相关论文: Exact Expressions for the Log-likelihood's Hessian…
We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in $\mathbb{R}^d$. Our study covers both the case where the true underlying density is…
We consider the problem of computing the maximum likelihood multivariate log-concave distribution for a set of points. Specifically, we present an algorithm which, given $n$ points in $\mathbb{R}^d$ and an accuracy parameter $\epsilon>0$,…
We present a coherent Bayesian framework for selection of the most likely model from the five genetic models (genotypic, additive, dominant, co-dominant, and recessive) commonly used in genetic association studies. The approach uses a…
Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Given a dataset of function-valued traits generated by evolution, we develop a practical statistical approach to infer ancestral…
The ancestral maximum-likelihood and phylogeography problems are two fundamental problems involving evolutionary studies. The ancestral maximum-likelihood problem involves identifying a rooted tree alongside internal node sequences that…
The model of a multi-level system interacting with several reservoirs is considered. The exact reduced density matrix evolution could be obtained for this model without Markov approximation. Namely, this evolution is fully defined by the…
Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many…
In this paper, we focus on statistical region-based active contour models where image features (e.g. intensity) are random variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to…
We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on…
We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof…
We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while…
The class of algorithms called Hessian Estimation Evolution Strategies (HE-ESs) update the covariance matrix of their sampling distribution by directly estimating the curvature of the objective function. The approach is practically…
The branching structure of biological evolution confers statistical dependencies on phenotypic trait values in related organisms. For this reason, comparative macroevolutionary studies usually begin with an inferred phylogeny that describes…
Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could…
We introduce an alternative closed form lower bound on the Gaussian process ($\mathcal{GP}$) likelihood based on the R\'enyi $\alpha$-divergence. This new lower bound can be viewed as a convex combination of the Nystr\"om approximation and…
We introduce an R package, PCMBase, to rapidly calculate the likelihood for multivariate phylogenetic comparative methods. The package is not specific to particular models but offers the user the functionality to very easily implement a…
Motivated by examples from genetic association studies, this paper considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating…
We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…
Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical…