We investigate Monte Carlo inference techniques for structured Bayesian networks. In particular,
we describe an algorithm for choosing the number of samples to make in static networks, ...



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4 Static Bayesian Networks
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4.1 Approximate Inference
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In structured Bayesian networks like those presented in [NLU09], ...

     [NLU09] K. S. Ng, J. W. Lloyd, and W. T. B. Uther. Probabilistic modelling, inference and learning using logical theories. Annals of Mathematics and Artificial Intelligence, 2009. In press. => downloaded


[HGJ07] gives an algorithm that starts with some nmin number of samples needed to put the sample mean in its asymptotic normal regime and then iteratively increases the sample size until a condition similar to (3) is reached (they scale the error bound by |\mu_f|).

     [HGJ07] Michael Holmes, Alexander Gray, and Charles Lee Isbell Jr. Ultrafast monte carlo for statistical summations. In NIPS, 2007. => downloaded

Our first example is a main example in [MMR+05]. An urn contains an unknown number of balls; the number is from a Poisson distribution with m

     [MMR+05] Brian Milch, Bhaskara Marthi, Stuart Russell, David Sontag, Daniel L. Ong, and Andrey Kolobov.  Blog: Probabilistic models with unknown objects. In L.P. Kaelbling and A. Saffiotti, editors, Proceedings of the 19th International Joint Conference on Artificial Intelligence, pages 1352–1359, 2005. => downloaded

This problem was modelled as a structured Bayesian network in [NLU09]. ... [NLU09] gives exact results for these queries that were calculated by exploiting symmetries in the problem and in repeated observations of the same color.

Radar problem
Our second example is also from [MMR+05],