A stationary AR(1) process

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Probability, statistics and stochastic methods · Probability, statistics and stochastic methods

Scientific Computing for Physicists, Ch The uncertainty of a simulated number: inputs, sensitivity and correlated output

Problem

A stationary AR(1) process xn+1=ϕxn+ηnx_{n+1} = \phi x_n + \eta_n, with ηn\eta_n independent zero-mean noise, has ϕ=0.6\phi = 0.6. A run produces N=2000N = 2000 correlated samples. ((a)) Compute the integrated autocorrelation time τint=12+ϕ/(1−ϕ)\tau_{\rm int} = \tfrac12 + \phi/(1-\phi). ((b)) Compute the statistical inefficiency s=2τints = 2\tau_{\rm int}. ((c)) Compute the effective sample size Neff=N/sN_{\rm eff} = N/s.

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