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This article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be present. By construction the method is numerically stable and convergent, and enables smoothing parameter uncertainty to be quantified. The latter enables us to fix a well known problem with AIC for such models, thereby improving the range of model selection tools available. The smooth functions are represented by reduced rank spline like smoothers, with associated quadratic penalties measuring function smoothness. Model estimation is by penalized likelihood maximization, where the smoothing parameters controlling the extent of penalization are estimated by Laplace approximate marginal likelihood. The methods cover, for example, generalized additive models for nonexponential family responses (e.g., beta, ordered categorical, scaled t distribution, negative binomial and Tweedie distributions), generalized additive models for location scale and shape (e.g., two stage zero inflation models, and Gaussian location-scale models), Cox proportional hazards models and multivariate additive models. The framework reduces the implementation of new model classes to the coding of some standard derivatives of the log-likelihood. Supplementary materials for this article are available online.

Many population genetics tools employ composite likelihoods, because fully modeling genomic linkage is challenging. But traditional approaches to estimating parameter uncertainties and performing model selection require full likelihoods, so these tools have relied on computationally expensive maximum-likelihood estimation (MLE) on bootstrapped data. Here, we demonstrate that statistical theory can be applied to adjust composite likelihoods and perform robust computationally efficient statistical inference in two demographic inference tools: ∂a∂i and TRACTS. On both simulated and real data, the adjustments perform comparably to MLE bootstrapping while using orders of magnitude less computational time.

Forest inventory estimates of tree volume for large areas are typically calculated by adding model predictions of volumes for individual trees. However, the uncertainty in the model predictions is generally ignored with the result that the precision of the large area volume estimates is overestimated. The primary study objective was to estimate the effects of model residual variability and model parameter uncertainty on large area volume estimates and their uncertainties for a study area in northeastern Minnesota, USA. Monte Carlo simulation approaches were used because of the complexities associated with multiple sources of uncertainty and the nonlinear nature of the models. Two conclusions were important. First, for this study, the effects of uncertainty in model predictions on the large area volume estimates and their uncertainties were small when the models were calibrated using an average of 100 or more observations per species and when the average proportion of variance explained by the models was at least 0.95. Second, large area estimates and their uncertainties based on coniferous/deciduous and nonspecific models deviated very little from large area estimates based on species-specific models.

This article address a novel adaptive error port controlled Hamiltonian scheme for nonlinear systems with parameters uncertainty and external disturbances. Considering the input saturation phenomenon in real complex systems, a new smooth saturation function is used to deal with the limitations between the control signal and the actuator. The adaptive control technique is introduced to resolve the influence of model parameters uncertainty, and the nonlinear disturbance observer (NDO) is utilized to address external disturbances in real complex systems. Furthermore, a novel NDO-based adaptive error port controlled Hamiltonian (EPCH-NDO) strategy with the smooth switching gain optimization control technique is presented to enhance the accuracy of position tracking control for the target. Finally, the permanent magnet synchronous motor system is adopted to verify the proposed scheme. A large amounts of experiment results indicate that the proposed adaptive EPCH-NDO control strategy has perfect control performances compared with PI and port-controlled Hamiltonian based on load torque estimator methods.

Mathematical modeling is a method that uses mathematical methods to solve problems in real life. In the process of modeling, the inherent properties of the parameters and the change of the model design conditions will bring great uncertainty to the simulation results. In this paper, a deep neural network and dimension reduction method (DNN-DRM) is proposed to quantify the impact of parameter uncertainty on simulation results in modeling systems with multi-dimensional uncertainty, and reduce the risk caused by uncertainty. Firstly, the methods for training DNN substitute model and testing the generalization ability of models were investigated. Then the DRM based on DNN was constructed to solve the uncertain parameters in the system. In the experiments, three mathematical models with different types of complexity were modeled. Finally, the performance of the method was evaluated by probability distribution, mean and standard deviation of output values. The results show that compared with Monte Carlo simulation (MCS), the DNN-DRM can efficiently and accurately calculate the multi-dimensional uncertainty problem with a strong interaction, and effectively alleviate the “curse of dimensionality” difficulty, which provides a reference for the analysis of problems encountered in real life.

