.. role:: raw-math(raw)
    :format: latex html

Input file and data format
===========================

BED file
--------
BED (Browser Extensible Data) format is commonly used to describe blocks of genome. The
BED format consists of one line per feature, each containing 3-12 columns of data. It is
0-based (meaning the first base of a chromosome is numbered 0). It is s left-open,
right-closed. For example, the bed entry "chr1 10 15" contains the 11-th, 12-th, 13-th,
14-th and 15-th bases of chromosome-1.

BED12 file
	The standard BED file which has 12 fields. Each row in this file describes a
	gene or an array of disconnected genomic regions. Details are described `here <https://genome.ucsc.edu/FAQ/FAQformat.html#format1>`_
BED3 file 
	Only has the first three required fields (chrom, chromStart, chromEnd). Each row is
	used to represent a single genomic region where "score" and "strand" are not necessary.
BED3+ file
	Has at least three columns (chrom, chromStart, chromEnd). It could have other
	columns, but these additional columns will be ignored.
BED6 file
	Has the first six fields (chrom, chromStart, chromEnd, name, score, strand). Each row
	is used to represent a single genomic region and their associated scores, or in cases
	where "strand" information is essential.
BED6+ file
	Has at least six columns (chrom, chromStart, chromEnd, name, score, stand). It could
	have other columns, but these additional columns will be ignored.

Proportion values
-----------------
In `bisulfite sequencing <https://en.wikipedia.org/wiki/Bisulfite_sequencing>`_
(RRBS or WGBS), the methylation level of a particular CpG or
region can be represented by a "proportion" value. We define the proportion value as a
pair of integers separated by comma (",") with the first integer (m, 0 <- m <- n)
representing "number of methylated reads" and the second integer (n, n >- 0) representing
"number of total reads". for example:
::
 
 0,10	1,27	2,159	#Three proportions values indicated 3 hypo-methylated loci 
 7,7	17,19	30,34	#Three proportions values indicated 3 hyper-methylated loci

Beta values
------------
The Beta-value is a value between 0 and 1, which can be interpreted as the approximation
of the percentage of methylation for a given CpG or locus. One can convert proportion
value into beta value, but not vice versa. In the equation below, C is the "probe intensity"
or "read count" of methylated allele, while U is the "probe intensity" or "read count" of
unmethylated allele.

.. math::

   \beta=\frac{C}{U+C}, (0 \leq \beta \leq 1)

M values
--------
The M-value is calculated as the log2 ratio of the probe intensities (or read counts) of
methylated allele versus unmethylated allele. In the equation below, C is the "probe
intensity" or "read count" of methylated allele, while U is the "probe intensity" or
"read count" of unmethylated allele. w is the offset or pseudo count added to both
denominator and numerator to avoid unexpected big changes and performing log
transformation on zeros.

.. math::

	M=\log _{2}\left(\frac{C+w}{U+w}\right)


Convert Beta value to M value or *vice versa*
---------------------------------------------
The relationship between Beta-value and M-value is shown as equation and figure:

.. math::

	\beta=\frac{2^{M}}{2^{M}+1} ; M=\log _{2}\left(\frac{\beta}{1-\beta}\right)
	
.. image:: _static/beta_vs_M_curve.png
   :align: center
   :height: 400 px
   :width: 400 px
   :scale: 80 %  
