In several disciplines, measurement results occasionally are expressed using coverage intervals that are asymmetric relative to the measured value. The conventional treatment of such results, when there is the need to propagate their uncertainties to derivative quantities, is to replace the asymmetric uncertainties by ‘symmetrized’ versions thereof. We show that such simplification is unnecessary, illustrate how asymmetry may be modeled and recognized explicitly, and propagated using standard Monte Carlo methods. We present three distributions (Fechner, skew-normal, and generalized extreme value), among many available alternatives, that can be used as models for asymmetric uncertainties associated with scalar input quantities, in the context of the measurement model considered in the GUM. We provide an example where such uncertainties are propagated to the uncertainty of a ratio of mass fractions. We also show how a similar, model-based approach can be used in the context of data reductions from interlaboratory studies and other consensus building exercises where the reported uncertainties are expressed asymmetrically, illustrating the approach to obtain consensus estimates of the absorption cross-section of ozone, and of the distance to galaxy M83 in the Virgo cluster.

We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods. Our results can be used by researchers in physical modeling interested in a fast and accurate estimation of low dimensional stochastic models when the size of the observed time series is small and the noise process (perhaps) is non-Gaussian. The inference procedure is demonstrated specifically in the case of polynomial maps of an arbitrary degree and when a Geometric Stick Breaking mixture process prior over the space of densities, is applied to the additive errors. Our method is parsimonious compared to Bayesian nonparametric techniques based on Dirichlet process mixtures, flexible and general. Simulations based on synthetic time series are presented.

The Newtonian constant of gravitation, , stands out in the landscape of the most common fundamental constants owing to its surprisingly large relative uncertainty, which is attributable mostly to the dispersion of the values measured for it by di erent methods and in di erent experiments, each of which may have rather small relative uncertainty.This study focuses on a set of measurements of comprising results published very recently as well as older results, some of which have been corrected since the original publication. This set is inconsistent, in the sense that the dispersion of the measured values is signi cantly larger than what their reported uncertainties suggest that it should be. Furthermore, there is a loosely de ned group of measured values that lie fairly close to a consensus value that may reasonably be derived from all the measurement results, and then there are one or more groups with measured values farther away from the consensus value, some appreciably higher, others lower.This same general pattern is often observed in many other interlaboratory studies and meta-analyses. In the conventional treatments of such data, the mutual inconsistency is addressed by in ating the reported uncertainties, either multiplicatively, or by the addition of "random e ects", both re ecting the presence of dark uncertainty. The former approach is often used by CODATA and by the Particle Data Group, and the latter is common in medical meta-analysis and in metrology. However, both achieve consistency ignoring how the measured values are arranged relative to the consensus value, and measured values close to the consensus value often tend to be penalized excessively, by such "extra" uncertainty.We propose a new procedure for consensus building that models the results using latent clusters with di erent shades of dark uncertainty, which assigns a customized amount of dark uncertainty to each measured value, as a mixture of those shades, and does so taking into account both the placement of the measured values relative to the consensus value, and the reported uncertainties. We demonstrate this procedure by deriving a new estimate for , as a consensus value = 6.674 08 × 10 −11 m 3 kg −1 s −2 , with ( ) = 0.000 24 × 10 −11 m 3 kg −1 s −2 .

A new approach to the joint estimation of partially exchangeable observations is presented. This is achieved by constructing a model with pairwise dependence between random density functions, each of which is modeled as a mixture of geometric stick breaking processes. The claim is that mixture modeling with Pairwise Dependent Geometric Stick Breaking Process (PDGSBP) priors is sufficient for prediction and estimation purposes; that is, making the weights more exotic does not actually enlarge the support of the prior. Moreover, the corresponding Gibbs sampler for estimation is faster and easier to implement than the Dirichlet Process counterpart.

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimating the parameters of a system along with its unknown noise processes. In particular, we propose a Bayesian nonparametric approach for system identification in discrete time nonlinear random dynamical systems assuming only the order of the Markov process is known. The proposed method replaces the assumption of Gaussian distributed error components with a highly flexible family of probability density functions based on Bayesian nonparametric priors. Additionally, the functional form of the system is estimated by leveraging Bayesian neural networks which also leads to flexible uncertainty quantification. Asymptotically on the number of hidden neurons, the proposed model converges to full nonparametric Bayesian regression model. A Gibbs sampler for posterior inference is proposed and its effectiveness is illustrated in simulated and real time series.