We investigated the effects of fault parameter uncertainty on the deterministic assessment of tsunami hazards for the submarine and coastal active faults in the Sea of Japan that were recently modeled by the Integrated Research Project on Seismic and Tsunami Hazards around the Sea of Japan. A key parameter in scenario-based tsunami assessment is the fault slip amount, which is usually calculated from empirical scaling relations that relate the fault size to the slip. We examined four methods to estimate the fault slip amounts and compared the coastal tsunami heights from the slip amounts obtained by two different empirical relations. The resultant coastal tsunami heights were strongly affected by the choice of scaling relation, particularly the fault aspect ratio (fault length/fault width). The geometric means of the coastal tsunami heights calculated from the two methods ranged from 0.69 to 4.30 with an average of 2.01. We also evaluated the effects of fault slip angles, which are also important parameters for controlling coastal tsunami heights, by changing the slip angles for faults in the southwestern and central parts of the Sea of Japan, where the strike-slip faults are concentrated. The effects of uncertainty of the fault slip angles (± 30° from the standard) on the coastal tsunami heights were revealed to be equal to or greater than those resulting from the choice of scaling relations; the geometric means of the coastal tsunami heights from the modified fault slip angles relative to the standard fault slip angles ranged from 0.23 to 5.88. Another important characteristic is that the locations of the maximum coastal tsunami height and the spatial pattern of the coastal tsunami heights can change with varying fault slip angles.

A new parameter optimization and uncertainty assessment procedure using the Bayesian inference with an adaptive Metropolis–Hastings (AM-H) algorithm is presented for extreme rainfall frequency modeling. An efficient Markov chain Monte Carlo sampler is adopted to explore the posterior distribution of parameters and calculate their uncertainty intervals associated with the magnitude of estimated rainfall depth quantiles. Also, the efficiency of AM-H and conventional maximum likelihood estimation (MLE) in parameter estimation and uncertainty quantification are compared. And the procedure was implemented and discussed for the case of Chaohu city, China. Results of our work reveal that: (i) the adaptive Bayesian method, especially for return level associated to large return period, shows better estimated effect when compared with MLE; it should be noted that the implementation of MLE often produces overy optimistic results in the case of Chaohu city; (ii) AM-H algorithm is more reliable than MLE in terms of uncertainty quantification, and yields relatively narrow credible intervals for the quantile estimates to be instrumental in risk assessment of urban storm drainage planning.

Landslide susceptibility maps can provide important information for managing regional landslide risks. Traditionally, data-driven and physically-based models are widely used for rainfall-induced landslide susceptibility mapping, but each method has limitations. In this study, a hybrid method that integrates a data-driven model and a physically-based model is proposed for rainfall-induced landslide susceptibility mapping, where the uncertainty in the soil properties can be explicitly considered. The proposed method is illustrated with landslide susceptibility mapping in Shengzhou County, Zhejiang Province, China. Logistic regression is used as the data-driven model, and the regional assessment of rainfall-induced landslides model (RARIL) is used as the physically-based model. Three hybrid models are developed. Hybrid model I, which considers soil parameters uncertainty, is compared with hybrid models II and III, which do not consider it. Results indicate that all the three hybrid models outperform the conventional logistic regression and RARIL models. Notably, hybrid model I, which considers the soil parameters uncertainty, outperforms hybrid models II and III, which do not consider it.

Integrating intermittent wind power into power systems results in low or zero inertia, threatening their frequency stability. To accommodate intermittent generations, the demand response (DR) is introduced, and air conditioning loads (ACs) account for an increasing proportion of all loads. The replacement of traditional generators with wind turbines and the ACs user uncertainties produce parameter uncertainties. This paper aims to construct an equivalent input disturbance (EID)-based load frequency control (LFC) strategy for the power system by considering wind power and ACs. First, an open-loop model is constructed for the LFC scheme with parameter uncertainties. Then, the parameter uncertainties and external disturbance are lumped into a fictitious disturbance, which is estimated using an EID estimator. By incorporating the estimation of disturbance into the control input, the disturbance-rejection performance is achieved. Next, the Lyapunov theory is used to derive the two linear-matrix-inequality-based asymptotic stability criteria. A design algorithm is developed for the EID-based LFC scheme by exploiting an overall performance evaluation index. Finally, simulation results for the single-area and two-area LFC schemes show that, compared with the existing approaches, the method presented realizes the better disturbance rejection and higher robustness against parameter uncertainties, wind power fluctuation, and tie-line power changes. Additionally, its robustness to time delays is verified.

Nowadays, vehicles are being fitted with systems that improve their maneuverability, stability, and comfort in order to reduce the number of accidents. Improving these aspects is of particular interest thanks to the incorporation of autonomous vehicles onto the roads. The knowledge of vehicle sideslip and roll angles, which are among the main causes of road accidents, is necessary for a proper design of a lateral stability and roll-over controller system. The problem is that these two variables cannot be measured directly through sensors installed in current series production vehicles due to their high costs. For this reason, their estimation is fundamental. In addition, there is a time delay in the relaying of information between the different vehicle systems, such as, sensors, actuators and controllers, among others. This paper presents the design of an H ∞ -based observer that simultaneously estimates both the sideslip angle and the roll angle of a vehicle for a networked control system, with networked transmission delay based on an event-triggered communication scheme combined with neural networks (NN). To deal with the vehicle nonlinearities, NN and linear-parameter-varying techniques are considered alongside uncertainties in parameters. Both simulation and experimental results are carried out to prove the performance of observer design.