variable $Z \sim N(0,\sigma^2)$ that is uncorrelated with the death process. We suppose that the scale of the variance, $\sigma$, is different to the scale of the observations of the exponential decay process, giving a simple system with a two-dimensional parameter to infer: $\theta = (k, \sigma)$. Note that the scale of $z$ is determined by the standard deviation, $\sigma$, but the scale of the death process is affected by the initial condition, $A(0) = 10$, resulting in two distinct scales in these summary statistics.

![image](Fig3.eps){width="\textwidth"}

Results of parameter inference for this system using ABC-SMC are shown in Figure \[fig:Uniform\], where the true parameters used are $\theta = (0.1, 0.01)$ and a prior uniform on the logarithm of each of the parameters over the interval $[10^{-3},10^3]$ was used. Here we show marginal posterior distributions generated using uniform weights, weights scaled with the standard deviation of each summary statistic, and adaptively chosen weights via the method outlined in Algorithm 2. We observe similar performance in identification of the decay parameter $k$ using uniform weights, scaled weights and the adaptive choice of weights. Scaling the summary statistics with their standard deviation results in a posterior that does not provide much information over 