统计计算
In many large-scale inverse problems, such as computed tomography and image deblurring, characterization of sharp edges in the solution is desired. Within the Bayesian approach to inverse problems, edge-preservation is often achieved using…
Stein discrepancies have emerged as a powerful statistical tool, being applied to fundamental statistical problems including parameter inference, goodness-of-fit testing, and sampling. The canonical Stein discrepancies require the…
We present a new algorithm which detects the maximal possible number of matched disjoint pairs satisfying a given caliper when a bipartite matching is done with respect to a scalar index (e.g., propensity score), and constructs a…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
This work considers a continuous framework to characterize the population-level variability of structural connectivity. Our framework assumes the observed white matter fiber tract endpoints are driven by a latent random function defined…
We study Hamiltonian Monte Carlo (HMC) samplers based on splitting the Hamiltonian $H$ as $H_0(\theta,p)+U_1(\theta)$, where $H_0$ is quadratic and $U_1$ small. We show that, in general, such samplers suffer from stepsize stability…
Importance sampling (IS) is a Monte Carlo technique that relies on weighted samples, simulated from a proposal distribution, to estimate intractable integrals. The quality of the estimators improves with the number of samples. However, for…
We introduce L-hydra (landmarked hyperbolic distance recovery and approximation), a method for embedding network- or distance-based data into hyperbolic space, which requires only the distance measurements to a few 'landmark nodes'. This…
Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…
Bayesian inference under a set of priors, called robust Bayesian analysis, allows for estimation of parameters within a model and quantification of epistemic uncertainty in quantities of interest by bounded (or imprecise) probability.…
Health economic evaluations often require predictions of survival rates beyond the follow-up period. Parametric survival models can be more convenient for economic modelling than the Cox model. The generalized gamma (GG) and generalized F…
Many Bayesian inference problems involve target distributions whose density functions are computationally expensive to evaluate. Replacing the target density with a local approximation based on a small number of carefully chosen density…
We consider particle filters with weakly informative observations (or `potentials') relative to the latent state dynamics. The particular focus of this work is on particle filters to approximate time-discretisations of continuous-time…
Monte Carlo simulation is often used for the reliability assessment of power systems, but it converges slowly when the system is complex. Multilevel Monte Carlo (MLMC) can be applied to speed up computation without compromises on model…
Let $f$ be analytic on $[0,1]$ with $|f^{(k)}(1/2)|\leq A\alpha^kk!$ for some constant $A$ and $\alpha<2$. We show that the median estimate of $\mu=\int_0^1f(x)\,\mathrm{d}x$ under random linear scrambling with $n=2^m$ points converges at…
Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of Layered Adaptive Importance Sampling…
BHAM is a freely avaible R pakcage that implments Bayesian hierarchical additive models for high-dimensional clinical and genomic data. The package includes functions that generalized additive model, and Cox additive model with the…
A large amount of quantitative geospatial data are collected and aggregated in discrete enumeration units (e.g. countries or states). Smooth pycnophylactic interpolation aims to find a smooth, nonnegative function such that the area…
Probabilistic programming and statistical computing are vibrant areas in the development of the Julia programming language, but the underlying infrastructure dramatically predates recent developments. The goal of MeasureTheory.jl is to…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…