A Combined Model and Data-Driven Approach for the Determination of Rotor Temperature in an Induction Machine

The need for protection of electrical machines comes as a demand of safety regulations in the automotive industry as well as a result of the general desire to obtain a robust and reliable electric powertrain. This paper introduces a hybrid method for estimating the temperature of the rotor of an Induction Machine (IM) based on a Nonlinear Autoregressive Network with Exogenous inputs (NARX) used as a prediction function within a particle filter. The temperature of the stator case is measured, and the information is used as an input to a NARX network and as a variable to a thermal process with first-order dynamics which serves as an observation function. Uncertainties of the NARX and thermal model are determined and used to correct the posterior estimate. Experimental data are used from a real IM test-bench and the results prove the applicability and good performance.

Indignation moving singularity and analytical approximate solution of a nonlinear third-order equations

В данной работе представлено исследование рассматриваемого класса нелинейных дифференциальных уравнений с подвижными особыми точками. Учитывая авторскую разработку теоремы существования и единственности решения построена структура аналитического приближенного решения, для которой, в данной работе, было установлено влияние возмущения подвижной особой точки. Представленные теоретические положения подтверждены с помощью численного эксперимента. Для оптимизации априорных оценок применялась апостериорная оценка. This paper presents a study of one class of nonlinear differential equations with movable singular points. On the basis of the previously proved theorem of existence and uniqueness of the solution, the structure of the analytical approximate solution was obtained, for which, in this work, the influence of the perturbation of a moving singular point was established. Results are tested using a numerical experiment. To optimize the prior estimates, the posterior estimate was used.

Bayesian Estimation of the True Seroprevalence and Risk Factor Analysis of Bovine Leukemia Virus Infection in Pakistan

The objective of this study was to determine the true seroprevalence of bovine leukemia virus (BLV) infection in dairy cattle from Pakistan at the animal and herd-level. We tested 1380 dairy cattle from 451 herds and 92 water buffalo. The sera were tested by ELISA and the results were analyzed using Bayesian inference. The median posterior estimate of the herd level true BLV prevalence was 1.4%, with a 95% credible interval (CI) 0.7–3.1, whereas the median posterior estimate of the within-farm true seroprevalence was 3.8% with a 95% CI 2.8–4.8. All 92 sera collected from water buffalo were negative. Several risk factors potentially associated with seropositivity to BLV infections in Pakistan were analyzed using logistic regression model based on calculation of an odds ratio (OR). The study showed an association between seropositivity and medium herd (≥50) size (OR = 23.57, 95% CI: 3.01–103.48). Common housing of indigenous cattle with exotic-breed cattle (OR = 0.67, 95% CI: 06–2.35) or housing indigenous or their crossbred cattle with exotic-breed cattle (OR = 0.95, 95% CI: 0.14–3.01) had no effect on the BLV seroprevalence. Similarly, common housing of cattle and water buffalo was not risk factor for increased BLV seropositivity (OR = 27.10, 95% CI: 0.63–119.34).

Convergence of the Deep BSDE method for FBSDEs with non-Lipschitz coefficients

<p style='text-indent:20px;'>This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration. This posterior estimate validates the convergence of the recently proposed Deep BSDE method. In addition, we developed a numerical scheme based on the Deep BSDE method and presented numerical examples in financial markets to demonstrate the high performance.</p>

Sensitivity of the Posterior Mean on the Prior Assumptions: An Application of the Ellipsoid Bound Theorem

This study examines the sensitivity of the posterior mean to change in the prior assumptions. Three plausible choices of prior which include informative, relative-non informative and non-informative priors are considered. The paper considers information level for a prior to cause a notable change in the Bayesian posterior point estimate. The study develops a framework for evaluating a bound for a robust posterior point estimate. The Ellipsoid Bound theorem is employed to derive the Ellipsoid Bound for an independent normal gamma prior distribution. The proposed modification ellipsoid bound for the large prior was establised by varrying different variance co-variance sizes for the independent normal gamma prior. This bound represents the range for the posterior mean when is insensitive and when it’s sensitive in both location and spread. The result shows that; for a large prior parameter value (greater than the OLS estimate) with a positive definite prior variance covariance matrix, and prior parameter values interval which contains the OLS estimate then, the posterior estimate will be less than both the OLS and the prior estimates. Similarly, if the lower bound of the prior parameter values range is greater than the OLS estimate then: The posterior estimate will be greater than the OLS estimate but smaller than the prior estimate. Furthermore, it is observed that no matter the degrees of confidence in the prior values, data information is powerful enough to modify it.

Are skyline plot-based demographic estimates overly dependent on smoothing prior assumptions?

In Bayesian phylogenetics, the coalescent process provides an informative framework for inferring dynamical changes in the effective size of a population from a sampled phylogeny (or tree) of its sequences. Popular coalescent inference methods such as the Bayesian Skyline Plot, Skyride and Skygrid all model this population size with a discontinuous, piecewise-constant likelihood but apply a smoothing prior to ensure that posterior population size estimates transition gradually with time. These prior distributions implicitly encode extra population size information that is not available from the observed coalescent tree (data). Here we present a novel statistic, Ω, to quantify and disaggregate the relative contributions of the coalescent data and prior assumptions to the resulting posterior estimate precision. Our statistic also measures the additional mutual information introduced by such priors. Using Ω we show that, because it is surprisingly easy to over-parametrise piecewise-constant population models, common smoothing priors can lead to overconfident and potentially misleading conclusions, even under robust experimental designs. We propose Ω as a useful tool for detecting when posterior estimate precision is overly reliant on prior choices.

