30 citations · 169 across the 28 of their papers we have counts for
8 papers · 1 filter
Maximum Likelihood Estimation for Brownian Motion Tree Models Based on One Sample
Michael Truell, Jan-Christian Hütter, Chandler Squires +2
We study the problem of maximum likelihood estimation given one data sample () over Brownian Motion Tree Models (BMTMs), a class of Gaussian models on trees. BMTMs are often u…
Locally associated graphical models and mixed convex exponential families
Steffen Lauritzen, Piotr Zwiernik
The notion of multivariate total positivity has proved to be useful in finance and psychology but may be too restrictive in other applications. In this paper we propose a concept o…
Total positivity in exponential families with application to binary variables
Steffen Lauritzen, Caroline Uhler, Piotr Zwiernik
We study exponential families of distributions that are multivariate totally positive of order 2 (MTP2), show that these are convex exponential families, and derive conditions for…
Maximum likelihood estimation in Gaussian models under total positivity
Steffen Lauritzen, Caroline Uhler, Piotr Zwiernik
We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2). By exploiting connections to phylogen…
The correlation space of Gaussian latent tree models and model selection without fitting
Nathaniel Shiers, Piotr Zwiernik, John A. D. Aston +1
We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constrai…
Marginal likelihood and model selection for Gaussian latent tree and forest models
Mathias Drton, Shaowei Lin, Luca Weihs +1
Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that…
Binary distributions of concentric rings
N. Wermuth G. M. Marchetti P. Zwiernik
We introduce families of jointly symmetric, binary distributions that are generated over directed star graphs whose nodes represent variables and whose edges indicate positive depe…
The Dependence of Routine Bayesian Model Selection Methods on Irrelevant Alternatives
Piotr Zwiernik, Jim Q. Smith
Bayesian methods - either based on Bayes Factors or BIC - are now widely used for model selection. One property that might reasonably be demanded of any model selection method is t…