Search results for "Joint probability distribution"
showing 10 items of 52 documents
On Association Models Defined over Independence Graphs
1998
Conditions on joint distributions are given under which two variables will be conditionally associated whenever an independence graph does not imply a corresponding conditional independence statement. To this end the notions of parametric cancellation, of stable paths and of quasi-linear models are discussed in some detail.
Binary distributions of concentric rings
2014
We introduce families of jointly symmetric, binary distributions that are generated over directed star graphs whose nodes represent variables and whose edges indicate positive dependences. The families are parametrized in terms of a single parameter. It is an outstanding feature of these distributions that joint probabilities relate to evenly spaced concentric rings. Kronecker product characterizations make them computationally attractive for a large number of variables. We study the behavior of different measures of dependence and derive maximum likelihood estimates when all nodes are observed and when the inner node is hidden.
Holt–Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data
2007
Abstract This paper provides a formulation for the additive Holt–Winters forecasting procedure that simplifies both obtaining maximum likelihood estimates of all unknowns, smoothing parameters and initial conditions, and the computation of point forecasts and reliable predictive intervals. The stochastic component of the model is introduced by means of additive, uncorrelated, homoscedastic and Normal errors, and then the joint distribution of the data vector, a multivariate Normal distribution, is obtained. In the case where a data transformation was used to improve the fit of the model, cumulative forecasts are obtained here using a Monte-Carlo approximation. This paper describes the metho…
Identifying Causal Effects with the R Package causaleffect
2017
Do-calculus is concerned with estimating the interventional distribution of an action from the observed joint probability distribution of the variables in a given causal structure. All identifiable causal effects can be derived using the rules of do-calculus, but the rules themselves do not give any direct indication whether the effect in question is identifiable or not. Shpitser and Pearl constructed an algorithm for identifying joint interventional distributions in causal models, which contain unobserved variables and induce directed acyclic graphs. This algorithm can be seen as a repeated application of the rules of do-calculus and known properties of probabilities, and it ultimately eit…
Global and multiple test procedures using ordered p-values—a review
2004
This paper reviews global and multiple tests for the combination ofn hypotheses using the orderedp-values of then individual tests. In 1987, Rohmel and Streitberg presented a general method to construct global level α tests based on orderedp-values when there exists no prior knowledge regarding the joint distribution of the corresponding test statistics. In the case of independent test statistics, construction of global tests is available by means of recursive formulae presented by Bicher (1989), Kornatz (1994) and Finner and Roters (1994). Multiple test procedures can be developed by applying the closed test principle using these global tests as building blocks. Liu (1996) proposed represe…
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…
Time Trends in the Joint Distributions of Income and Age
2001
We propose a method of analyzing time changes of joint income-age densities. Change is decomposed into time invariant components which act on the densities as deformations with time varying strength. The functional form of these components is estimated non parametrically from cross sectional data. The method is applied to analyze British household data on income and age for the years 1968–95. It is learned that for the young and middle aged there is a trend towards increasing inequality, while during the early eighties there seems to occur a reversal in the evolution of the income distribution for the old.
Two ways to handle dependent uncertainties in multi-criteria decision problems☆
2009
Abstract We consider multi-criteria group decision-making problems, where the decision makers (DMs) want to identify their most preferred alternative(s) based on uncertain or inaccurate criteria measurements. In many real-life problems the uncertainties may be dependent. In this paper, we focus on multicriteria decision-making (MCDM) problems where the criteria and their uncertainties are computed using a stochastic simulation model. The model is based on decision variables and stochastic parameters with given distributions. The simulation model determines for the criteria a joint probability distribution, which quantifies the uncertainties and their dependencies. We present and compare two…
Joint probability distributions for wind speed and direction. A case study in Sicily
2015
In this study we analyze data of hourly average wind speed and direction measured at three different sampling stations located in Sicily (Italy) and provide a statistical model for their joint probability density function. Singly truncated from below Normal Weibull mixture distribution and a linear combination of von Mises distributions are used to model wind speed and direction. Sites with heterogeneous local conditions (prevailing wind direction and/or elevation) have been considered in order to investigate the reliability of the model here taken into consideration.
All-Possible-Couplings Approach to Measuring Probabilistic Context.
2013
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly" influence them, but (iii) other inputs provide a "context" for this response by influencing its probabilistic relations to other responses. These contextual influences are very different, say, in classical kinetic theory and in the entanglement paradigm of quantum mechanics, which are traditionally interpreted as representing different forms of physical determinism. One can mathematically construct systems with other types of contextuality, whether or not …