Trivial intersection of σ-fields and Gibbs sampling
نویسندگان
چکیده
منابع مشابه
Trivial Intersection of Σ-fields and Gibbs Sampling
Let (Ω,F , P ) be a probability space and N the class of those F ∈ F satisfying P (F ) ∈ {0, 1}. For each G ⊂ F , define G = σ G ∪ N . Necessary and sufficient conditions for A∩B = A ∩ B, where A,B ⊂ F are subσ-fields, are given. These conditions are then applied to the (two component) Gibbs sampler. Suppose X and Y are the coordinate projections on (Ω,F) = (X×Y,U⊗V) where (X ,U) and (Y,V) are ...
متن کاملAtomic Intersection of Σ-fields and Some of Its Consequences
Let (Ω,F , P ) be a probability space. For each G ⊂ F , define G as the σ-field generated by G and those sets F ∈ F satisfying P (F ) ∈ {0, 1}. Conditions for P to be atomic on ∩i=1Ai, with A1, . . . ,Ak ⊂ F sub-σ-fields, are given. Conditions for P to be 0-1-valued on ∩i=1Ai are given as well. These conditions are useful in various fields, including Gibbs sampling, iterated conditional expecta...
متن کاملMarkov Random Fields and Gibbs Sampling for Image Denoising
This project applies Gibbs Sampling based on different Markov Random Fields (MRF) structures to solve the image denoising problem. Compared with methods like gradient ascent, one important advantage that Gibbs Sampling has is that it provides balances between exploration and exploitation. This project also tested behaviors of different MRF structures, such as the high-order MRFs, various loss f...
متن کاملParallel Gibbs Sampling: From Colored Fields to Thin Junction Trees
We explore the task of constructing a parallel Gibbs sampler, to both improve mixing and the exploration of high likelihood states. Recent work in parallel Gibbs sampling has focused on update schedules which do not guarantee convergence to the intended stationary distribution. In this work, we propose two methods to construct parallel Gibbs samplers guaranteed to draw from the targeted distrib...
متن کاملOn the Exchange of Intersection and Supremum of Σ-fields in Filtering Theory∗ by Ramon
We construct a stationary Markov process with trivial tail σ-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection ...
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: The Annals of Probability
سال: 2008
ISSN: 0091-1798
DOI: 10.1214/07-aop387