Related papers: Laplace based approximate posterior inference for …
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this…
A major challenge in state estimation with model-based observers are low-quality models that lack of relevant dynamics. We address this issue by simultaneously estimating the system's states and its model uncertainties by a square root UKF.…
We consider the problem of approximate Bayesian parameter inference in non-linear state-space models with intractable likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is one approach to approximate the…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of non-linear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…
Gaussian covariance graph model is a popular model in revealing underlying dependency structures among random variables. A Bayesian approach to the estimation of covariance structures uses priors that force zeros on some off-diagonal…
In this article, a new modified Laplace-Fourier method is developed in order to obtain the solutions of linear neutral delay differential equations. The proposed method provides a more accurate solution than the one provided by the pure…
The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e. numerical approximations whose energy decreases, just like in the original differential equation. With this aim, a discrete gradient method is…
Laplace's method is used to approximate intractable integrals in a statistical problems. The relative error rate of the approximation is not worse than $O_p(n^{-1})$. We provide the first statistical lower bounds showing that the $n^{-1}$…
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…
Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…
Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…
In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodology is the use of coarse-proxy models (i.e., lower…
Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…
Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides…
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…
Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…