  Biological sequences do not come at random. Instead, they appear with
particular frequencies that reflect properties of the associated system or
phenomenon. Knowing how biological sequences are distributed in sequence space
is thus a natural first step toward understanding the underlying mechanisms.
Here we propose a new method for inferring the probability distribution from
which a sample of biological sequences were drawn for the case where the
sequences are composed of elements that admit a natural ordering. Our method is
based on Bayesian field theory, a physics-based machine learning approach, and
can be regarded as a nonparametric extension of the traditional maximum entropy
estimate. As an example, we use it to analyze the aneuploidy data pertaining to
gliomas from The Cancer Genome Atlas project. In addition, we demonstrate two
follow-up analyses that can be performed with the resulting probability
distribution. One of them is to investigate the associations among the sequence
sites. This provides us a way to infer the governing biological grammar. The
other is to study the global geometry of the probability landscape, which
allows us to look at the problem from an evolutionary point of view. It can be
seen that this methodology enables us to learn from a sample of sequences about
how a biological system or phenomenon in the real world works.
