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

Input File and Data Format
==========================

BED File
--------

The **BED** (Browser Extensible Data) format is commonly used to describe blocks of genomic regions.  
Each line in a BED file represents one genomic feature and contains between **3 and 12 columns** of data.  

The BED format is **0-based**, meaning the first base of a chromosome is numbered **0**, and it follows a **left-open, right-closed** interval convention.  
For example, the BED entry ``chr1 10 15`` corresponds to the **11th to 15th bases** of chromosome 1 (i.e., bases 11–15 inclusive).

**BED Variants**

- **BED12 file**  
  The standard BED format containing 12 fields. Each line represents a gene or a set of disconnected genomic regions.  
  Detailed specifications are available `here <https://genome.ucsc.edu/FAQ/FAQformat.html#format1>`_.

- **BED3 file**  
  Contains only the first three required fields: ``chrom``, ``chromStart``, and ``chromEnd``.  
  Each line represents a single genomic region where *score* and *strand* information are not required.

- **BED3+ file**  
  Contains at least three columns (``chrom``, ``chromStart``, ``chromEnd``).  
  Any additional columns will be **ignored**.

- **BED6 file**  
  Includes the first six fields: ``chrom``, ``chromStart``, ``chromEnd``, ``name``, ``score``, and ``strand``.  
  Each line represents a single genomic region and may include strand information or associated scores.

- **BED6+ file**  
  Contains at least six columns (``chrom``, ``chromStart``, ``chromEnd``, ``name``, ``score``, ``strand``).  
  Any columns beyond these six will be **ignored**.

---

Proportion Values
-----------------

In `bisulfite sequencing <https://en.wikipedia.org/wiki/Bisulfite_sequencing>`_ (e.g., RRBS or WGBS),  
the methylation level of a CpG site or region is represented by a **proportion value**.  

A proportion value is a pair of integers separated by a comma (``m,n``), where:

- **m** = number of methylated reads (``0 ≤ m ≤ n``)  
- **n** = total number of reads (``n ≥ 0``)

For example:

::

   0,10   1,27   2,159   # three hypo-methylated loci
   7,7    17,19  30,34   # three hyper-methylated loci

---

Beta Values
-----------

The **Beta-value** represents the proportion of methylation for a given CpG or locus.  
It ranges from **0 to 1**, and can be interpreted as an approximation of the **percentage of methylation**.

A proportion value can be converted to a Beta-value, but **not vice versa**.  
In the equation below:

- **C** = probe intensity or read count of the methylated allele  
- **U** = probe intensity or read count of the unmethylated allele  

.. math::

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

---

M Values
--------

The **M-value** represents the log2 ratio of methylated versus unmethylated probe intensities (or read counts).  
It is calculated as follows:

- **C** = probe intensity or read count of the methylated allele  
- **U** = probe intensity or read count of the unmethylated allele  
- **w** = offset (pseudo count) added to both numerator and denominator to prevent division by zero and reduce noise in low-coverage regions.

.. 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** can be expressed as:

.. math::

   \beta = \frac{2^{M}}{2^{M} + 1} \quad ; \quad M = \log_{2}\left(\frac{\beta}{1 - \beta}\right)

The following figure illustrates this relationship:

.. image:: _static/beta_vs_M_curve.png
   :align: center
   :height: 400px
   :width: 400px
   :scale: 80%