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This chapter develops a return forecasting methodology that allows for instability in the relationship between stock returns and predictor variables, model uncertainty, and parameter estimation uncertainty. The predictive regression specification that is put forward allows for occasional structural breaks of random magnitude in the regression parameters, uncertainty about the inclusion of forecasting variables, and uncertainty about parameter values by employing Bayesian model averaging. The implications of these three sources of uncertainty and their relative importance are investigated from an active investment management perspective. It is found that the economic value of incorporating all three sources of uncertainty is considerable. A typical investor would be willing to pay up to several hundreds of basis points annually to switch from a passive buy-and-hold strategy to an active strategy based on a return forecasting model that allows for model and parameter uncertainty as well as structural breaks in the regression parameters.

The purpose of this paper is to examine the effects of parameter uncertainty in the returns process with regime shifts on optimal portfolio choice over the long run for a static buy-and-hold investor who is investing in industry portfolios.

This paper uses a Markov switching model to model returns on industry portfolios and propose a Gibbs sampling approach to take into account parameter uncertainty. This paper compares the results with a linear benchmark model and estimates without taking into account parameter uncertainty. This paper also checks the predictive power of additional predictive variables.

Incorporating parameter uncertainty and taking into account the possible regime shifts in the returns process, this paper finds that such investors can allocate less in the long run to stocks. This holds true for both the NASDAQ portfolio and the individual high tech and manufacturing industry portfolios. Along with regime switching returns, this paper examines dividend yields and Treasury bill rates as potential predictor variables, and conclude that their predictive effect is minimal: the allocation to stocks in the long run is still generally smaller.

Studying the effect of regime switching behavior in returns on the optimal portfolio choice with parameter uncertainty is our main contribution.

This paper aims to focus on the assessment of the ability of computer models with imperfect functional forms and uncertain input parameters to represent reality.

In this assessment, both the agreement between a model’s predictions and available experiments and the robustness of this agreement to uncertainty have been evaluated. The concept of satisfying boundaries to represent input parameter sets that yield model predictions with acceptable fidelity to observed experiments has been introduced.

Satisfying boundaries provide several useful indicators for model assessment, and when calculated for varying fidelity thresholds and input parameter uncertainties, reveal the trade-off between the robustness to uncertainty in model parameters, the threshold for satisfactory fidelity and the probability of satisfying the given fidelity threshold. Using a controlled case-study example, important modeling decisions such as acceptable level of uncertainty, fidelity requirements and resource allocation for additional experiments are shown.

Traditional methods of model assessment are solely based on fidelity to experiments, leading to a single parameter set that is considered fidelity-optimal, which essentially represents the values which yield the optimal compensation between various sources of errors and uncertainties. Rather than maximizing fidelity, this study advocates for basing model assessment on the model’s ability to satisfy a required fidelity (or error tolerance). Evaluating the trade-off between error tolerance, parameter uncertainty and probability of satisfying this predefined error threshold provides us with a powerful tool for model assessment and resource allocation.

The uncertainty evaluation for coordinate measuring machine metrology is problematic due to the diversity of the parameters that can influence the measurement result. From discrete coordinate data taken on curve (or surface) the software of these machines proceeds to an identification of the measured feature, the parameters of the substitute feature serve in the phase of calculation to estimate the form error of form, and the decisions made based on the result measurement may be outliers when the uncertainty associated to the measurement result is not taken into account. The paper aims to discuss these issues.

The authors relied on the orthogonal distance regression (ODR) algorithm to estimate the parameters of the substitute geometrical elements and their uncertainties. The solution of the problem is resolved by an iterative calculation according to the Levenberg Marquard optimization method. The authors have also presented in this paper the propagation model of uncertainties to the circularity error. This model is based on the law of propagation of the uncertainties defined in the GUM.

This work proposes a model based on ODR to estimates parameters of the substitute geometrical elements and their uncertainties. This contribution allows us to estimate the uncertaintof the form error by applying the law of propagation of uncertainties. An example of calculating the circularity error and the associated uncertainty is explained. This method can be applied to others geometry type: line, plan, sphere, cylinder and cone.

This work interested manufacturing firms by allowing them: to meet the normative, which requires that each measurement must be accompanied by its uncertainty-in conformity assessment, the decision-making must take account of this uncertainty to avoid the aberrant decisions. Informing the operators on the capability of their measurement process

This work proposes a model based on ODR to estimates parameters of the substitute geometrical elements and its uncertainties. without the hypothesis of small displacements torsor, this method integrates the uncertainty on the coordinates of points and can be applied in any reference placemark. This contribution allows us also to estimate the uncertainty of the form error by applying the law of propagation of uncertainties.

