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We discuss the paper "Citation Statistics" by the Joint Committee on Quantitative Assessment of Research [arXiv:0910.3529]. In particular, we focus on a necessary feature of "good" measures for ranking scientific authors: that good measures…

For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…

We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning…

These notes are dedicated to whom may be interested in algorithms, Markov chain, coupling, and graph theory etc. I present some preliminaries on coupling and explanations of the important formulas or phrases, which may be helpful for us to…

In astro-ph/0702542v2, Linder and Miquel seek to criticize the use of Bayesian model selection for data analysis and for survey forecasting and design. Their discussion is based on three serious misunderstandings of the conceptual…

The consistency of the Bayesian estimation of a parameter is shown for a class of ergodic discrete Markov chains. J.L. Doob's method was used, offered earlier for the i.i.d. situation. The result may be useful in the reliability theory for…

We settle a conjecture by Bik and Marigliano stating that the degree of a one-dimensional discrete model with rational maximum likelihood estimator is bounded above by a linear function in the size of its support, therefore showing that…

For Bayesian D-optimal design, we define a singular prior distribution for the model parameters as a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such…

We are deeply appreciative of the initiative of the editor, Marina Vanucci, in commissioning a discussion of our paper, and extremely grateful to all the discussants for their insightful and thought-provoking comments. We respond to the…

I would like to thank the authors for their interesting and very clearly presented paper discussing probabilistic solvers for ODEs and PDEs.

We consider the problem of choosing between parametric models for a discrete observable, taking a Bayesian approach in which the within-model prior distributions are allowed to be improper. In order to avoid the ambiguity in the marginal…

This note is a discussion of the article "Bayesian model selection based on proper scoring rules" by A.P. Dawid and M. Musio, to appear in Bayesian Analysis. While appreciating the concepts behind the use of proper scoring rules, including…

Let $n$ be a large integer and $M_n$ be a random $n$ by $n$ matrix whose entries are i.i.d. Bernoulli random variables (each entry is $\pm 1$ with probability 1/2). We show that the probability that $M_n$ is singular is at most $(3/4…

Consider a multinomial regression model where the response, which indicates a unit's membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of…

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate…

The paper sheds a new light on the fundamental theorems of complex analysis due to P. Fatou, F. and M. Riesz, N. N. Lusin, I. I. Privalov, and A. Beurling. Only classical tools available at the times of Fatou are used. The proofs are very…

Previous work on sensitivity analysis in Bayesian networks has focused on single parameters, where the goal is to understand the sensitivity of queries to single parameter changes, and to identify single parameter changes that would enforce…

This paper presents a Bayesian parameter estimation approach and identifiability analysis for a lithium-ion battery model, to determine the uniqueness, evaluate the sensitivity and quantify the uncertainty of a subset of the model…

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…

In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the…