Search results for "Conditional"
showing 10 items of 294 documents
Estimating the decomposition of predictive information in multivariate systems
2015
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of co…
Extending graphical models for applications: on covariates, missingness and normality
2021
The authors of the paper “Bayesian Graphical Models for Modern Biological Applications” have put forward an important framework for making graphical models more useful in applied settings. In this discussion paper, we give a number of suggestions for making this framework even more suitable for practical scenarios. Firstly, we show that an alternative and simplified definition of covariate might make the framework more manageable in high-dimensional settings. Secondly, we point out that the inclusion of missing variables is important for practical data analysis. Finally, we comment on the effect that the Gaussianity assumption has in identifying the underlying conditional independence graph…
A Distribution-Free Two-Sample Equivalence Test Allowing for Tied Observations
1999
A new testing procedure is derived which enables to assess the equivalence of two arbitrary noncontinuous distribution functions from which unrelated samples are taken as the data to be analyzed. The equivalence region is defined to consist of all pairs (F, G) of distribution functions such that for independent X ∼F, Y ∼G the conditional probability of {X > Y} given {X ¬= Y} lies in some short interval around 1/2. The test rejects the null hypothesis of nonequivalence if and only if the standardized distance between the U-statistics estimator of P|X > Y | X ¬= Y] and the center of the equivalence interval (1/2 - e 1 , 1/2 + e 2 ) does not exceed a critical upper bound which has to be comput…
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.
Spatio-temporal modelling of COVID-19 incident cases using Richards’ curve: An application to the Italian regions
2021
Abstract We introduce an extended generalised logistic growth model for discrete outcomes, in which spatial and temporal dependence are dealt with the specification of a network structure within an Auto-Regressive approach. A major challenge concerns the specification of the network structure, crucial to consistently estimate the canonical parameters of the generalised logistic curve, e.g. peak time and height. We compared a network based on geographic proximity and one built on historical data of transport exchanges between regions. Parameters are estimated under the Bayesian framework, using Stan probabilistic programming language. The proposed approach is motivated by the analysis of bot…
The conditional censored graphical lasso estimator
2020
© 2020, Springer Science+Business Media, LLC, part of Springer Nature. In many applied fields, such as genomics, different types of data are collected on the same system, and it is not uncommon that some of these datasets are subject to censoring as a result of the measurement technologies used, such as data generated by polymerase chain reactions and flow cytometer. When the overall objective is that of network inference, at possibly different levels of a system, information coming from different sources and/or different steps of the analysis can be integrated into one model with the use of conditional graphical models. In this paper, we develop a doubly penalized inferential procedure for…
Reassessing Accuracy Rates of Median Decisions
2007
We show how Bruno de Finetti''s fundamental theorem of prevision has computable applications in statistical problems that involve only partial information. Specifically, we assess accuracy rates for median decision procedures used in the radiological diagnosis of asbestosis. Conditional exchangeability of individual radiologists'' diagnoses is recognized as more appropriate than independence which is commonly presumed. The FTP yields coherent bounds on probabilities of interest when available information is insufficient to determine a complete distribution. Further assertions that are natural to the problem motivate a partial ordering of conditional probabilities, extending the computation …
Explicit, identical maximum likelihood estimates for some cyclic Gaussian and cyclic Ising models
2017
Cyclic models are a subclass of graphical Markov models with simple, undirected probability graphs that are chordless cycles. In general, all currently known distributions require iterative procedures to obtain maximum likelihood estimates in such cyclic models. For exponential families, the relevant conditional independence constraint for a variable pair is given all remaining variables, and it is captured by vanishing canonical parameters involving this pair. For Gaussian models, the canonical parameter is a concentration, that is, an off-diagonal element in the inverse covariance matrix, while for Ising models, it is a conditional log-linear, two-factor interaction. We give conditions un…
Recursive estimation of the conditional geometric median in Hilbert spaces
2012
International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirm…
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…