Suppose I have several groups of signal measurements, each containing multiple replicates, and I know that within each group the signal "shape" is approximately the same but with variance/error that depends on the signal. E.g. for each group I would have a set of vectors of the same length, which are strongly correlated, but which exhibit irregular variance across the length of the signal.
Ultimately I would like to ask if some test signal X is more likely to belong to group 1, 2, etc. but while taking this variance into account.
Is it then reasonable to treat each group as a multi-variate normal distribution? At each time point group values are approximately normal, although correlations will obviously be high between time points, and the variance across the signal will not be independent at each point, but related to its neighbors. If this is an appropriate modeling then one could simply compare the likelihood of the test vector belonging to the different groups' multivariate distributions.
Why or why not would this be an appropriate single-signal to group-of-signals comparison method? Are there alternative methodologies already in place for asking if some signal belongs to one group or another? Thank you!
Edit for clarification: the data in question are actually nucleosome coverage profiles in specific regions of the genome, which are known to show consistent signals within disease types. The question is then whether a single test signal can be grouped with one or another groups of signals, say a set of healthy or diseased replicates. The measurements can be considered simultaneous, not a true time signal, and variance will be highly correlated with neighboring points. The reason I wish to include the noise/variance when asking this question is because it varies considerably along the signal and between groups, so simply taking the mean signal, for instance, would not capture some of the expected range. I have attached a picture of three such "groups" and their uncertainties.