Adaptive Percolation Using Subjective Likelihoods

A phenomenon that I call “adaptive percolation” commonly arises in biology, business, economics, defense, finance, manufacturing, and the social sciences. Here one wishes to select a handful of entities from a large pool of entities via a process of screening through a hierarchy of sieves. The process is not unlike the percolation of a liquid through a porous medium. The probability model developed here is based on a nested and adaptive Bayesian approach that results in the product of beta-binomial distributions with common parameters. The common parameters happen to be the observed data. I call this the percolated beta-binomial distribution . The model turns out to be a slight generalization of the probabilistic model used in percolation theory. The generalization is a consequence of using a subjectively specified likelihood function to construct a probability model. The notion of using likelihoods for constructing probability models is not a part of the conventional toolkit of applied probabilists. To the best of my knowledge, a use of the product of beta-binomial distributions as a probability model for Bernoulli trials appears to be new. The development of the material of this article is illustrated via data from the 2009 astronaut selection program, which motivated this work.     

水平井九点井网产能研究

从基本的渗流理论(保角变换、镜像反映、叠加原理等理论)出发,推导出了三种水平井九点井网产能计算公式,并与电解模型实验结果进行了对比验证。结果表明,计算公式具有一定的精度,完全可以满足工程的需要。     

一种吸渗曲线测定新方法

本丈针对致密宕样吸渗曲线测定误差大的问题,提出丁-种新测定方法,并对该方法的原理、实鉴情况作了较详细介绍.实脸表明该方法测定精度高,简单易行。     

Diffusion in small worlds with homophily and social reinforcement: A theoretical model

We introduce homophily in a percolation model of word-of-mouth diffusion in social networks by reorganizing the nodes according to similarity in preferences for adoption of an innovation. Such preferences are described by a “minimum utility requirement” for an agent to adopt. We show that homophily removes the non-linear relation between preferences and diffusion in the standard percolation model with a high diffusion regime (“hit”) and a low diffusion regime (“flop”). Instead, in a model with perfect homophily, the final diffusion scales linearly with individual preferences: all agents who are willing to adopt, do adopt the innovation. We also investigate the combined effect of homophily and social reinforcement in diffusion. Results indicate that social reinforcement renders clustered networks more efficient in terms of diffusion size for network with strong homophily, while the opposite is true for networks without homophily. The simple structure of our model allows to disentangle the effect of social influence, homophily and the network structure on diffusion. However, the controllability of the theoretical structure comes at the expenses of the realism of the model. For this, we discuss possible extensions and empirical applications.