Higher Order Expansions for Posterior Distributions Using Posterior Modes
نویسندگان
چکیده
منابع مشابه
The modes of posterior distributions for mixed linear models
Mixed linear models, also known as two-level hierarchical models, are commonly used in many applications. In this paper, we consider the marginal distribution that arises within a Bayesian framework, when the components of variance are integrated out of the joint posterior distribution. We provide analytical tools for describing the surface of the distribution of interest. The main theorem and ...
متن کاملLocal Influence on Posterior Distributions under Multiplicative Modes of Perturbation
Any unperturbed and perturbed posterior density can formally be linked by a mixture. Many divergences between the unperturbed and perturbed posterior density global measures of influence of the perturbation are then essentially determined by the Fisher information with respect to the mixing parameter evaluated at the unperturbed density. It is investigated which aspect of change this Fisher inf...
متن کاملQuantitative Comparisons between Finitary Posterior Distributions and Bayesian Posterior Distributions
Abstract. The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to considering a finite horizon framework. However, assuming infinite exchangeability gives rise to fairly tractable a posteriori quantities, which is very at...
متن کاملPosterior Mapping and Posterior Predictive Distributions
”If we view statistics as a discipline in the service of science, and science as being an attempt to understand (i.e., model) the world around us, then the ability to reveal sensitivity of conclusions from fixed data to various model specifications, all of which are scientifically acceptable, is equivalent to the ability to reveal boundaries of scientific uncertainty. When sharp conclusions are...
متن کاملPosterior consistency for Gaussian process approximations of Bayesian posterior distributions
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior distribution and various approximations based on the Gaussian process emulator. Our analysis includes approximations based on the mean of the predictive process, as w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: JOURNAL OF THE JAPAN STATISTICAL SOCIETY
سال: 2008
ISSN: 1348-6365,1882-2754
DOI: 10.14490/jjss.38.415