C. Oates, J. Cockayne, R. G. Aykroyd, and M. Girolami. Bayesian probabilistic numerical methods in time-dependent state estimation for industrial hydrocyclone equipment. J. Amer. Statist. Assoc., 2019. URL https://arxiv.org/abs/1707.06107....
Bayesian probabilistic numerical methods for industrial process monitoring, 2017. arXiv:1707.06107.C. J. Oates, J. Cockayne, R. G. Aykroyd, and M. Girolami. Bayesian probabilistic nu- merical methods in time-dependent state estimation for industrial hydrocyclone equip- ment. Journal of the ...
In recent years, Bayesian numerical analysis [48] with its different variants, such as Bayesian probabilistic optimization [49], Bayesian Probabilistic Integration (BPI) [50], [51], and Bayesian probabilistic Partial Differential Equation (PDE) solution [52], has emerged as a cutting-edge method ...
These parameters are added to the parameters of the numerical model of the structure by forming a set of general parameters. This is equivalent to adding the probabilistic model classes to the design model class parameterized with parameters that include model parameters, measurement parameters, and ...
3: Train the chosen probabilistic model based on dataD 4: Calculate the selected acquisition functionu(x∣D) 5: Choose the next experiment point by\({{{\bf{x}}}^{s+1}={{{\mathrm{argmax}}}\,}_{\{{{\bf{x}}}^{s+1}\in {{{\mathcal{X}}}\}}u({{{\bf{x}}}| {...
Normalizing flows for probabilistic modeling and inference. Preprint at https://arxiv.org/abs/1912.02762 (2019). Korshunova, I. et al. in Advances in Neural Information Processing Systems 31 (eds Bengio, S.et al.) 7190–7198 (Curran Associates, 2018). Zhang, R., Li, C., Zhang, J.,...
6. Current methods typically involve two components: 1) a probabilistic statistical model trained to predict both the value and the uncertainty of a measurable property at any point in the design space (here, defined as a discrete set of all possible measurement or synthesis conditions) and 2)...
The unknown material parameters for the convection-diffusion problem denoted as\(\textsc {F2}\)then follow from the probabilistic Bayesian inversion $$\begin{aligned} {\mathfrak {P}}\leftarrow \textsc {BI}\big (\textsc {F2}({\mathfrak {u}})\big ) \quad {{\text {with}}}\quad {...
When used in a probabilistic framework, such models provide a sound foundation for data mining, inference, and decision making under uncertainty. We describe a methodology for encapsulating knowledge in the form of ordinary differential equations (ODEs) in dynamic Bayesian networks (DBNs). The ...
Variational autoencoders (VAEs) [99] are effective methods to model the posterior. They cast learning representations for high-dimensional distributions as a VI problem [128]. A probabilistic model Pθ(x) of sample x in a data space with a latent variable z in a latent space can be ...