New inputs and methods for Markov chain quasi-Monte Carlo
نویسندگان
چکیده
We present some new results on incorporating quasi-Monte Carlo rules into Markov chain Monte Carlo. First, we present some new constructions of points, fully equidistributed LFSRs, which are small enough that the entire point set can be used in a Monte Carlo calculation. Second, we introduce some antithetic and round trip sampling constructions and show that they preserve the completely uniformly distributed property necessary for QMC in MCMC. Finally, we also give some new empirical results. We see large improvements in sampling some GARCH and stochastic volatility models.
منابع مشابه
Consistency of Markov chain quasi-Monte Carlo on continuous state spaces
The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [24] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than IID U(0, 1) points shows consisten...
متن کاملChapter 1 Quasi - Monte Carlo Sampling
In Monte Carlo (MC) sampling the sample averages of random quantities are used to estimate the corresponding expectations. The justification is through the law of large numbers. In quasi-Monte Carlo (QMC) sampling we are able to get a law of large numbers with deterministic inputs instead of random ones. Naturally we seek deterministic inputs that make the answer converge as quickly as possible...
متن کاملDiscrepancy estimates for variance bounding Markov chain quasi-Monte Carlo
Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of such Markov chain quasi-Monte Carlo methods. We define a pull-back discrepancy of the driver sequence and state a close relation to the star-discrepancy of the...
متن کاملCONSISTENCY OF MARKOV CHAIN QUASI-MONTE CARLO ON CONTINUOUS STATE SPACES By
The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [24] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than IID U(0, 1) points shows consisten...
متن کاملQuasi-Monte Carlo and Monte Carlo Methods and their Application in Finance
We give an introduction to and a survey on the use of Quasi-Monte Carlo and of Monte Carlo methods especially in option pricing and in risk management. We concentrate on new techniques from the Quasi-Monte Carlo theory.
متن کامل