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CONJUGATE PRIORS FOR EXPONENTIAL FAMILIES
Random vector distribution natural parameter parameters
2015/7/15
Let X be a random vector distributed according to an exponential family
with natural parameter 0 E O.We characterize conjugate prior measures on O
through the property of linear posterior expectat...
Gibbs Sampling, Exponential Families and Orthogonal Polynomials
Family convergence rate gibbs sampler standard index
2015/7/8
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 pri...
Horizon-Independent Optimal Prediction with Log-Loss in Exponential Families
SNML Exchangeability Exponential Family Online Learning Logarithmic Loss Bayesian Strategy Jeffreys Prior Fisher Information
2013/6/17
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...
Infinitely imbalanced binomial regression and deformed exponential families
binomial regression extreme value theory imbalanced data Poisson point process q-exponential family
2013/4/28
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 ...
Functional Regression for General Exponential Families
Functional Regression General Exponential Families
2010/3/9
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...
Natural and modified conjugate priors in exponential families of stochastic processes
Natural and modified conjugate exponential families stochastic processes
2009/9/21
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
...
On the geometry of discrete exponential families with application to exponential random graph models
Exponential families normal cone maximum likelihood estimates exponential random graphs
2009/9/16
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...
Likelihood inference in exponential families and directions of recession
exponential family existence of maximum likelihood estimate BarndorffNielsen completion
2009/9/16
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...
Empirical null and false discovery rate inference for exponential families
Multiple testing multiple comparisons mixture model Poissonregression genome-wide association brain imaging
2010/3/17
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” ...
Likelihood Inference in Exponential Families and Directions of Recession
exponential family existence of maximum likelihood estimate Barndorff-Nielsen completion
2010/3/17
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...
On the Geometry of Discrete Exponential Families with Application to Exponential Random Graph Models
Geometry Discrete Exponential Families Exponential Random Graph Models
2010/3/17
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...
Gibbs Sampling，Exponential Families and Orthogonal Polynomials
Gibbs sampler running time analyses exponential families conjugate priors location families orthogonal polynomials
2010/4/30
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
...
Comment：Gibbs Sampling，Exponential Families and Orthogonal Polynomials
Comment Gibbs Sampling Exponential Families Orthogonal Polynomials
2010/4/30
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 ...
Rejoinder：Gibbs Sampling，Exponential Families and Orthogonal Polynomials
Rejoinder Gibbs Sampling Exponential Families Orthogonal Polynomials
2010/4/30
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...