uwerr: Time Series Analysis With Gamma Method

In hadron: Analysis Framework for Monte Carlo Simulation Data in Physics

Time Series Analysis With Gamma Method

Description

Analyse time series data with the so called gamma method

Usage

uwerr(f, data, nrep, S = 1.5, pl = FALSE, ...)

Arguments

f	function computing the derived quantity. If not given it is assumed that a primary quantity is analysed. f must have the data vector of length Nalpha as the first argument. Further arguments to f can be passed to uwerr via the ... argument. f may return a vector object of numeric type.
data	array of data to be analysed. It must be of dimension (N x Nalpha) (i.e. N rows and Nalpha columns), where N is the total number of measurements and Nalpha is the number of primary observables
nrep	the vector (N1, N2, ...) of replica length N1, N2
S	initial guess for the ratio tau/tauint, with tau the exponetial autocorrelation length.
pl	logical: if TRUE, the autocorrelation function, the integrated autocorrelation time as function of the integration cut-off and (for primary quantities) the time history of the observable are plotted with plot.uwerr
...	arguments passed to function f.

Value

In case of a primary observable (uwerrprimary), an object of class uwerr with basis class list containing the following objects

value	the expectation value of the obsevable
dvalue	the error estimate
ddvalue	estimate of the error on the error
tauint	estimate of the integrated autocorrelation time for that quantity
dtauint	error of tauint
Qval	the p-value of the weighted average in case of several replicas

In case of a derived observable (uwerrderived), i.e. if a function is specified, the above objects are contained in a list called res.

uwerrprimary returns in addition

data	input data

whereas uwerrderived returns

datamean

(vector of) mean(s) of the (vector of) data

and in addition

fgrad

the estimated gradient of f

and

f	the input statistics

In both cases the return object containes

Wopt	value of optimal cut-off for the Gamma function integration
Wmax	maximal value of the cut-off for the Gamma function integration
tauintofW	integrated autocorrelation time as a function of the cut-off W
dtauintofW	error of the integrated autocorrelation time as a function of the cut-off W
S	input parameter S
N	total number of observations
R	number of replicas
nrep	vector of observations per replicum
Gamma	normalised autocorrelation function
primary	set to 1 for uwerrprimary and 0 for uwerrderived

Author(s)

Carsten Urbach, [e-mail]

References

“Monte Carlo errors with less errors”, Ulli Wolff, Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum), hep-lat/0306017

See Also

plot.uwerr

Examples

data(plaq.sample)
plaq.res <- uwerrprimary(plaq.sample)
summary(plaq.res)
plot(plaq.res)

hadron documentation built on Sept. 9, 2022, 5:06 p.m.