sdre - Stochastic Divison Rate Estimations

A lightweight tool for performing divison rate estimation of cellular populations based using the multi-stage birth process model proposed by David Kendall, 1948. Forward simulations of the stochastic model are performed using a C++-implemented $\tau$-leaping algorithm.

Installation

This package is available on PyPI, so you can just run

pip install sdre

Usage

import sdre
import matplotlib.pyplot as plt

# artifical data
n_cells = [1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 8]
data = {i: [n] for i, n in enumerate(n_cells)}

# plot the data
plt.figure(figsize=(3.2, 3.2))
plt.scatter(data.keys(), data.values(), color='black')
plt.show()

# set up the model with the data from before
target = sdre.LikelihoodModel(data, n_samples=64)

fig, axs = plt.subplots(1, 2, figsize=(6.4, 3.2))

# we define two parameter combinations which by default are the cell cycle time, 
# log number of stages, and initial population size
x0, x1 = [.9, 2, 1], [1.2, 1, 1]

for i, x in enumerate([x0, x1]):
    # we perform forward simulation by drawing 64 samples
    t, n = target.sample(x)
    
    # computes the synthetic log likelihood loss
    nll = target.compute_negative_log_likelihood(x)
    
    axs[i].set_title('NLL='+str(round(nll, 2)))
    
    axs[i].step(t, n.T, alpha=.2, color=plt.cm.tab10(i))
    axs[i].scatter(data.keys(), data.values(), color='black', zorder=10)
    
plt.show()

A lower negative log-likelihood (NLL) suggests a better fit, as we can confirm visually.