Basic Empathy Scale: A Systematic Review and Reliability Generalization Meta-Analysis

The Basic Empathy Scale (BES) has been internationally used to measure empathy. A systematic review including 74 articles that implement the instrument since its development in 2006 was carried out. Moreover, an evidence validity analysis and a reliability generalization meta-analysis were performed to examine if the scale presented the appropriate values to justify its application. Results from the systematic review showed that the use of the BES is increasing, although the research areas in which it is being implemented are currently being broadened. The validity analyses indicated that both the type of factor analysis and reliability are reported in validation studies much more than the consequences of testing are. Regarding the meta-analysis results, the mean of Cronbach’s α for cognitive empathy was 0.81 (95% CI: 0.77–0.85), with high levels of heterogeneity (I2 = 98.81%). Regarding affective empathy, the mean of Cronbach’s α was 0.81 (95% CI: 0.76–0.84), with high levels of heterogeneity. It was concluded that BES is appropriate to be used in general population groups, although not recommended for clinical diagnosis; and there is a moderate to high heterogeneity in the mean of Cronbach’s α. The practical implications of the results in mean estimation and heterogeneity are discussed.

A Bayesian analysis of classical shadows

The method of classical shadows proposed by Huang, Kueng, and Preskill heralds remarkable opportunities for quantum estimation with limited measurements. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations—such as high-fidelity ground truth states—which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.

On Using the Conventional and Nonconventional Measures of the Auxiliary Variable for Mean Estimation

In this paper, we propose an improved new class of exponential-ratio-type estimators for estimating the finite population mean using the conventional and the nonconventional measures of the auxiliary variable. Expressions for the bias and MSE are obtained under large sample approximation. Both simulation and numerical studies are conducted to validate the theoretical findings. Use of the conventional and the nonconventional measures of the auxiliary variable is very common in survey research, but we observe that this does not add much value in many of the estimators except for our proposed class of estimators.

Diffusion Adaptive Filtering Algorithm Based on the Fair Cost Function

To better perform distributed estimation, this paper, by combining the Fair cost function and adapt-then-combine scheme at all distributed network nodes, a novel diffusion adaptive estimation algorithm is proposed from an M-estimator perspective, which is called the diffusion Fair (DFair) adaptive filtering algorithm. The stability of the mean estimation error and the computational complexity of the DFair are theoretically analyzed. Compared with the RDLMS, DNLMM, DGCLD, and DPLMS algorithms, the simulation experiment results show that the DFair algorithm is more robust to input signals and impulsive interference. In conclusion, Theoretical analysis and simulation results show that the DFair algorithm performs better when estimating an unknown linear system in the changeable impulsive interference environments.