Min-BDeu and Max-BDeu Scores for Learning Bayesian Networks

This work presents two new score functions based on the Bayesian Dirichlet equivalent uniform (BDeu) score for learning Bayesian network structures. They consider the sensitivity of BDeu to varying parameters of the Dirichlet prior. The scores take on the most adversary and the most beneficial priors among those within a contamination set around the symmetric one. We build these scores in such way that they are decomposable and can be computed efficiently. Because of that, they can be integrated into any state-of-the-art structure learning method that explores the space of directed acyclic graphs and allows decomposable scores. Empirical results suggest that our scores outperform the standard BDeu score in terms of the likelihood of unseen data and in terms of edge discovery with respect to the true network, at least when the training sample size is small. We discuss the relation between these new scores and the accuracy of inferred models. Moreover, our new criteria can be used to identify the amount of data after which learning is saturated, that is, additional data are of little help to improve the resulting model.

Max Weber and the First World War: Protestant and Catholic living standards in Germany, 1914-1919

We assess informal institutions of Protestants and Catholics by investigating their economic resilience in a natural experiment. The First World War constitutes an exogenous shock to living standards since the duration and intensity of the war exceeded all expectations. We assess the ability of Protestant and Catholic communities to cope with increasing food prices and wartime black markets. Literature based on Weber (1904, 1905) suggests that Protestants must be more resilient than their Catholic peers. Using individual height data on some 2,800 Germans to assess levels of malnutrition during the war, we find that living standards for both Protestants and Catholics declined; however, the decrease of Catholics’ height was disproportionately large. Our empirical analysis finds a large statistically significant difference between Protestants and Catholics for the 1915–19 birth cohort, and we argue that this height gap cannot be attributed to socioeconomic background and fertility alone.

Max Weber and the First World War: Protestant and Catholic living standards in Germany, 1915-1919

We assess informal institutions of Protestants and Catholics by investigating their economic
resilience in a natural experiment. The First World War constitutes an exogenous shock to living standards since the duration and intensity of the war exceeded all expectations. We assess the ability of Protestant and Catholic communities to cope with increasing food prices and wartime black markets. Literature based on Weber (1904, 1905) suggests that Protestants must be more resilient than their Catholic peers. Using individual height data on some 2,800 Germans to assess levels of malnutrition during the war, we find that living standards for both Protestants and Catholics declined; however, the decrease of Catholics’ height was disproportionately large. Our empirical analysis finds a large statistically significant difference between Protestants and Catholics for the 1914-19 birth cohort, and we argue that this height gap cannot be attributed to socioeconomic background and fertility alone.

Scaled Heavy-Ball Acceleration of the Richardson-Lucy Algorithm for 3D Microscopy Image Restoration

The Richardson–Lucy algorithm is one of the most important in image deconvolution. However, a drawback is its slow convergence. A significant acceleration was obtained using the technique proposed by Biggs and Andrews (BA), which is implemented in the deconvlucy function of the image processing MATLAB toolbox. The BA method was developed heuristically with no proof of convergence. In this paper, we introduce the heavy-ball (H-B) method for Poisson data optimization and extend it to a scaled H-B method, which includes the BA method as a special case. The method has a proof of the convergence rateof O(K^2), where k is the number of iterations. We demonstrate the superior convergence performance, by a speedup factor off ive, of the scaled H-B method on both synthetic and real 3D images.