Multivariate T-Distributions and Their Applications

By Samuel Kotz, Saralees Nadarajah. 2004

746 citations recorded by the source corpus.

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Citations in the corpus

Using MCMC chain outputs to efficiently estimate Bayes factors (2011, methodology): “Here,we choose amultivariate generalization of the Cauchy distribution, the multivariate Student’s t(1) distribution (Kotz & Nadarajah, 2004): δ ∼ t ν = 1, Σ0 = r2IJ , where ν denotes the degrees of freedom of the multivariate t distribution, Σ0 denotes a covariance matrix, and IJ denotes the J ×…”
Robust Likelihood Methods Based on the Skew‐t and Related Distributions (2008, methodology): “A relatively simpler formulation, at least for the bivariate case, is the one of Jones (2002); see also additional proposals reviewed in chapters 4 and 5 of Kotz & Nadarajah (2004).”
Maximizing acquisition functions for Bayesian optimization (2018, background): “Such plateaus typically emerge when corresponding regions of X are thought to be inferior and are therefore excluded from the search process.”
Identifiability of Finite Mixtures of Elliptical Distributions (2006, background): “Indeed, the respective characteristic generator (Kotz & Nadarajah, 2004, p. 39) is given by (u; )= (u ) /4 2 /2−1 ( /2) K /2 (√ u ) , u ≥0, (7) © Board of the Foundation of the Scandinavian Journal of Statistics 2006. where K /2 denotes the McDonald or modified Bessel function of the second kind…”
On the Conditional Distribution of the Multivariate t Distribution (2016, methodology): “wb/2−1e−cw/2.We exploit the following representation of the MVT distribution: X =µ+Σ1/2Z/ √ q, (2) where Z follows a p dimensional standard normal distribution, q ∼ χ2 ν/ν, and Z is independent of q (Kotz and Nadarajah 2004; Nadarajah and Kotz 2005). It differs from the multivariate normal distribut”
Divisive Normalization: Justification and Effectiveness as Efficient Coding Transform (2010, background): “(1) can be shown to be equivalent to the standard definition of multivariate t density in [14].”
The student-t mixture as a natural image patch prior with application to image compression (2014, background): “A multivariate Student-t distribution has the following density function (Kotz and Nadarajah, 2004): T (x|ν, µ, Σ) = Γ ν+p 2 Γ ν 2 ν p 2 π p 2 |Σ| 1/2 1 + 1 ν (x − µ) T Σ −1 (x − µ) − ν+p 2 .”
Sampling Student’s T distribution – use of the inverse cumulative distribution function (2006, background): “As well, there is the issue that Equation (18) is not in fact the only possible choice when all degrees of freedom are the same! Some of the possibilities are discussed in the book devoted to the matter by Kotz and Nadarajah (2004), who also cite recent work (Fang et al 2002) suggesting a distributi”
Statistical Size Distributions in Economics and Actuarial Sciences (2004, background): “The second author is arguably the world’s leading chronicler of statistical distributions, a coauthor for a large list of books on distributions, most significantly the book by Kotz, Read, and Banks (1999) and most recently that by Kotz and Nadarajah (2004). This book is partly a history of the appl”
Default Bayes factors for ANOVA designs (2012, background): “The second generalization, conventionally termed the multivariate Cauchy (Kotz & Nadarajah, 2004), is given by the joint probability density function π(θ) = Γ [(1 + p)/2] Γ(1/2)πp/2 [1 + ∑p i=1 θ 2 i ] (1+p)/2 .”
Construction of multivariate distributions: a review of some recent results (2008, background): “In recent years several books containing theory about multivariate nonnormal distributions have been published: Hutchinson and Lai (1990), Joe (1997), Arnold, Castillo and Sarabia (1999), Kotz, Balakrishnan and Johnson (2000), Kotz and Nadarajah (2004), Nelsen (2006).”
A New Approach to Assessing Model Risk in High Dimensions (2015, positive): “An interesting variant on this approach was considered in Lee and Mykland (2008). These authors reject observations when their distance is not in the usual range of maximum distances (its distribution can be derived based on the available data). Thus, in the same spirit, one may choose c equal to th”