Covariance method

The information content resulting from both processing methods is identical insofar as correlation information is concerned. The matrix-square-root transformation can minimize artefacts due to relay effects and chemical shift near degeneracy (pseudo-relay effects80-82 98). The application of covariance methods to compute HSQC-1,1-ADEQUATE spectra is described in the following section. 

In view of the difficulties in determining gas transfer coefficients accurately, direct methods for CO2 flux measurements aboard the ship are desirable. Sea-air CO2 flux was measured directly by means of the shipboard eddy-covariance method over the North Atlantic Ocean by Wanninkhof and McGillis in 1999. The net flux of CO2 across the sea surface was determined by a covariance analysis of the tri-axial motion of air with CO2 concentrations in the moving air measured in short time intervals ( ms) as a ship moved over the ocean. The results obtained over awind speed range of 2-13.5 m s are consistent with eqn [3] within about +20%. If the data obtainedin wind speeds up to 15 m s are taken into consideration, they indicate that the gas transfer piston velocity tends to increase as a cubeof wind speed. However, because of a large scatter ( + 35%) ofthe flux values at high wind speeds, further work is needed to confirm the cubic dependence. 

While this also uses a variance-covariance matrix much like the full covariance method, the actual matrix is much more condensed. As an example, the matrix used in a 20-factor model would have a size of (20 X 20) 400 cells, which is moderate compared with the one-million-cell matrix mentioned previously for the full variance-covariance model. The advantages of using a multifactor model are that it easily allows for mapping a new issue into past data for similar bonds by looking at its descriptive characteristics, and it can be inverted for use in a portfolio optimizer without too much effort. The multifactor model is also more tolerant to pricing errors in individual securities since prices are averaged within each factor bucket. 

If the underlying process is normal, the simulated distribution must converge to a normal distribution. In this situation, Monte Carlo analysis theoretically should yield exactly the same result as the multifactor variance-covariance method. The VaR estimated from the sample quantile must (not considering sampling variation) converge to the value of ao, where... 

A slightly different method know as the autocorrelation method can also be used, and as this has many practical advantages over the covariance method, it is often the method most used in practice. 

This is similar in form to Equation 12.20, and if we can calculate the autocorrelation, we can make use of important properties of this signal. To do so, in effect we have to calculate the squared error from —to This differs from the covariance method, where we just consider the speech samples from a specific range. To perform the calculation from —to we window the waveform using a banning, hamming or other window, which has the effect of setting all values outside the range 0 < = < A to 0. 

The linear prediction equations can be solved by the autocorrelation or covariance methods. Each involves solving the equations by means of efficient matrix inversion. 

This is the most commonly used method for calculating the principal components of a data set. It gives more numerically accurate results when compared with the decomposition of covariance method but is slower to calculate. The steps are as follows ... 

Lee et al. used PTR-MS and eddy covariance methods to determine mixing ratios and fluxes of total monoterpenes above a ponderosa pine plantation [34], The results from these studies were compared to those obtained using GC-FID and a relaxed eddy accumulation system. It was found that the daytime measurements resulted in values that agreed well with each other. However, at night PTR-MS detected additional reactive terpenes which... 

Rinne et al. used PTR-MS with a disjunct eddy covariance method to measure the fluxes of methanol, acetaldehyde and monoterpenes above a Scots pine (Pirns sylvestris) forest in Finland [90]. Chemical modeling showed that there was little loss owing to reaction and that the VOC fluxes followed the traditional exponential temperature-dependent emission... 

The perennial plant alfalfa is an important forage crop that is cultivated in many countries. Warneke et al. measured the fluxes of selecfed oxygenated VOCs coming from an alfalfa field before, during and after harvesting, using disjunct eddy covariance methods combined... 

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