Asymptotics of Continuous Bayes for Non-i.i.d. Sources
نویسندگان
چکیده
Clarke and Barron analysed the relative entropy between an i.i.d. source and a Bayesian mixture over a continuous class containing that source. In this paper a comparable result is obtained when the source is permitted to be both non-stationary and dependent. The main theorem shows that Bayesian methods perform well for both compression and sequence prediction even in this most general setting with only mild technical assumptions.
منابع مشابه
Refined Asymptotics for Rate-Distortion using Gaussian Codebooks for Arbitrary Sources
The rate-distortion saddle-point problem considered by Lapidoth (1997) consists in finding the minimum rate to compress an arbitrary ergodic source when one is constrained to use a random Gaussian codebook and minimum (Euclidean) distance encoding is employed. We extend Lapidoth’s analysis in several directions in this paper. Firstly, we consider refined asymptotics. In particular, when the sou...
متن کاملLimiting Shape for Directed Percolation Models
We consider directed first-passage and last-passage percolation on the non-negative lattice Zd+, d ≥ 2, with i.i.d. weights at the vertices. Under certain moment conditions on the common distribution of the weights, the limits g(x) = limn→∞ n T (⌊nx⌋) exist and are constant a.s. for x ∈ Rd+, where T (z) is the passage time from the origin to the vertex z ∈ Zd+. We show that this shape function ...
متن کاملGeneralization of discrimination-rate theorems of Chernoff and Stein
We consider a simple hypothesis and alternative about an abstract random observation parametrized by A from a directed set A. The asymptotics over A is evaluated for mixed errors of the Bayes tests and second kind errors of the Neyman-Pearson tests. Similar asymptotics has been first evaluated by H. ChernofT and Ch. Stein when A is the set of naturals and the observation consists of the first X...
متن کاملA short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights
We obtain some new results concerning the small deviation problem for S = ∑ n q Xn and M = supn q Xn, where 0 < q < 1 and (Xn) are i.i.d. non-negative random variables. In particular, the asymptotics is shown to be the same for S and M in some cases.
متن کاملFine Asymptotics for Universal One-to-One Compression of Parametric Sources
Universal source coding at short blocklengths is considered for an exponential family of distributions. The Type Size code has previously been shown to be optimal up to the third-order rate for universal compression of all memoryless sources over finite alphabets. The Type Size code assigns sequences ordered based on their type class sizes to binary strings ordered lexicographically. To general...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1411.2918 شماره
صفحات -
تاریخ انتشار 2014