MCONF Confidence intervals for the multitaper spectral estimate. [RA,RB]=MCONF(K,GAMMA) returns the level GAMMA confidence interval for the direct multitaper power spectral estimate of an average over K eigenspectra. RA and RB lower and upper ratios to the true value. More specifically, if S0 is the true value of the spectrum, and if S is the spectral estimate, then RA and RB satisfy Probability that RA < S/S0 < RB = GAMMA with RA and RB defined to be symmetrically placed around 1. For example, GAMMA=0.95 computes the 95% confidence interval. For the default settings of the multitaper spectrum implemented by MSPEC, K is equal to 2P-1 where P is the time-bandwidth product. The estimated confidence intervals can then be plotted as plot(f,S),hold on,plot(f,S*ra),plot(f,S*rb) where S is the spectral estimated computed by MSPEC, while is the Fourier frequencies. MCONF relies upon the fact that S/S0 is approximately distributed as 1/(2K) times a chi-squared distribution with 2K degrees of freedom. _____________________________________________________________________ Logarithmic confidence intervals When plotting the logarithm of the spectrum, one should use a different set of confidence intervals. MCONF(K,GAMMA,'log10') returns the confidence intervals for the base-10 logarithm of the multitaper spectral estimate. In this case, RA and RB are defined such that Probability that RA < LOG10(S)/LOG10(S0) < RB = GAMMA and the confidence intervals can be plotted using either plot(f,S),hold on,plot(f,10.^ra*S),plot(f,10.^rb*S) set(gca,'yscale','log') or else plot(f,log10(S)),hold on,plot(f,ra+log10(S)),plot(f,rb+log10(S)). MCONF(K,GAMMA,'natural') similarly returns the confidence intervals for the natural logarithm of the multitaper spectral estimate. _____________________________________________________________________ See also MSPEC, CHISQUARED. 'mconf --t' runs a test. 'mconf --f' generates a sample figure. Usage: [ra,rb]=mconf(K,gamma); [ra,rb]=mconf(K,gamma,'log10'); __________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2020 J.M. Lilly --- type 'help jlab_license' for details