Testing hypotheses for Markov chains when the parameter space is finite
نویسندگان
چکیده
منابع مشابه
When Can Finite Testing Ensure Infinite Trustworthiness?
In this paper we contribute to the general philosophical question as to whether empirical testing can ever prove a physical law. Problems that lead to this question arise under several contexts, and the matter has been addressed by the likes of Bayes and Laplace. After pointing out that a Bayesian approach is the proper way to address this problem, we show that the answ...
متن کاملFinite Markov Chains
This paper provides basic information and theorems about finite Markov chains. The inspiration for this paper came from Professor Laci Babai’s Discrete Mathematics lecture notes from the REU program of 2003. After reading through his chapter on Markov chains, I decided to proceed by answering as many exercises from the notes as possible. Below is what I have finished.
متن کاملParameter Synthesis for Parametric Interval Markov Chains
Interval Markov Chains (IMCs) are the base of a classic probabilistic specification theory introduced by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems. In this paper we study parameter synthesis for a parametric extension of Interval Markov Chains in which the endpoints of intervals may be replaced with parameters. In particular, we propose constructi...
متن کاملTaylor Expansion for the Entropy Rate of Hidden Markov Chains
We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...
متن کاملThe Rate of Rényi Entropy for Irreducible Markov Chains
In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.
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: Kodai Mathematical Journal
سال: 1963
ISSN: 0386-5991
DOI: 10.2996/kmj/1138844784