What are the natural loss functions for binary class probability estimation? This question has a simple answer: so-called "proper scoring rules". These loss functions, known from subjective probability, measure the discrepancy between true probabilities and estimates thereof. They comprise all...

Despite the widespread use of graphs in empirical research, little is known about readers' ability to process the statistical information they are meant to convey ("visual inference"). We study visual inference within the context of regression discontinuity (RD) designs by measuring how...

Identification in a regression discontinuity (RD) design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known threshold. If the assignment variable is measured with error, however, the discontinuity in the first stage relationship...

In this paper, we show that noise can transform a hybrid neural networks, whose solution may grow exponentially, into a new stochastic one, whose solution grows at most polynomially. In other words, we reveal that noise can suppress the exponential growth in hybrid Hopfield neural networks.

In this paper, we propose a weighted modularity QW based on the similarity of weights on edges and a threshold coefficient ζ to evaluate the equivalence of edge weights. Simulations on benchmark networks and real networks show that optimization on the modularity enable us to obtain groups of...

In this paper, we focus on the search ability of Brownian particles with an adaptive mechanism. In the adaptive mechanism, nodes are allowed to be able to change their own accepting probability according to their congestion states. Two searching-traffic models, the static one in which nodes have...

The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching. Linear NSDDEs with Markovian switching and nonlinear examples will be discussed to illustrate the theory.