Related papers: Bayesian Post-Processor and other Enhancements of …
We consider the problem of estimating a probability of failure $\alpha$, defined as the volume of the excursion set of a function $f:\mathbb{X} \subseteq \mathbb{R}^{d} \to \mathbb{R}$ above a given threshold, under a given probability…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
The estimation of small probabilities of failure from computer simulations is a classical problem in engineering, and the Subset Simulation algorithm proposed by Au & Beck (Prob. Eng. Mech., 2001) has become one of the most popular method…
Identifying the parameters of a model and rating competitive models based on measured data has been among the most important but challenging topics in modern science and engineering, with great potential of application in structural system…
The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the…
This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an (unknown) fraction of (fixed size) of the available data that is randomly…
Statistical inference of multiple parameters often involves a preliminary parameter selection stage. The selection stage has an impact on subsequent estimation, for example by introducing a selection bias. The post-selection maximum…
Estimating the probabilities of rare failure events is a key challenge in the reliability analysis of physical systems. Subset simulation (SS) is a very popular adaptive Monte Carlo method for this problem. In SS, the small failure…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…
Bayesian methods are critical for quantifying the behaviors of systems. They capture our uncertainty about a system's behavior using probability distributions and update this understanding as new information becomes available. Probabilistic…
Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and…
A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable…
We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by…
The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by…
Prominent features of simulated moving bed (SMB) chromatography processes in the downstream processing is based on the determination of operating conditions. However, effects of different types of uncertainties have to be studied and…
Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…
Bayesian inference via standard Markov Chain Monte Carlo (MCMC) methods is too computationally intensive to handle large datasets, since the cost per step usually scales like $\Theta(n)$ in the number of data points $n$. We propose the…
A multi-fidelity simulator is a numerical model, in which one of the inputs controls a trade-off between the realism and the computational cost of the simulation. Our goal is to estimate the probability of exceeding a given threshold on a…