as an indicator of the e0ciency of resources distribution. Our approach is based on methods of statistical physics in which the states of economic systems are described in terms of the density functions � (g; � ) of the variable — — — — � �
Objective Priors for Discrete Parameter Spaces
2012
This article considers the development of objective prior distributions for discrete parameter spaces. Formal approaches to such development—such as the reference prior approach—often result in a constant prior for a discrete parameter, which is questionable for problems that exhibit certain types of structure. To take advantage of structure, this article proposes embedding the original problem in a continuous problem that preserves the structure, and then using standard reference prior theory to determine the appropriate objective prior. Four different possibilities for this embedding are explored, and applied to a population-size model, the hypergeometric distribution, the multivariate hy…
Deriving Reference Decisions
1998
To solve a statistical decision problem from a Bayesian viewpoint, the decision maker must specify a probability distribution on the parameter space, his prior distribution. In order to analyze the influence of this prior distribution on the solution of the problem, Bernardo (1981) proposed to compare the results with those that one would obtain by using that prior distribution which maximizes the useful experimental information, thus introducing the concept of reference decision. This definition is too involved for most of the problems usually found in practice. Here we analyze situations in which it is possible to simplify the definition of the reference decision, and we provide condition…
Estimating completeness in cancer registries--comparing capture-recapture methods in a simulation study.
2008
Completeness of registration is one of the quality indicators usually reported by cancer registries. This allows researchers to assess how useful and representative the data is. Several methods have been suggested to estimate completeness. In this paper a multi-state model for the process of cancer diagnosis and treatment is presented. In principle, every contact with a doctor during diagnosis, treatment, and aftercare can give rise to a cancer registry notification with a certain probability. Therefore the states included in the model are "incident tumour" and "death" but also contacts with doctors such as consultation of a general practitioner or specialised doctor, diagnostic procedures,…
On easily interpretable multivariate reference regions of rectangular shape
2011
Till now, multivariate reference regions have played only a marginal role in the practice of clinical chemistry and laboratory medicine. The major reason for this fact is that such regions are traditionally determined by means of concentration ellipsoids of multidimensional Gaussian distributions yielding reference limits which do not allow statements about possible outlyingness of measurements taken in specific diagnostic tests from a given patient or subject. As a promising way around this difficulty we propose to construct multivariate reference regions as p-dimensional rectangles or (in the one-sided case) rectangular half-spaces whose edges determine univariate percentile ranges of the…
Hitting Time Distributions in Financial Markets
2006
We analyze the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is composed by daily price of 1071 stocks trade for the 12-year period 1987-1998, the second one is composed by high frequency data for 100 stocks for the 4-year period 1995-1998. We compare the probability distribution obtained by our empirical analysis with those obtained from different models for stock market evolution. Specifically by focusing on the statistical properties of the hitting times to reach a barrier or a given threshold, we compare the prob…
The distribution of velocities in an ensemble of accelerated particles on a surface
2016
An ensemble of particles diffusing with acceleration on a surface is considered as a 2D billiard system. The process of the finite-time diffusion of particles is studied using the balance equation. The probability distribution functions of the velocity and lifetime of particles are obtained analytically and by means of numerical simulations. A thermodynamic interpretation of the process is discussed. The effective temperature and entropy obey the relationship for an ideal gas.