For a small number of sinusiods, the total number of
parameters for the SINAR model is small, so
the feature PDF can be approximated by Gaussian mixtures, etc.
the acid using Gaussian mixtures test with method='gmm'.
However, for more sinusoids, a PDF estimation method
more suited for SINAR should be used.
The fixed parameters for the SINAR
model of AR order and sinusoids
include the AR parameter estimates
the vector of frequencies ,
and the -dimensional vector of
real and imaginary amplitudes .
Let be an arbitrary (real data) hypothesis
and assume we want to estimate
We make the simplifying assumption that
the AR and sinusoidal parameters are independent:
If we expand
we can implement
as a histogram.
If we assume the individual frequencies are independent,
where is the frequency histogram for class .
In addition, we can assume a standard exponential distribution for the
where can be constant or can depend on the frequency.
In the second case, a means of estimating
should be used.
These ideas are implemented by the function
the acid using histogram with method='hist'.