to produce a higher quality approximation of the posterior for a given number of parameter samples compared to other methods of weighting the summary statistics. The true parameter is $\theta = 10$, a prior uniform on the logarithm of the parameters over the interval $[10^{0},10^2]$ was used, and $r=10$ samples of the uniform model were used as the dataset.

Death process {#exp-decay}
-------------

For our first test problem, we consider estimating the rate parameter for a single, first order degradation reaction: $$\begin{aligned}
\label{exponential}
\ce{A
->[k]
{ \emptyset }.
} \end{aligned}$$ We will consider for this, and subsequent, test problems that time has been non-dimensionalized. Initially, we assume there are $A(0) = 10$ particles in the system, which is observed over a (non-dimensional) time period $[0,20]$. We assume it is possible to measure the state of the system (in this case the number of molecules of species $A$) without observation noise at given time points $t_0, t_1, \ldots , t_n$. For this test problem, we assume that we measure at $n$ equally spaced time intervals, where $n=32$.

As our summary statistics, we take $s(\mathbf{x}) = [A(t_0), A(t_1), \linebreak \ldots , A(t_n), z] $ where $z$ is an observation of a random 