Related papers: Parameterizations for Gradient-based Markov Chain …
A common tool in the practice of Markov Chain Monte Carlo is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or intractable. A limited set of quantitative tools exist to assess the…
Markov chain Monte Carlo (MCMC) sampling is an important and commonly used tool for the analysis of hierarchical models. Nevertheless, practitioners generally have two options for MCMC: utilize existing software that generates a black-box…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization…
We consider matrices $\boldsymbol{A}(\boldsymbol\theta)\in\mathbb{R}^{m\times m}$ that depend, possibly nonlinearly, on a parameter $\boldsymbol\theta$ from a compact parameter space $\Theta$. We present a Monte Carlo estimator for…
Improving efficiency of importance sampler is at the center of research in Monte Carlo methods. While adaptive approach is usually difficult within the Markov Chain Monte Carlo framework, the counterpart in importance sampling can be…
We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems…
Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…
The analysis of parametrised systems is a growing field in verification, but the analysis of parametrised probabilistic systems is still in its infancy. This is partly because it is much harder: while there are beautiful cut-off results for…
The Stiefel manifold $V_{p,d}$ is the space of all $d \times p$ orthonormal matrices, with the $d-1$ hypersphere and the space of all orthogonal matrices constituting special cases. In modeling data lying on the Stiefel manifold, parametric…
Segmenting images of low quality or with missing data is a challenging problem. Integrating statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Most shape-based segmentation…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
We present a novel Bayesian inference tool that uses a neural network to parameterise efficient Markov Chain Monte-Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of…
Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue…
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo, combining MCMC and sequential Monte Carlo to form "exact approximations" to…
Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…
We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The…