A Graphical Tool For Assessing The Suitabilty Of A Count Regression Model

Whilst many numeric methods, such as AIC and deviance, exist for assessing or comparing model fit, diagrammatic methods are few. We present here a diagnostic plot, which we refer to as a `Quantile Band plot', that may be used to visually assess the suitability of a given count data model. In the case of diagnosed model inadequacy, the plot has the unique feature of conveying precise information on the character of the violation, hence pointing the data analyst towards a potentially better model choice.

Causal inference from data. On some inadequacy problems of structures with hidden causes

The reliability of causal inference from data (by independence-based methods) is analyzed. We uncover some mechanisms which may result in model inadequacy due to sample bias and hidden variables. We detect some specific problems in recognition of direction of influence when some causes are hidden. Incorrectness of known rule for edge orientation (under causal insufficiency) is revealed. We suggest the correction to the rule aiming to retain model adequacy.

Checking Model Adequacy for Count Time Series by Using Pearson Residuals

After having fitted a model to a given count time series, one has to check the adequacy of this model fit. The (standardized) Pearson residuals, being easy to compute and interpret, are a popular diagnostic approach for this purpose. But which types of model inadequacy might be uncovered by which statistics based on the Pearson residuals? In view of being able to apply such statistics in practice, it is also crucial to ask for the properties of these statistics under model adequacy. We look for answers to these questions by means of a comprehensive simulation study, which considers diverse types of count time series models and inadequacy scenarios. We illustrate our findings with two real-data examples about strikes in the U.S., and about corporate insolvencies in the districts of Rhineland–Palatinate. We conclude with a theoretical discussion of Pearson residuals.

Using Statistical Calibration for Model Verification and Validation, Diagnosis of Model Inadequacy, and Improving Simulation Accuracy

The paper presents an application of statistical calibration techniques to a bracket design fatigue model simulated in COMSOL Multiphysics®. The calibration will tune the bracket’s material properties and fatigue characteristics. For illustrative purposes, the test data used to calibrate the simulation model will be generated from the same simulation routine with the addition of an intentionally applied bias and random noise to simulate model form and physical testing errors. The accuracy and conclusions from the statistically calibrated model will be compared with the uncalibrated model as well as a model calibrated with conventional error minimization methods. Multiple metrics will be shown which can be used for model validation, including a discrepancy map which characterizes inadequacies in the simulation. The metrics used in the comparison will also include results from optimization, sensitivity analysis, and propagation of uncertainties motivated by manufacturing variations during bracket fabrication. The results will demonstrate the importance of calibrating a model before drawing design conclusions.

Model Uncertainty Approximation Using a Copula-Based Approach for Reliability Based Design Optimization

Reliability-based design optimization (RBDO) has been widely used to design engineering products with minimum cost function while meeting defined reliability constraints. Although uncertainties, such as aleatory uncertainty and epistemic uncertainty, have been well considered in RBDO, they are mainly considered for model input parameters. Model uncertainty, i.e., the uncertainty of model bias which indicates the inherent model inadequacy for representing the real physical system, is typically overlooked in RBDO. This paper addresses model uncertainty characterization in a defined product design space and further integrates the model uncertainty into RBDO. In particular, a copula-based bias correction approach is proposed and results are demonstrated by two vehicle design case studies.