Chapter 8 Linear prediction and singular value decomposition in nmr signal analysis

Publisher Summary Prediction is a statistical estimation procedure where one or more random variables are estimated from observations of other random variables. It is called prediction when the variables to be estimated are in some sense associated with the “future” and the observable variables are associated with the “past” (or “present”). The most common use of prediction is to estimate a sample of a stationary (random) process from observation of several prior samples. This chapter considers that the results are in good agreement with the expected values and these tests enable to apply the method described in this chapter for T 2 determinations in unknown biological systems in which the prior knowledge of the constituents is improbable. The assets of this algorithm over others are: (1) the algorithm provides a clear answer to the question of whether the quality of the data justifies fitting by a sum of exponentials; (2) no need to know in advance the number of exponentials that characterise the data; (3) no need to provide a suitable starting point for iterations; (4) less chance of breakdown if the exponents are close; and (5) shorter computation time.