Abstract
In this chapter we discuss basic notions of Markov chains and their use for numerical evaluation of p-values of a test statistic. Again we use the example of the independence model of two-way contingency tables. We give an informal introduction to Markov bases for constructing a connected chain on a conditional sample space. Also we discuss Metropolis–Hastings procedure for constructing a Markov chain over discrete sample space with the desired stationary distribution.
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References
Häggström, O.: Finite Markov Chains and Algorithmic Applications. In: London Mathematical Society Student Texts, vol. 52. Cambridge University Press, Cambridge (2002)
Hastings, W.K.: Monte carlo sampling methods using markov chains and their applications. Biometrika 57, 97–109 (1970)
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© 2012 Springer Science+Business Media New York
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Aoki, S., Hara, H., Takemura, A. (2012). Markov Chain Monte Carlo Methods over Discrete Sample Space. In: Markov Bases in Algebraic Statistics. Springer Series in Statistics, vol 199. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3719-2_2
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DOI: https://doi.org/10.1007/978-1-4614-3719-2_2
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