Empirical Bayes Method for Boltzmann Machines

The framework of the empirical Bayes method allows the estimation of the values of the hyperparameters in the Boltzmann machine by maximizing a specific likelihood function referred to as the empirical Bayes likelihood function. However, the maximization is computationally difficult because the empirical Bayes likelihood function involves intractable integrations of the partition function. The method presented in this chapter avoids this computational problem by using the replica method and the Plefka expansion, which is quite simple and fast because it does not require any iterative procedures and gives reasonable estimates under certain conditions.

Identifying Expressway Accident Black Spots Based on the Secondary Division of Road Units

For the purpose of reducing the harm of expressway traffic accidents and improving the accuracy of traffic accident black spots identification, this paper proposes a method for black spots identification of expressway accidents based on road unit secondary division and empirical Bayes method. Based on the modelling ideas of expressway accident prediction models in HSM (Highway Safety Manual), an expressway accident prediction model is established as a prior distribution and combined with empirical Bayes method safety estimation to obtain a Bayes posterior estimate. The posterior estimated value is substituted into the quality control method to obtain the black spots identification threshold. Finally, combining the Xi'an-Baoji expressway related data and using the method proposed in this paper, a case study of Xibao Expressway is carried out, and sections 9, 19, and 25 of Xibao Expressway are identified as black spots. The results show that the method of secondary segmentation based on dynamic clustering can objectively describe the concentration and dispersion of accident spots on the expressway, and the proposed black point recognition method based on empirical Bayes method can accurately identify accident black spots. The research results of this paper can provide a basis for decision-making of expressway management departments, take targeted safety improvement measures.

Pemetaan Risiko Penyakit Tuberkulosis (TBC) di Kota Surakarta dengan Spatial Empirical Bayes

<p>Tuberculosis is an infectious disease that can attack human with a poor immune system. In 2017, there were 723 residents of Surakarta tested positive for tuberculosis. The spatial empirical Bayes method is a good method for mapping the risk of tuberculosis because this method includes spatial dependency information and can overcome small area problems. This method can help the prevention of tuberculosis in Surakarta. In the analysis, it was found that the number of cases of tuberculosis in Surakarta has a spatial dependency that has an impact of the spread of tuberculosis. Sub-district classification with the highest risk value is Jebres, Tegalharjo, Jajar, Laweyan, Sondakan, Purwosari, Mangkubumen, Keratonan, Timuran, and Punggawan.</p><p><strong>Keywords</strong> : tuberculosis, mapping, spatial empirical Bayes, Surakarta</p>

Safety Effects of Freeway Hard Shoulder Running

Hard shoulder running (HSR) has been increasingly used as a sustainable and viable way to increase road capacity. This study investigated the safety effect of HSR on freeways in South Korea using the empirical Bayes method. This study found an increase in the total number of crashes. In terms of crash severity, a higher proportion of crashes (25.3%) on 2(3)-lane sections were found to be serious (involving injuries and/or fatalities) compared to those on 4(5)-lane sections (3.6%). Also, a positive relationship was found between the length of the hard shoulder running and changes in crash frequencies. Thus, hard shoulder running on lengthy 2(3)-lane freeways should be avoided.