A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

Hiriart-Urruty, Jean-Baptiste; Malick, Jérôme

doi:10.1007/s10957-011-9980-6

Cited by 27 publications

(15 citation statements)

References 44 publications

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“…04 , so in effect there are three independent parameters to consider. 7 In fact, it is possible to not only exchange the fields but to rotate them by an arbitrary angle α. variable, since the remaining λ 13 term is only linear in φ 1 . In this case the condition Q > 0 ∨ R > 0 takes the form λ 22 + 2 √ λ 40 λ 04 > 0.…”

Section: Vacuum Stability Conditions From Positivity Of a Quartic Polmentioning

confidence: 99%

Vacuum stability of a general scalar potential of a few fields

2016

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We calculate analytical vacuum stability or bounded from below conditions for general scalar potentials of a few fields. After a brief review of copositivity, we show how to find positivity conditions for more complicated potentials. We discuss the vacuum stability conditions of the general potential of two real scalars, without and with the Higgs boson included in the potential. As further examples, we give explicit vacuum stability conditions for the two Higgs doublet model with no explicit CP breaking, and for the Z 3 scalar dark matter with an inert doublet and a complex singlet. We give a short overview of positivity conditions for tensors of quartic couplings via tensor eigenvalues.

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Section: Vacuum Stability Conditions From Positivity Of a Quartic Polmentioning

confidence: 99%

Vacuum stability of a general scalar potential of a few fields

2016

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“…The proof of Proposition 1 relies on technical elements from convex analysis (see Hiriart-Urruty and Malick [2012]) and is postponed to the Appendix. Results for covariance matrices of general structures can be easily proven using similar tools.…”

Section: Assume Thatmentioning

confidence: 99%

Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models

Baey

Cournède

Kuhn

2019

Computational Statistics & Data Analysis

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Mixed effects models are widely used to describe heterogeneity in a population. A crucial issue when adjusting such a model to data consists in identifying fixed and random effects. From a statistical point of view, it remains to test the nullity of the variances of a given subset of random effects. Some authors have proposed to use the likelihood ratio test and have established its asymptotic distribution in some particular cases. Nevertheless, to the best of our knowledge, no general variance components testing procedure has been fully investigated yet. In this paper, we study the likelihood ratio test properties to test that the variances of a general subset of the random effects are equal to zero in both linear and nonlinear mixed effects model, extending the existing results. We prove that the asymptotic distribution of the test is a chi-bar-square distribution, that is to say a mixture of chi-square distributions, and we identify the corresponding weights. We highlight in particular that the limiting distribution depends on the presence of correlations between the random effects but not on the linear or nonlinear structure of the mixed effects model. We illustrate the finite sample size properties of the test procedure through simulation studies and apply the test procedure to two real datasets of dental growth and of coucal growth.

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“…A GMC within Gibbs approach could alternate a small number of iterations between GMC samplers targetting p(β|A, κ, y 1:T ), p(κ|β, A, y 1:T ) and p(A|β, κ, y 1:T ). The GMC sampler for p(κ|β, A, y 1:T ) can be designed using a projection P based on eigendecompositions or optimization (see [28,Section 4.2.3]) and geodesics found in [31] together with a similar GMC approach. In the interest of brevity we will not pursue this further.…”

Section: Using Gmc Within a Gibbs Sampler Approachmentioning

confidence: 99%

Some recent developments in Markov Chain Monte Carlo for cointegrated time series

et al. 2017

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Abstract. We consider multivariate time series that exhibit reduced rank cointegration, which means a lower dimensional linear projection of the process becomes stationary. We will review recent suitable Markov Chain Monte Carlo approaches for Bayesian inference such as the Gibbs sampler of [41] and the Geodesic Hamiltonian Monte Carlo method of [3]. Then we will propose extensions that can allow the ideas in both methods to be applied for cointegrated time series with non-Gaussian noise. We illustrate the efficiency and accuracy of these extensions using appropriate numerical experiments.

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A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

Cited by 27 publications

References 44 publications

Vacuum stability of a general scalar potential of a few fields

Vacuum stability of a general scalar potential of a few fields

Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models

Some recent developments in Markov Chain Monte Carlo for cointegrated time series

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