Related papers: General Bayesian L2 calibration of mathematical mo…

A learning procedure takes as input a dataset and performs inference for the parameters $\theta$ of a model that is assumed to have given rise to the dataset. Here we consider learning procedures whose output is a probability distribution,…

Estimation of model parameters of computer simulators, also known as calibration, is an important topic in many engineering applications. In this paper, we consider the calibration of computer model parameters with the help of engineering…

Quality control in industrial processes is increasingly making use of prior scientific knowledge, often encoded in physical models that require numerical approximation. Statistical prediction, and subsequent optimization, is key to ensuring…

Climate models are generally calibrated manually by comparing selected climate statistics, such as the global top-of-atmosphere energy balance, to observations. The manual tuning only targets a limited subset of observational data and…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…

We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This…

Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows…

The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…

Dropout is one of the key techniques to prevent the learning from overfitting. It is explained that dropout works as a kind of modified L2 regularization. Here, we shed light on the dropout from Bayesian standpoint. Bayesian interpretation…

A neural network computes a function. A central property of neural networks is that they are "universal approximators:" for a given continuous function, there exists a neural network that can approximate it arbitrarily well, given enough…

Recent work has developed a non-parametric Bayesian approach to the calibration of a computer model, which abstractly amounts to the inversion of a pushforward of stochastic input parameters by a smooth map. The framework has been used in…

Bayesian Model Calibration is used to revisit the problem of scaling factor calibration for semi-empirical correction of ab initio harmonic properties (e.g. vibrational frequencies and zero-point energies). A particular attention is devoted…

We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…

We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…

Assimilation of continuously streamed monitored data is an essential component of a digital twin; the assimilated data are used to ensure the digital twin is a true representation of the monitored system. One way this is achieved is by…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…

Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…