Related papers: An importance sampling approach for reliable and e…
Model fitting is possibly the most extended problem in science. Classical approaches include the use of least-squares fitting procedures and maximum likelihood methods to estimate the value of the parameters in the model. However, in recent…
Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…
It is important to estimate the errors of probabilistic inference algorithms. Existing diagnostics for Markov chain Monte Carlo methods assume inference is asymptotically exact, and are not appropriate for approximate methods like…
Many Bayesian inference problems involve high-dimensional models where the performance of standard importance sampling (IS) methods often degrades rapidly as the dimensionality increases. Classical analyses of IS typically rely on the…
Finite element model updating is challenging because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield responses that are similar with respect to…
In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and…
Bayesian methods have proven themselves to be successful across a wide range of scientific problems and have many well-documented advantages over competing methods. However, these methods run into difficulties for two major and prevalent…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…
Bayesian sociality models provide a scalable and flexible alternative for network analysis, capturing degree heterogeneity through actor-specific parameters while mitigating the identifiability challenges of latent space models. This paper…
We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…
Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…