A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices

Córdoba, Irene; Varando, Gherardo; Bielza, Concha; Larrañaga, Pedro

doi:10.1007/978-3-030-03493-1_13

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…The repetition number was 1,000. gmat v. 0.2.2 and cocor v. 1.1-3 R packages were used in the processes of data generating and implementing the statistical tests. 22,23 In real data example normality of the data was tested with the Shapiro-Wilk test. Relationships between the variables were evaluated with the Pearson correlation coefficient.…”

Section: Simulation Scenariosmentioning

confidence: 99%

A Simulation Study for the Performances of Two Dependent Correlation Coefficients Comparison Tests with a Real Data Application on Acute Appendicitis

Sığırlı¹,

Tasar²

2023

Turkiye Klinikleri J Biostat

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Objective: Although it is frequently encountered in many studies to examine the relationships between different features of the individuals by using correlation coefficient, it is a situation that can be ignored to statistically test whether there is a difference between the correlation coefficients obtained. In this study, it is aimed to compare the performances of statistical tests proposed for the comparison of dependent overlapping correlation coefficients, in terms of their Type I error rates, within the framework of a wide simulation scenario. Material and Methods: The 6 test procedures were compared with a simulation study, conducted at 5 different intercorrelation magnitudes, with 5 different null correlation coefficient magnitudes, at 6 different sample sizes. Results: Pearson and Filon's z (PF) test performed poorly compared to other 5 procedures in most cases. For small intercorrelation magnitudes Steiger's modification of Dunn and Clark's z (SM) test, Meng, Rosenthal, and Rubin's z (MRR) test, Rosenthal, and Rubin's z test, Hittner, May, and Silver's modification of Dunn and Clark's z (HMS) test and ZOU's approach for overlapping correlations (ZA) procedures outperformed PF test and Hendrickson, Stanley, and Hills' modification of Williams' t test (HSHM) especially in small to moderate sample sizes. For larger intercorrelation coefficients, HSHM test gave better results in small to moderate sample sizes and ZA procedure maintained its superiority at the 0.7 intercorrelation level. Conclusion: Tests' performances in terms of Type I error are affected from the magnitude of null correlation, magnitude of intercorrelation and sample size, in different ways. It will be helpful to consider these issues when selecting the appropriate statistical test.

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Section: Simulation Scenariosmentioning

confidence: 99%

A Simulation Study for the Performances of Two Dependent Correlation Coefficients Comparison Tests with a Real Data Application on Acute Appendicitis

Sığırlı¹,

Tasar²

2023

Turkiye Klinikleri J Biostat

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“…, n. This reparametrization avoids having to estimate the components of R from ( 7) and instead estimates the elements of U since this will still uniquely determine R. Because of this uniqueness, subsequently we will refer to these u i,j as the correlation components of the GARCH process. For more details on fast sampling of correlation matrices, see [33]. The only exception in using this parametrization is when n = 2, the bivariate case.…”

Section: Reparametrization Of the Correlation Matrix Rmentioning

confidence: 99%

A Bayesian Non-Stationary Heteroskedastic Time Series Model for Multivariate Critical Care Data

Omar¹,

Stephens²,

Schmidt³

et al. 2023

Preprint

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We propose a multivariate GARCH model for non-stationary health time series by modifying the variance of the observations of the standard state space model. The proposed model provides an intuitive way of dealing with heteroskedastic data using the conditional nature of state space models. We follow the Bayesian paradigm to perform the inference procedure. In particular, we use Markov chain Monte Carlo methods to obtain samples from the resultant posterior distribution. Due to the natural temporal correlation structure induced on model parameters, we use the forward filtering backward sampling algorithm to efficiently obtain samples from the posterior distribution. The proposed model also handles missing data in a fully Bayesian fashion. We validate our model on synthetic data, and then use it to analyze a data set obtained from an intensive care unit in a Montreal hospital. We further show that our proposed models offer better performance, in terms of WAIC, than standard state space models. The proposed model provides a new way to model multivariate heteroskedastic non-stationary time series data and the simplicity in applying the WAIC allows us to compare competing models.

