cointf¶

Fast, exact likelihoods for the Housworth–Stahl model of crossover interference.

cointf is a Python package with an R interface. It evaluates the likelihood of observed crossover positions under a two-pathway model: crossovers that obey interference (a gamma-type renewal process governed by \(\nu\)) and crossovers that escape it (a Poisson process carrying a fraction \(p\) of all crossovers). It is built for repeated evaluation inside optimisers and samplers, and for parameters that vary between meioses.

Contents¶

Page	What it covers
Model and likelihood	The generative model, the forward recursion for single meioses, and the \(O(n^3)\) recursion for phase-unknown (quartet) data
User guide	Data format, pooled and per-meiosis parameters, kernels, quartets and simulation
Numerics, accuracy and speed	How the series are truncated, the Chebyshev kernel, how correctness is tested, and benchmarks
Using cointf from R	Installing the R package, how it finds Python, data conversion, an R maximum-likelihood fit
Example: maximum-likelihood fit	Estimating \(\nu\) and \(p\) from a dataset, with standard errors and a likelihood surface
Python API	Every public class and function, with parameters, return values and examples
R API	Every function in the R package, generated from its help pages

Installation¶

cointf is installed from a clone of the GitHub repository, not from PyPI or CRAN.

git clone https://github.com/aabiddanda/cointf.git && cd cointf
pip install .        # Python
R CMD INSTALL r      # R (needs the reticulate package); see "Using cointf from R"

At a glance¶

from cointf import Meioses, loglik_fast, simulate_meioses

data = simulate_meioses(L=1.5, nu=4.0, p=0.05, n=200, seed=7)  # positions in Morgans
mz = Meioses(data, 1.5)                                         # prepare once
loglik_fast(mz, None, nu=4.0, p=0.05)                           # evaluate many times

Function	Purpose
`loglik_fast`	Exact log-likelihood of single meioses (vectorised)
`loglik_quartet`	Log-likelihood of phase-unknown data: crossovers of two meioses pooled
`ChebyshevKernel`	Faster approximate kernel for either likelihood (errors ~1e-14 to 3e-12 in the log kernel terms)
`loglik_naive`, `loglik_meiosis_naive`, `loglik_quartet_naive`	Slow reference implementations used for validation
`simulate_meioses`, `simulate_quartets`	Simulation from the same model

The R functions have the same names and arguments (meioses() and chebyshev_kernel() stand in for Meioses and ChebyshevKernel); see Using cointf from R.

Conventions¶

Positions and lengths are in Morgans (1 M = 100 cM), not base pairs.
A “meiosis” is one chromosome in one gamete. The expected number of crossovers per meiosis is \(L\), for every \((\nu, p)\).
\(\nu = 1\) means no interference; \(\nu > 1\) means positive interference. \(p = 0\) is the pure interference model and \(p = 1\) a Poisson process.