Author Correction: Robust MFC anti-windup scheme for LTI systems with norm-bounded uncertainty

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Estimating the Distribution of Treatment Effects From Random Design Experiments

Background: Random design experiments are a powerful device for estimating average treatment effects, but evaluators sometimes seek to estimate the distribution of treatment effects. For example, an evaluator might seek to learn the proportion of treated units who benefit from treatment, the proportion who receive no benefit, and the proportion who are harmed by treatment. Method: Imbens and Rubin (I&R) recommend a Bayesian approach to drawing inferences about the distribution of treatment effects. Drawing on the I&R recommendations, this article explains the approach; provides computing algorithms for continuous, binary, ordered and countable outcomes; and offers simulated and real-world illustrations. Results: This article shows how the I&R approach leads to bounded uncertainty intervals for summary measures of the distribution of treatment effects. It clarifies the nature of those bounds and shows that they are typically informative. Conclusions: Despite identification issues, bounded solutions provide useful insight into the distribution of treatment effects. We recommend that evaluators incorporate analyses of the distribution of treatment effects into new studies and that evaluators revisit completed studies to estimate the distribution of treatment effects.

Modified First-Order Compound Function-Based Interval Perturbation Method for Luffing Angular Response of Dual Automobile Crane System With Interval Variables

The accuracy of conventional crane engineering problems with bounded uncertainty is limited to cases where only first-order terms are retained. However, the impact of high-order terms on the luffing angular response (LAR) may be significant when it comes to compound functions. A modified first-order compound-function-based interval perturbation method (MFCFIPM) is proposed for the prediction of the LAR field of a dual automobile crane system (DACS) with narrowly bounded uncertainty. In an interval model, all uncertain variables with bounded uncertainty comprise an interval vector. The equilibrium equations of the interval LAR vectors of the DACS are established based on the interval model. The MFCFIPM employs the surface rail generation method to expand the compound-function-based vectors. A modified Sherman–Morrison–Woodbury formula is introduced to analyze the impact of the high-order terms of the Neumann series expansion on the LAR field. Several numerical examples are presented to verify the accuracy and the feasibility of the MFCFIPM. The results show that the MFCFIPM can achieve a better accuracy than the first-order compound-function-based interval perturbation method and a higher efficiency than the Monte Carlo method for the LAR field problem with narrow interval variables. The effects of different numbers of interval variables on the LAR field by the MFCFIPM are also investigated.