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“…Gaussian graphical model simulation is covered in both Chapters 4 and 5. In particular, Chapter 4 is based on the conference article Córdoba et al (2018b), with Section 4.4.2 and the proof of Proposition 4.2.1 being novel material first appearing in this thesis. Such chapter serves as an introduction to the sampling methodology that is later applied to Gaussian graphical models in Chapter 5, largely based on both the conference article Córdoba et al (2018c) and the journal article Córdoba et al (2020c).…”

Section: Discussion Of the Resultsmentioning

confidence: 99%

“…It is primarily addressed in Córdoba et al (2018c), where a new simulation method for Gaussian Markov networks is proposed, and it is shown how it deeply affects different validation scenarios where several state-of-the-art learning methods are tested. In parallel, as a first step towards providing unbiased simulation for Gaussian graphical models, in Córdoba et al (2018b) a new method for uniform sampling of correlation matrices is detailed. This method is extended in Córdoba et al (2020a), providing uniform sampling for special types of Gaussian Markov and Bayesian networks.…”

Section: Contributionsmentioning

confidence: 99%

Unifying methodologies for graphical models with Gaussian parametrization

Sánchez¹

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Graphical models represent conditional independences of a multivariate distribution by absent edges in a graph, which typically is directed, undirected or mixed. This compact modelling allows to decompose statistical inference into efficient computations over the associated graph. As such, graphical models originated mainly at the interface between statistics and artificial intelligence, with Markov networks (undirected graph) and Bayesian networks (acyclic digraph) being the classic representatives. Nowadays graphical models are widely applied and a significant amount of research is devoted to them.Gaussian Markov networks and Gaussian Bayesian networks, although not being equivalent models, share a common intersection consisting of chordal graphs (or acyclic digraphs with no v-structures). A typical approach for model selection in both model classes is hypothesis testing, which amounts to selecting the graph that parametrizes the model. Absent edges in both models are represented by a zero pattern in the inverse covariance or partial correlation matrix (Gaussian Markov networks) or in its Cholesky decomposition (Gaussian Bayesian networks). Afterwards, their parameters are estimated by maximum likelihood. Alternatively, there exist state-of-the-art regularisation methods for both model classes, which simultaneously perform model selection and estimation.A popular method for model selection via hypothesis testing is the PC algorithm, which can be applied for both Gaussian Markov networks and Gaussian Bayesian networks. This method mainly depends on two parameters: the statistical test type and the significance level at which the hypotheses are tested. However, the usual approach in the literature is to use a Gaussian test for a transformation of the partial correlation, and a grid search for its significance level. By contrast, when using an automatic procedure for parameter tuning, such as Bayesian optimization, it is shown how model selection performance is significantly improved when employing an uncommonly used test in the literature. Furthermore, these automatic parameter tuning procedures allow to select a significance level optimized for each test type.Validation of methodologies for Gaussian graphical model selection is also deeply affected, apart from how parameter tuning is performed, by how synthetic test models are simulated. It can be shown that state-of-the-art methodologies addressing this task are biased towards certain regions, thereby significantly influencing validation results. It would be therefore desirable to have a uniform sampling procedure for Gaussian graphical models. In particular, both Gaussian Bayesian networks and Gaussian Markov networks are intimately related with the partial correlation matrix, thereby uniform sampling methods for such set, called elliptope, can be a departing point. A novel Metropolis uniform sampling from the elliptope is proposed, which can be straightforwardly extended to chordal Gaussian graphical models. However, in the general case, a partial orthogonali...

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A Fast Metropolis-Hastings Method for Generating Random Correlation Matrices

Cited by 4 publications

References 13 publications

A Simulation Study for the Performances of Two Dependent Correlation Coefficients Comparison Tests with a Real Data Application on Acute Appendicitis

A Simulation Study for the Performances of Two Dependent Correlation Coefficients Comparison Tests with a Real Data Application on Acute Appendicitis

A Bayesian Non-Stationary Heteroskedastic Time Series Model for Multivariate Critical Care Data

Unifying methodologies for graphical models with Gaussian parametrization

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