Objective Bayesian analysis for the multivariate skew-t model

Parisi, Antonio; Liseo, Brunero

doi:10.1007/s10260-017-0404-0

Cited by 9 publications

(4 citation statements)

References 31 publications

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“…and follow Liseo and Parisi (2013) and Parisi and Liseo (2018) in the assignment of a prior for the skewness parameter:…”

Section: Methods 21 a Bayesian Nonparametric Hierarchical Modelmentioning

confidence: 99%

Coarsened mixtures of hierarchical skew normal kernels for flow cytometry analyses

Gorsky¹,

Chan²,

Ma³

2020

Preprint

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Flow cytometry (FCM) is the standard multi-parameter assay used to measure single cell phenotype and functionality. It is commonly used to quantify the relative frequencies of cell subsets in blood and disaggregated tissues. A typical analysis of FCM data involves cell classification-that is, the identification of cell subgroups in the sample-and comparisons of the cell subgroups across samples or conditions. While modern experiments often necessitate the collection and processing of samples in multiple batches, analysis of FCM data across batches is challenging because the locations in the marker space of cell subsets may vary across samples due to batch effects. Differences across samples may occur because of true biological variation or technical reasons such as antibody lot effects or instrument optics. An important step in comparative analyses of multi-sample FCM data is cross-sample calibration, whose goal is to align cell subsets across multiple samples in the presence of variations in locations, so that variation due to technical reasons is minimized and true biological variation can be meaningfully compared. We introduce a Bayesian nonparametric hierarchical modeling approach for accomplishing both calibration and cell classification simultaneously in a unified probabilistic manner. Three important features of our method make it particularly effective for analyzing multi-sample FCM data: a nonparametric mixture avoids prespecifying the number of cell clusters; the hierarchical skew normal kernels allow flexibility in the shapes of the cell subsets and cross-sample variation in their locations; and finally the "coarsening" strategy makes inference robust to small departures from the model, a feature that becomes crucial with massive numbers of observations such as those encountered in FCM data. We demonstrate the merits of our approach in simulated examples and carry out a case study in the analysis of two FCM data sets.

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“…and follow Liseo and Parisi (2013) and Parisi and Liseo (2018) in the assignment of a prior for the skewness parameter:…”

Section: Methods 21 a Bayesian Nonparametric Hierarchical Modelmentioning

confidence: 99%

Coarsened mixtures of hierarchical skew normal kernels for flow cytometry analyses

Gorsky¹,

Chan²,

Ma³

2020

Preprint

View full text Add to dashboard Cite

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“…The quantity under square root in (7) influences the stability of parameter estimates and will be used later in a related discussion. Thus, we add a notation for it:…”

Section: Momentsmentioning

confidence: 99%

“…From these developments multivariate skew t-distribution has become most frequently used [4]. This distribution became an important tool in many data modeling applications because of heavier tail area than the normal and skew normal distributions (see, for instance, Lee and McLachan [5], Marchenko [6], Parisi and Liseo [7], Fernandez and Steel [8], Jones [9]). A review of applications in finance and insurance mathematics is given in Adcock et al [10].…”

Section: Introductionmentioning

confidence: 99%

Multivariate Skew t-Distribution: Asymptotics for Parameter Estimators and Extension to Skew t-Copula

2021

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Symmetric elliptical distributions have been intensively used in data modeling and robustness studies. The area of applications was considerably widened after transforming elliptical distributions into the skew elliptical ones that preserve several good properties of the corresponding symmetric distributions and increase possibilities of data modeling. We consider three-parameter p-variate skew t-distribution where p-vector μ is the location parameter, Σ:p×p is the positive definite scale parameter, p-vector α is the skewness or shape parameter, and the number of degrees of freedom ν is fixed. Special attention is paid to the two-parameter distribution when μ=0 that is useful for construction of the skew t-copula. Expressions of the parameters are presented through the moments and parameter estimates are found by the method of moments. Asymptotic normality is established for the estimators of Σ and α. Convergence to the asymptotic distributions is examined in simulation experiments.

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“…Ref. [53] carried out a Bayesian analysis of a p -variate skew-t distribution by providing a new parameterization, considering a set of non-informative priors and a sampler designed to obtain the posterior model based on the parameters. The methodology can be extended to multivariate regression models with skewed errors and also stochastic frontier models.…”

Section: Overview On Related Topicsmentioning

confidence: 99%

Bayesian Inference for Skew-Symmetric Distributions

2020

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Skew-symmetric distributions are a popular family of flexible distributions that conveniently model non-normal features such as skewness, kurtosis and multimodality. Unfortunately, their frequentist inference poses several difficulties, which may be adequately addressed by means of a Bayesian approach. This paper reviews the main prior distributions proposed for the parameters of skew-symmetric distributions, with special emphasis on the skew-normal and the skew-t distributions which are the most prominent skew-symmetric models. The paper focuses on the univariate case in the absence of covariates, but more general models are also discussed.

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Objective Bayesian analysis for the multivariate skew-t model

Cited by 9 publications

References 31 publications

Coarsened mixtures of hierarchical skew normal kernels for flow cytometry analyses

Coarsened mixtures of hierarchical skew normal kernels for flow cytometry analyses

Multivariate Skew t-Distribution: Asymptotics for Parameter Estimators and Extension to Skew t-Copula

Bayesian Inference for Skew-Symmetric Distributions

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