The Bayes Estimators of the Variance and Scale Parameters of the Normal Model With a Known Mean for the Conjugate and Noninformative Priors Under Stein’s Loss

For the normal model with a known mean, the Bayes estimation of the variance parameter under the conjugate prior is studied in Lehmann and Casella (1998) and Mao and Tang (2012). However, they only calculate the Bayes estimator with respect to a conjugate prior under the squared error loss function. Zhang (2017) calculates the Bayes estimator of the variance parameter of the normal model with a known mean with respect to the conjugate prior under Stein’s loss function which penalizes gross overestimation and gross underestimation equally, and the corresponding Posterior Expected Stein’s Loss (PESL). Motivated by their works, we have calculated the Bayes estimators of the variance parameter with respect to the noninformative (Jeffreys’s, reference, and matching) priors under Stein’s loss function, and the corresponding PESLs. Moreover, we have calculated the Bayes estimators of the scale parameter with respect to the conjugate and noninformative priors under Stein’s loss function, and the corresponding PESLs. The quantities (prior, posterior, three posterior expectations, two Bayes estimators, and two PESLs) and expressions of the variance and scale parameters of the model for the conjugate and noninformative priors are summarized in two tables. After that, the numerical simulations are carried out to exemplify the theoretical findings. Finally, we calculate the Bayes estimators and the PESLs of the variance and scale parameters of the S&P 500 monthly simple returns for the conjugate and noninformative priors.

The Compound Inverse Rayleigh as an Extreme Wind Speed Distribution and its Bayes Estimation

The paper deals with the Compound Inverse Rayleigh distribution, shown to constitute a proper model for the characterization of the probability distribution of extreme values of wind-speed, a topic which is gaining growing interest in the field of renewable generation assessment, both in view of wind power production evaluation and the wind-tower mechanical reliability and safety. The first part of the paper illustrates such model starting from its origin as a generalization of the Inverse Rayleigh model - already proven to be a valid model for extreme wind-speeds - by means of a continuous mixture generated by a Gamma distribution on the scale parameter, which gives rise to its name. Moreover, its validity to interpret different field data is illustrated, also by means of numerous numerical examples based upon real wind speed measurements. Then, a novel Bayes approach for the estimation of such extreme wind-speed model is proposed. The method relies upon the assessment of prior information in a practical way, that should be easily available to system engineers. In practice, the method allows to express one’s prior beliefs both in terms of parameters, as customary, and/or in terms of probabilities. The results of a large set of numerical simulations – using typical values of wind-speed parameters - are reported to illustrate the efficiency and the accuracy of the proposed method. The validity of the approach is also verified in terms of its robustness with respect to significant differences compared to the assumed prior information.

Measurement Invariance of Negative Affect in Ambulatory Assessments of Young-Old and Old-Old Adults

Gero-psychological research increasingly considered intense longitudinal assessments of momentary affect to address affective aging. In particular, many studies employed negative emotion item lists for ambulatory assessments of negative affect. However, frequent self-reports on emotion items within short time intervals might change alertness towards and perception of one’s emotional experiences. From an item-response-theoretic point of view, this might impair the stability of item functioning in terms of item discrimination between levels of affectivity and item severity (difficulty). Thus, we examined measurement invariance of negative emotion items commonly used for ambulatory assessments of negative affect. Ambulatory assessments from the EMIL study, obtained over seven consecutive days at six occasions per day from 123 young-old (aged 66-69) and 47 old-old (86-89) adults, were analyzed. Respondents self-reported on 13 negative emotion items, using a 0-100 slider to express the degree to which they felt the respective emotion. We ran multilevel structural equation models with Bayes estimation to analyze variability of negative affect factor loadings, item intercepts, and measurement error variances across repeated measures, thus checking for metric, scalar, and strict factorial invariance. For all sets of parameters, the findings do not strongly support measurement invariance, but point at partial invariance for item subsets. Taking on literature suggesting that criteria for invariance testing should not be too restrictive to meet pragmatic measurement equivalence requirements, further analyses and our conclusions focus on strategies that might allow for acceptable degrees of differential item functioning, enabling reliable analyses of intra-individual short-term variability in negative affect.

Automatic Recognition Algorithm of Information Architecture Reliability Based on Energy Internet Network Topology

As a type of energy network, the scale of the power network is constantly expanding, and its structure has become more and more complicated. Correspondingly, the risks to the energy network are even less likely to be discovered, which will undoubtedly cause great troubles for the safe operation of the network. The traditional manual inspection method can no longer meet the requirements of huge and complex energy networks. Therefore, this paper proposes the algorithm, a research on the automatic identification of reliability of information architecture based on the topology of the energy Internet network. Abstract the server, storage, and other devices in the Energy Internet as network nodes, divide them according to service modules, and use Bayes estimation to evaluate and judge the impact of these nodes on the system function, so as to find the nodes with hidden risks. The results show that, compared with the traditional manual inspection method, the method proposed in this paper can efficiently and accurately find the nodes with risks and can help optimize the topology of the energy Internet network.