2.4.9 | Posterior parameter estimation error
We wanted to evaluate the posterior error performed by the NN-ABC
approach in the vicinity of our observed data rather than randomly on
the entire parameter space. To do so, we first identified the 1,000
simulations closest to the real data with a tolerance level of 1%, for
the ACB and ASW respectively. Then, we performed 1,000 separate NN-ABC
parameter estimations similarly parameterized as above, using in turn
the other 99,999 simulations as reference table, and recorded the median
point estimate for each parameter. We then compared each parameter
estimate with the true parameter used for each 1,000 pseudo-observed
target and provide three types of error measurements in Table
3 . The mean-squared error scaled by the variance of the true parameter\(\frac{\sum_{1}^{1000}\left({\hat{\theta}}_{i}-\theta_{i}\right)^{2}}{\left(1000\times Variance\left(\theta_{i}\right)\right)}\)as previously (Csilléry et al. 2012); the mean-squared error\(\frac{\sum_{1}^{1000}\left({\hat{\theta}}_{i}-\theta_{i}\right)^{2}}{1000}\),
to compare errors for a given scenario-parameter between the ACB and ASW
analyses; and the mean absolute error\(\frac{\sum_{1}^{1000}\left|{\hat{\theta}}_{i}-\theta_{i}\right|}{1000}\),
which provides a more intuitive parameter estimation error. For
comparison, we conducted the above analysis using instead parameters
estimated under the loosing scenario Afr2P-Eur2P (Supplementary
Table S3 ).