Monte Carlo integration with subtraction
نویسندگان
چکیده
This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration domain into a set of bins specified by some parameters. We then consider two adaptations; the first is to subtract the histogram approximation, whose integral we may easily evaluate explicitly, from the function and integrate the difference using Monte Carlo; the second is to modify the bin parameters in order to make the variance of the Monte Carlo estimate of the integral the same for all bins. This allows us to use Student’s t-test as a trigger for rebinning, which we claim is more stable than the χ2 test that is commonly used for this purpose. We provide a program that we have used to study the algorithm for the case where the histogram is represented as a product of onedimensional histograms. We discuss the assumptions and approximations made, as well as giving a pedagogical discussion of the myriad ways in which the results of any such Monte Carlo integration program can be misleading.
منابع مشابه
Analysis of the Quasi-Monte Carlo Integration of the Rendering Equation
Quasi-Monte Carlo integration is said to be better than Monte-Carlo integration since its error bound can be in the order of O(N (1 )) instead of the O(N 0:5) probabilistic bound of classical Monte-Carlo integration if the integrand has finite variation. However, since in computer graphics the integrand of the rendering equation is usually discontinuous and thus has infinite variation, the supe...
متن کاملPolarizing the Dipoles
We extend the massless dipole formalism of Catani and Seymour, as well as its massive version as developed by Catani, Dittmaier, Seymour and Trocsanyi, to arbitrary helicity eigenstates of the external partons. We modify the real radiation subtraction terms only, the primary aim being an improved efficiency of the numerical Monte Carlo integration of this contribution as part of a complete next...
متن کاملQuasi-monte Carlo Integration over a Simplex and the Entire Space
Monte Carlo integration is a widely used method to approximate high dimensional integrals. However, the randomness of this method causes the convergence to be very slow. Quasi-Monte Carlo integration uses low discrepancy sequences instead of pseudorandom sequences. The points from these sequences are more uniformly distributed. This causes the convergence to be much faster. Most research in qua...
متن کاملFiEstAS sampling -- a Monte Carlo algorithm for multidimensional numerical integration
This paper describes a new algorithm for Monte Carlo integration, based on the Field Estimator for Arbitrary Spaces (FiEstAS). The algorithm is discussed in detail, and its performance is evaluated in the context of Bayesian analysis, with emphasis on multimodal distributions with strong parameter degeneracies. Source code is available upon request.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computer Physics Communications
دوره 184 شماره
صفحات -
تاریخ انتشار 2013