WIP - Stochastic Logistic Growth (ABC Toy problem) #1025
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…city birth-only growth
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@jarthur36 Looking good. Thanks. If you look through my and @MichaelClerx 's comments here, and make these few changes, then we can get it merged.
- Can we add a full references to the notebook? I.e. Simpson et al. and Gillespie et al. should be given in full at the bottom of the first block of text.
- Can we add a reference to Radek Erban's book please? This was our main reference for the Gillespie algorithm.
- In the example noetbook, at the moment, we aren't converging on the deterministic mean? Can we either change the text or up the number of particles so that we do?
- We need value-based tests of the stochastic degradation model outputs? @MichaelClerx suggests we do this by seeding the random number generator, which sounds reasonable.
- We need docstrings for the class itself.
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Just found out why there was the discrepancy between the deterministic model and the 1000-realisation average. Long in short, it all depends on the choice of parameters (in particular the initial size of the population)! With the parameters that Jack used, the population was small, so each step gave a big variation, so it had a large 'noise'. Although we thought by running more simulations it'd converge to the deterministic solution, it'd not be the case when the initial population size is small (with some quick experiments, seems like n_0 > 10 would be a reasonable size, but needs some proper sensitivity anaylsis to give a better estimate). The reason seems to be that with a small initial population, the big noise at the beginning can drift (or shift?) the whole process (e.g., to delay the growth at a later time), then the 'time point-wise' average from these shifted solutions would give a bias. So a simple fix to that is simply scaling up the whole population which solves the bias seen in the plot above, see below:
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Thanks @chonlei -- looks really good. Only a few minor comments then fine to go.
Just wondering -- did you see #1067 ? This was Jack's attempt to create a more generic stochastic simulation approach (basically it should automate the Gillespie algorithm for many types of stochastic reaction equation). I just remembered it, sorry. Do you think merge this then later someone tries to adapt it to fit into such a framework?
Think I would go for merging this first then adapt it to fit into a better framework later, since we've been quite slow on SDE and/or ABC... |
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Thanks @chonlei and @jarthur36 !
Two tiny comments now, happy for this to be merged without further review once they're done
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@MichaelClerx Any idea why the "build-and-test" thing isn't running? |
I think that's an old test name that no longer exist. Will investigate! |
Adds the spatially implicit birth-only logistic growth model (Simpson et al., 2019) to pints. Simulated using the interpretation of the Gillespie algorithm from (Erban et al., 2007)
This version is work in progress as the empirical mean of n stochastic runs does not converge to the deterministic mean as n->∞ as shown below
