OxfordRSE / abc-miniproject

A short project to code up ABC, with unit tests

pagetitle
ABC

Implementing an ABC rejection algorithm

Some background information will go here.

Write a function to simulate from a logistic model

The logistic model looks like:

$C(t) = \frac{k}{1 + (\frac{k}{C_0}-1)e^{-rt}} + \epsilon$

where C(t) is the population of cells at time $t$, C_0 is the population at time $t=0$, $k$ is the population carrying capacity, $r$ is the population growth rate, and $\epsilon$ is random noise drawn from $N(0,s)$.

1. Create a python file abc_rejction.py.

2. Write a function with the following signature that will simulate a time-course from the logistic model above:

   def logistic(t, r, k, s):
   

   Where $t$ is expected to be a numpy array of time points (for instance, from np.linspace(0, 10, 100)), $r$ is expected to be a positive real number representing the population growth rate, $k$ is a positive real number representing the carrying capacity, and $s$ is a small positive real number representing the scale of the normal noise term.

   This function should return a numpy array, the same length as $t$, where the logistic function above has been evaluated at teach of the time points.

3. Using matplotlib, plot a simulated time course from your logistic model:

   import matplotlib.pyplot as plt
   import numpy as np
   
   t = np.linspace(0, 10, 100)
   c = logistic(t, 1.23, 24.5, 0.345)
   
   plt.plot(t, c)
   plt.show()
   

4. Create a python file test_abc.py.

5. Write a function with the following signature that will test your logistic function:

   def test_logistic():
   

6. Check that, with $t=0$ and no noise, your logistic model returns $C_0$:

   t = np.array(0.0)
   assert logistic(t, 1.23, 2.34, 0.0) == C0
   

7. Add as many more checks as you can think of, to assure yourself that your logistic function is implemented correctly.