Aiming at the problems of poor accuracy and limitation in strength assessment of spot welding vehicle body caused by uncertain factors, such as key component size and nugget diameter, the numerical models of strength uncertainty analysis of spot-welded joints were constructed based on evidence theory and fuzzy theory.

Evidence theory and fuzzy theory are used to deal with the uncertainty of design parameter, and differential evolution algorithms are used to calculate the propagation process of uncertainty in this model. Furthermore, efficient relationship between the strength of welded joints and each design parameter is constructed by using response surface proxy model, which effectively avoids the problem of repeated complex finite element analysis in uncertainty analysis.

The results show that the constructed uncertainty numerical model is effective for the multiple uncertainties and give interval results under different probabilities and affiliations, which can more effectively evaluate the strength of the welded body structure to avoid overly conservative estimates for deterministic design.

The evidence theory is improved and combined with differential evolution algorithm and response surface method to effectively improve the computational efficiency. Based on the improved evidence theory and fuzzy algorithm, the numerical models for the uncertainty analysis of solder joint strength of welded structures are constructed and their feasibility is verified.

For the measurement of large-scale components in aircraft assembly, the evaluation of coordinate transformation parameters between the coordinate frames of individual measurement systems to the assembly frame is an essential task, which is usually completed by registration of the enhanced reference system (ERS) points. This paper aims to propose an analytical method to evaluate the uncertainties of transformation parameters considering both the measurement error and the deployment error of ERS points.

For each measuring station, the measured coordinates of ERS points are first roughly registered to the assembly coordinate system using the singular value decomposition method. Then, a linear transformation model considering the measurement error and deployment error of ERS points is developed, and the analytical solution of transformation parameters’ uncertainties is derived. Moreover, the covariance matrix of each ERS points in the transformation evaluation is calculated based on a new uncertainty ellipsoid model and variance-covariance propagation law.

For the transformation of both single and multiple measuring stations, the derived uncertainties of transformation parameters by the proposed analytical method are identical to that obtained by the state-of-the-art iterative method, but the solution process is simpler, and the computation expenses are much less.

The proposed uncertainty evaluation method would be useful for in-site measurement and optimization of the configuration of ERS points in the design of fixture and large assembly field. It could also be applied to other registration applications with errors on both sides of registration points.

Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components.

First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory.

Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods.

In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements.

The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

This study aims to design a proper supply chain network for the vaccine industry in Iran, which considers several features such as uncertainties in demands and cost, perishability of vaccines, wastages in storage, limited capacity and different priorities for demands.

This study presents a mixed-integer linear programming (MILP) model and using a robust counterpart approach for coping with uncertainties of model.

The presented robust model in comparison with the deterministic model has a better performance and is more reliable for network design of vaccine supply chain.

This study considers uncertainty in the network design of vaccine supply chain for the first time in the vaccine context It presents an MILP model where strategic decisions for each echelon and tactical decisions among different echelons of supply chain are determined. Further, it models the difference between high- and low-priority demands for vaccine.

Reliability models are generally estimated from small samples. This paper seeks to calculate the uncertainty affecting reliability parameters in function of the sample size.

The confidence intervals are calculated on the basis of Monte Carlo simulations and using the variance‐covariance matrix; the two methods are compared.

Numerical results for the estimation of uncertainty have been obtained for standard reliability models, non‐homogeneous Poisson process and generalized renewal process.

For the generalized renewal process, the article points out the influence of the age correction factor on the number of repairs authorized and on uncertainty. The surface plot of the likelihood function with respect to parameters is a convenient tool to interpret the uncertainty.

The main purpose of this research is to find an optimal allocation of marketing budgets which maximizes customer equity in an uncertain environment. Since markets are naturally uncertain environments, the aim is to incorporate uncertainty into the model.

Researchers have developed a mathematical programming model which employs customer equity as an objective function in order to allocate marketing budgets. The robust optimization approach is employed to tackle the proposed model, which deals with uncertainty.

The solution of the robust model is shown to be feasible and satisfactory in all uncertain situations. The robust solutions (of the presented model) are stable in volatile situations; while if the solution of deterministic models is used, it may be suboptimal or even infeasible. Sensitivity analysis of the deterministic solution only describes how stable is the suggested solution, but a robust optimization approach always provides a stable solution.

The presented model will be most effective where uncertainty is high; if uncertainty is not a matter of concern or estimates are reliable, deterministic models are also effective.

Companies periodically decide on marketing budgets in order to achieve predefined marketing targets in future periods. The results of this research may be useful and applicable in marketing departments for allocating marketing budgets, especially in uncertain environments.

The main contribution of this research lies in providing an approach to allocate marketing budgets in uncertain environments. Unlike previous studies, the presented method takes into account the uncertainty of parameters in a systematic way. Hence, in case of high degrees of uncertainty, the use of robust optimization is strictly recommended.