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We study online learning under logarithmic loss with regular parametric models. Hedayati and Bartlett (2012b) showed that a Bayesian prediction strategy with Jeffreys prior and sequential normalized m...
The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinitely imbalanced. In this paper, it is shown that this phenomenon is universal ...
The paper derives a minimax lower bound for rates of convergence for an infinite-dimensional parameter in an exponential family model. An estimator that achieves the optimal rate is constructed by m...
Two members of an exponential family can be represented as two points in the natural parameter space of that family or as two points in the expectation parameter space. The theorem describes a simp...
Modified eonjugate families OF prior distributiorrs are ia-uestigatcd and their propefiies are examined in the context d applica~ ons trr admissible md mi-dx eestEmatiaa far the general cxponentid ...
There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with...
When in a full exponential family the maximum likelihood estimate (MLE) does not exist, the MLE may exist in the Barndorff-Nielsen completion of the family. We propose a practical algorithm for findin...
In large scale multiple testing, the use of an empirical null distribution rather than the theoretical null distribution can be critical for correct inference. This paper proposes a “mode matching” ...
When in a full exponential family the maximum likelihood estimate (MLE) does not exist, the MLE may exist in the Barndorff-Nielsen completion of the family. We propose a practical algorithm for find...
There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with...
We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate ...
Let K be a reversible Markov kernel on a measurable space (S,B) with stationary distribution P. Regard K as a linear operator, K:L2(P)→L2(P), and suppose that L2(P) admits an orthonormal basis of ...
We are thankful to the discussants for their hard, interesting work. The main purpose of our paper was to give reasonably sharp rates of convergence for some simple examples of the Gibbs sampler. We...

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