Gaussian Mean Field Regularizes by Limiting Learned Information

Variational inference with a factorized Gaussian posterior estimate is a widely-used approach for learning parameters and hidden variables. Empirically, a regularizing effect can be observed that is poorly understood. In this work, we show how mean field inference improves generalization by limiting mutual information between learned parameters and the data through noise. We quantify a maximum capacity when the posterior variance is either fixed or learned and connect it to generalization error, even when the KL-divergence in the objective is scaled by a constant. Our experiments suggest that bounding information between parameters and data effectively regularizes neural networks on both supervised and unsupervised tasks.

Potential of European ¹⁴CO₂ observation network to estimate the fossil fuel CO₂ emissions via atmospheric inversions

Combining measurements of atmospheric CO2 and its radiocarbon (14CO2) fraction and transport modeling in atmospheric inversions offers a way to derive improved estimates of CO2 emitted from fossil fuel (FFCO2). In this study, we solve for the monthly FFCO2 emission budgets at regional scale (i.e., the size of a medium-sized country in Europe) and investigate the performance of different observation networks and sampling strategies across Europe. The inversion system is built on the LMDZv4 global transport model at 3.75∘ × 2.5∘ resolution. We conduct Observing System Simulation Experiments (OSSEs) and use two types of diagnostics to assess the potential of the observation and inverse modeling frameworks. The first one relies on the theoretical computation of the uncertainty in the estimate of emissions from the inversion, known as “posterior uncertainty”, and on the uncertainty reduction compared to the uncertainty in the inventories of these emissions, which are used as a prior knowledge by the inversion (called “prior uncertainty”). The second one is based on comparisons of prior and posterior estimates of the emission to synthetic “true” emissions when these true emissions are used beforehand to generate the synthetic fossil fuel CO2 mixing ratio measurements that are assimilated in the inversion. With 17 stations currently measuring 14CO2 across Europe using 2-week integrated sampling, the uncertainty reduction for monthly FFCO2 emissions in a country where the network is rather dense like Germany, is larger than 30 %. With the 43 14CO2 measurement stations planned in Europe, the uncertainty reduction for monthly FFCO2 emissions is increased for the UK, France, Italy, eastern Europe and the Balkans, depending on the configuration of prior uncertainty. Further increasing the number of stations or the sampling frequency improves the uncertainty reduction (up to 40 to 70 %) in high emitting regions, but the performance of the inversion remains limited over low-emitting regions, even assuming a dense observation network covering the whole of Europe. This study also shows that both the theoretical uncertainty reduction (and resulting posterior uncertainty) from the inversion and the posterior estimate of emissions itself, for a given prior and “true” estimate of the emissions, are highly sensitive to the choice between two configurations of the prior uncertainty derived from the general estimate by inventory compilers or computations on existing inventories. In particular, when the configuration of the prior uncertainty statistics in the inversion system does not match the difference between these prior and true estimates, the posterior estimate of emissions deviates significantly from the truth. This highlights the difficulty of filtering the targeted signal in the model–data misfit for this specific inversion framework, the need to strongly rely on the prior uncertainty characterization for this and, consequently, the need for improved estimates of the uncertainties in current emission inventories for real applications with actual data. We apply the posterior uncertainty in annual emissions to the problem of detecting a trend of FFCO2, showing that increasing the monitoring period (e.g., more than 20 years) is more efficient than reducing uncertainty in annual emissions by adding stations. The coarse spatial resolution of the atmospheric transport model used in this OSSE (typical of models used for global inversions of natural CO2 fluxes) leads to large representation errors (related to the inability of the transport model to capture the spatial variability of the actual fluxes and mixing ratios at subgrid scales), which is a key limitation of our OSSE setup to improve the accuracy of the monitoring of FFCO2 emissions in European regions. Using a high-resolution transport model should improve the potential to retrieve FFCO2 emissions, and this needs to be investigated.

Estimation of gross land-use change and its uncertainty using a Bayesian data assimilation approach

We present a method for estimating land-use change using a Bayesian data assimilation approach. The approach provides a general framework for combining multiple disparate data sources with a simple model. This allows us to constrain estimates of gross land-use change with reliable national-scale census data, whilst retaining the detailed information available from several other sources. Eight different data sources, with three different data structures, were combined in our posterior estimate of land use and land-use change, and other data sources could easily be added in future. The tendency for observations to underestimate gross land-use change is accounted for by allowing for a skewed distribution in the likelihood function. The data structure produced has high temporal and spatial resolution, and is appropriate for dynamic process-based modelling. Uncertainty is propagated appropriately into the output, so we have a full posterior distribution of output and parameters. The data are available in the widely used netCDF file format from http://eidc.ceh.ac.uk/.

Estimation of land-use change using a Bayesian data assimilation approach

We present a method for estimating land-use change using a Bayesian data assimilation approach. The approach provides a general framework for combining multiple disparate data sources with a simple model. This allows us to constrain estimates of gross land-use change with reliable national-scale census data, whilst retaining the detailed information available from several other sources. Eight different data sources, with three different data structures, were combined in our posterior estimate of land-use and land-use change, and other data sources could easily be added in future. The tendency for observations to underestimate gross land-use change is accounted for by allowing for a skewed distribution in the likelihood function. The data structure produced has high temporal and spatial resolution, and is appropriate for dynamic process-based modelling. Uncertainty is propagated appropriately into the output, so we have a full posterior distribution of output and parameters. The data are available in the widely used netCDF file format from http://eidc.ceh.ac.uk/ (doi pending).