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Identifying several biased coins encountered by a hidden random walk
Author(s) -
Levin David A.,
Peres Yuval
Publication year - 2004
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20018
Subject(s) - random walk , coin flipping , path (computing) , position (finance) , simple (philosophy) , reflection (computer programming) , mathematics , struct , simple random sample , combinatorics , computer science , algorithm , statistics , philosophy , epistemology , economics , sociology , population , demography , finance , programming language
Suppose that attached to each site z ∈ ℤ is a coin with bias θ( z ), and only finitely many of these coins have nonzero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its current position. Then we can determine the biases {θ( z )} z ∈ℤ , using only the outcomes of these coin tosses and no information about the path of the random walker , up to a shift and reflection of ℤ. This generalizes a result of Harris and Keane. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004