(2015-05) Wang, Mengjie; Walker, Stephen G., 1945-; Lin, Lizhen

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There are numerous frequentist statistics variable selection methods such as Stepwise regression, AIC and BIC etc. In particular, the latter two criteria include a penalty term which discourages overfitting. In terms of the framework of Bayesian variable selection, a popular approach is using Bayes Factor (Kass & Raftery 1995), which also has a natural built-in penalty term (Berger & Pericchi 2001). Zellner's g prior (Zellner 1986) is a common prior for coefficients in the linear regression model due to its computational speed of analytic solutions for posterior. However, the choice of g is a problem which has attracted a lot of attention. (Zellner 1986) pointed out that if g is unknown, a prior can be introduced and g can be integrated out. One of the prior choices is Hyper-g Priors proposed by (Liang et al. 2008). Instead of proposing a prior for g, we will assign a fixed value for g based on controlling the Type I error for the test based on the Bayes factor. Since we are using Bayes factor to do model selection, the test statistic is Bayes factor. Every test comes with a Type I error, so it is reasonable to restrict this error under a critical value, which we will take as benchmark values, such as 0.1 or 0.05. This approach will automatically involve setting a value of g. Based on this idea, a fixed g can be selected, hence avoiding the need to find a prior for g.

(2013-12) Boretz, Yingyue Li; Reichl, Linda E.; Petrosky, Tomio Y.

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We demonstrate the existence of tunable bound-states in continuum (BIC) in a 1-dimensional quantum wire with two impurities by an intense monochromatic radiation field. We found that there is a new type of BIC due to the Fano interference between two optical transition channels, in addition to the ordinary BIC due to a geometrical interference between electron wave functions emitted by impurities. In both cases the BIC can be achieved by tuning the frequency of the radiation field.