Abstract
Let us reconsider the problem of determining the output probability law p Y (y) from a system, when the input law has a known form P X (x). This problem was originally considered in Chapter 5. We found there that the Jacobian approach called “transformation of a random variable” did the trick. Actually, this analytic approach was somewhat misleading. In a great number of real problems the system is too complicated to take an analytic approach. In these problems, the output RV y is the result of a great many intermediary events, each randomly conditional upon its predecessor. This causes the Jacobian approach to become extremely complicated and unwieldy since even the number of intermediary events that occur under such circumstances is a random variable. Hence, a different approach must be resorted to.
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Binder, K. (ed.): Monte Carlo Methods in Statistical Physics, Topics in Current Physics, Vol. 7 (Springer, Berlin, Heidelberg, New York 1978)
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© 1991 Springer-Verlag Berlin Heidelberg
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Frieden, B.R. (1991). The Monte Carlo Calculation. In: Probability, Statistical Optics, and Data Testing. Springer Series in Information Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97289-8_7
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DOI: https://doi.org/10.1007/978-3-642-97289-8_7
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