demos: Demonstrations which debunk some methods and analytical...
In brasmus/replicationDemos: replicationDemos

Description Usage Arguments Value Author(s) Examples

This set of function provide demonstrations showing how different methods or models work. This computer code is also used to do the analysis on which the paper 'Agnotology: learning from mistakes' by Benestad et al. is based.

Some of these analyses are indeed very trivial, but carried out nevertheless. The objective with this R-package is partly to show that code sharing and open-source can be an effective means of resolving differences. Methods and analytical set-up should be tested with surrogate data for which the anwers are known a priori (a kind of method calibration and evaluation). The spirit of this is very much like the replication carried out by Benestad and Schmidt (2009) http://pubs.giss.nasa.gov/abs/be02100q.html

ENSO.example() shows how the strategy adopbed in Scafetta (2012) fails when applied to ENSO (the NINO3.4 index). resonance() shows that a system with resonance will pick up the resonant frequency from any noisy forcing - this is analogous to the whine from the wind blowing aroundcorners, and how musical pipes/trumpets work (the function resonanceTest provides some demonstrations). A regression to harmoincs uses hfit fits harmonics according to eq. (3)in Scafetta (2011). decomposeFT() shows how any curve can be represented as a sum of harmonics - Fourier series. REference: Scafetta,N.,Testing an astronomically based decadal-scale empirical harmonic climate model versus the IPCC (2007) general...., Journal of Atmospheric and Solar-Terrestrial Physics (2011) doi:10.1016/j.jastp.2011.12.005. Also on http://arxiv.org/abs/1201.1301

Walker.test() is the function for the Walker test to test the significance when many tests are made (problem of multiplicity/field significance).

testLTP provides a demonstration/test showing that sophisticated trend fits will also be affected by the trend in data. This function compares the auto-correlation functions (showACF) of time series from a global climate model: both global mean and interpolated to Svalbard, where one uses constant boundary conditions (e.g. no trend) and the other includes the 20th century greenhouse gas forcings (non-zero trends). This analysis is applied to the annual mean values (am). These tests apply to the papers http://dx.doi.org/10.1029/2005GL024476 and http://dx.doi.org/10.1029/2012GL054244, where sophisticated trend models were used for hypothesis testing. It is important to keep in mind that these trend models then take the trends to be part of the noise, and hence are unsuitable for testing whether the trends are statistical significant.

demoConf and demoRange demonstrate how the confidence interval gets narrower for the estimate of the mean value as the sample size increases. This is done by generating a large set of random numbers ("original data") with known mean and standard deviation (indicator of the data range), and then a set of random subsets of the data. The mean values and standard deviation are computed for each of these subsets. As the sample size increases, the estimates converge towards the prescribed ("true") value. However, the range of the original master sample is not affected by the subsampling, and the range of the subsamples converge towards that of the original data as their sample size approach that of the original master sample. The data range and the confidence interval for the estimate of the mean were mixed up in http://dx.doi.org/10.1002/joc.1651.

diffdemo(x=0.7*cos(seq(0,10*pi,length=1000))+0.4*rnorm(1000),
                     y=0.9*cos(seq(0,10*pi,length=1000))+0.3*rnorm(1000))
diff12demo(x=0.5*cos(seq(0,10*pi,length=1200))+rnorm(1200),
                     y=0.7*cos(seq(0,10*pi,length=1200))+rnorm(1200),
                     wfl=12)
decomposeFT(N=1000)
ENSO.example(interval=1980:1989)
resonance(x0=1,v0=0,t0=0,t1=1000,N=1000,
          LHS=cos(2*pi*(1:1000)/75),
          f=0.001,m=0.1,w0=0.07)
resonanceTest(N=1000)
testLTP()
demoConf(m=3,s=2,N=10000,n=c(10,50,100,200,500,1000,5000))
demoRange(m=3,s=1)

`interval`	Time interval to analyse
`x0`	Initial condition for x of oscillator; or time series for control
`v0`	Initial condition for v = dx/td
`t0`	Initial time index
`t1`	Finalt time index
`LHS`	Left hand side of the equation
`f`	friction term for damped oscillator
`m`	inertia term for oscillator; mean value
`w0`	frequency term
`x`	curve to which harmonics are fitted or time series - a vector of numbers; or a time series
`y`	time series - a vector of numbers
`N`	length of time series; Size of data sample
`wfl`	window filter length
`s`	standard deviation
`n`	size of subsets

A table or lists containing the relevant data.

R.E. Benestad

## Not run: 

# Demonstrate the limitations of the diff-operator for two noisy signals
# (red and black in the upper panel respectively) with similar long-term
# harmonics. The lower panel shows the lagged correlation for the
# diff-operated series. 
diffdemo()
diff12demo()

# Demonstration: show that a noise consists of many Fourier components/harmonics
decomposeFT()


# Test the assumption about on good cycle-fit for a curve-fit toanother
# cycle, as done in Scafetta (2011)     
ENSO.example()
# Test the Runge-Kutta integration of a forced damped oscillator to test
# the claim about resonance made by Scafetta.
resonanceTest()




## End(Not run)