Related papers: Bayesian inference of covariate-parameter relation…
Data in many applications follows systems of Ordinary Differential Equations (ODEs). This paper presents a novel algorithmic and symbolic construction for covariance functions of Gaussian Processes (GPs) with realizations strictly following…
Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as…
We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…
We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…
Indirect comparisons of treatment-specific outcomes across separate studies often inform decision-making in the absence of head-to-head randomized comparisons. Differences in baseline characteristics between study populations may introduce…
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…
Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…
We consider the identification of a scalar coefficient in a PDE-based parameter estimation problem with contact constraints. The considered problem can be used as an idealized model of a membrane under forces, constrained by a barrier or…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…
Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary…
OC-DeepIV is a neural network model designed for estimating causal effects. It characterizes heterogeneity by adding interaction features and reduces redundancy through orthogonal constraints. The model includes two feature extractors, one…
In statistical inference, a discrepancy between the parameter-to-observable map that generates the data and the parameter-to-observable map that is used for inference can lead to misspecified likelihoods and thus to incorrect estimates. In…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…
Studies often estimate associations between an outcome and multiple variates. For example, studies of diagnostic test accuracy estimate sensitivity and specificity, and studies of predictive and prognostic factors typically estimate…
Inverse optimization (IO) is used to estimate unknown parameters of an optimization model from observed decisions. In the data-driven context, the estimated parameters are inherently uncertain, yet quantifying this uncertainty has received…
This paper is devoted to studying a type of contact problems modeled by hemivariational inequalities with small periodic coefficients appearing in PDEs, and the PDEs we considered are linear, second order and uniformly elliptic. Under the…
Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we…