simulate_cell

Simulation function of the cell biology example.

Bayesian synthetic likelihood (BSL, Price et al. (2018) <doi:10.1080/10618600.2017.1302882>)
is an alternative to standard, non-parametric approximate Bayesian
computation (ABC). BSL assumes a multivariate normal distribution
for the summary statistic likelihood and it is suitable when the
distribution of the model summary statistics is sufficiently regular.
This package provides a Metropolis Hastings Markov chain Monte Carlo
implementation of four methods (BSL, uBSL, semiBSL and BSLmisspec) and two
shrinkage estimators (graphical lasso and Warton's estimator).
uBSL (Price et al. (2018) <doi:10.1080/10618600.2017.1302882>) uses
an unbiased estimator to the normal density. A semi-parametric version
of BSL (semiBSL, An et al. (2018) <arXiv:1809.05800>) is more robust
to non-normal summary statistics. BSLmisspec (Frazier et al. 2019
<arXiv:1904.04551>) estimates the Gaussian synthetic likelihood whilst
acknowledging that there may be incompatibility between the model and the
observed summary statistic. Shrinkage estimation can help to decrease the
number of model simulations when the dimension of the summary statistic is
high (e.g., BSLasso, An et al. (2019) <doi:10.1080/10618600.2018.1537928>).
Extensions to this package are planned. For a journal article describing how
to use this package, see An et al. (2022) <doi:10.18637/jss.v101.i11>.

Leah F. South

Bayesian Synthetic Likelihood

Ziwen An

Christopher C. Drovandi

simulate_cell function

<dl><dt>x</dt>
<dd>The initial matrix of cell presences of size <code>rows</code>
\(\times\) <code>cols</code>.</dd>
<dt>rows</dt>
<dd>The number of rows in the lattice (rows in the cell location
matrix).</dd>
<dt>cols</dt>
<dd>The number of columns in the lattice (columns in the cell
location matrix).</dd>
<dt>Pm</dt>
<dd>Parameter \(P_m\),
the probability of cell movement.</dd>
<dt>Pp</dt>
<dd>Parameter \(P_p\),
the probability of cell proliferation.</dd>
<dt>sim_iters</dt>
<dd>The number of discretisation steps to get to when an
observation is actually taken. For example, if observations are taken every
5 minutes but the discretisation level is 2.5 minutes, then
<code>sim_iters</code> would be 2. Larger values of <code>sim_iters</code> lead to more
``accurate'' simulations from the model, but they also increase the
simulation time.</dd>
<dt>num_obs</dt>
<dd>The total number of images taken after initialisation.</dd></dl>

Arguments

Simulation function of the cell biology example — simulate_cell

<dl>

<dt>x</dt>
<dd>The initial matrix of cell presences of size <code>rows</code>
\(\times\) <code>cols</code>.</dd>


<dt>rows</dt>
<dd>The number of rows in the lattice (rows in the cell location
matrix).</dd>


<dt>cols</dt>
<dd>The number of columns in the lattice (columns in the cell
location matrix).</dd>


<dt>Pm</dt>
<dd>Parameter \(P_m\),
the probability of cell movement.</dd>


<dt>Pp</dt>
<dd>Parameter \(P_p\),
the probability of cell proliferation.</dd>


<dt>sim_iters</dt>
<dd>The number of discretisation steps to get to when an
observation is actually taken. For example, if observations are taken every
5 minutes but the discretisation level is 2.5 minutes, then
<code>sim_iters</code> would be 2. Larger values of <code>sim_iters</code> lead to more
``accurate'' simulations from the model, but they also increase the
simulation time.</dd>


<dt>num_obs</dt>
<dd>The total number of images taken after initialisation.</dd>

</dl>

simulate_cell: Simulation function of the cell biology example

Description

Usage

Value

Arguments