adds percentile to posterior figure, rebuilds pdf.

joss/paper.md

@@ -176,7 +176,7 @@ P(\theta|D) = \frac{P(D|\theta)P(\theta)}{P(D)},
 
 where $P(\theta|D)$ is the posterior parameter distribution, $P(D|\theta)$ is the likelihood function, $P(\theta)$ is the prior parameter distribution, and $P(D)$ is the model evidence, or marginal likelihood, which acts as a normalising constant. In the case of maximum likelihood estimation or maximum a posteriori estimation, one wishes to maximise $P(D|\theta)$ or $P(\theta|D)$, respectively, and this may be formulated as an optimisation problem as per \autoref{eqn:parameterisation}. However, to estimate the full posterior parameter distribution one must use sampling or other inference methods to reconstruct the function $P(\theta|D)$. The posterior distribution provides information about the uncertainty of the identified parameters, e.g., by calculating the variance or other moments. Monte Carlo methods are used here to sample from the posterior. The selection of Monte Carlo methods available in `PyBOP` includes gradient-based methods such as no-u-turn [@NUTS:2011] and Hamiltonian [@Hamiltonian:2011], as well as heuristic methods such as differential evolution [@DiffEvolution:2006], and also conventional methods based on random sampling with rejection criteria [@metropolis:1953]. `PyBOP` offers a sampler class that provides the interface to samplers, the latter being provided by the probabilistic inference on noisy time-series (`PINTS`) package. \autoref{fig:posteriors} below shows the sampled posteriors for the synthetic model described above, using an adaptive covariance-based sampler called Haario Bardenet [@Haario:2001].
 
-![Posterior distributions of model parameters alongside identified noise on the observations. Shaded area denotes credible interval for each parameter.  \label{fig:posteriors}](figures/joss/posteriors.png){ width=100% }
+![Posterior distributions of model parameters alongside identified noise on the observations. Shaded area denotes the 95th percentile credible interval for each parameter.  \label{fig:posteriors}](figures/joss/posteriors.png){ width=100% }
 
 ## Design optimisation