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Monte Carlo techniques have become popular in different areas of medical physics over the last 50 years. Factors which have contributed to the wider use include the improved description of radiation transport as well as the optimization of the computing systems. The main advantage of Monte Carlo methodology deals with the simulation of stochastic processes involving random behavior and the quan...

There have been few studies on practical error estimation methods of quasi-Monte Carlo integrations. Recently, some theoretical works were developed by Owen to analyze the quasi-Monte Carlo integration error. However his method given by those works is complicated to be implemented and needs huge computational e orts, so it would be of some interest to investigate into a simple error estimation ...

We review and discuss some recent progress on the theory of Markov chain Monte Carlo applications, particularly oriented to applications in statistics. We attempt to assess the relevance of this theory for practical applications.

This paper has several folds. We make first new permutation choices in Halton sequences to improve their distributions. These choices are multi-dimensional and they are made for two different discrepancies. We show that multi-dimensional choices are better for standard quasi-Monte Carlo methods. We also use these sequences as a variance reduction technique in Monte Carlo methods, which greatly ...

In this report, we revisit the work of Pilleboue et al. [2015], providing a representation-theoretic derivation of the closed-form expression for the expected value and variance in homogeneous Monte Carlo integration. We show that the results obtained for the variance estimation of Monte Carlo integration on the torus, the sphere, and Euclidean space can be formulated as specific instances of a...