ior probability for the true model, $p_{u^*} = \hat{\mathbb{P}}(U=u^*|y_{1:T},s_{1:T})$, is evaluated.

  Number of MUs, $u^*$                            $\leq 5$     6       7       8       9      10
  ---------------------------------------------- ---------- ------- ------- ------- ------- -------
  No. where $\hat{u}=u^*$                           100       19      19      16      15      12
  No. where $u^*$ in HPCS                           100       20      20      19      19      20
  Avg. size of HPCS                                 1.11     1.70    2.10    2.05    2.35    2.45
  Avg. $\hat{p}_{u^*}$ (%)                         97.95     89.20   80.45   69.42   62.70   54.68
  Avg. particle set size for $u^*$                  5000     5250    6000    7500    7500    8250
  Avg. particle set size for $\hat{u}$              5000     5000    6000    7500    9250    7750
  Avg. $n{\times}n$ lattice size for $u^*$          30.0     30.5    30.5    32.0    32.5    32.0
  Avg. $n{\times}n$ lattice size for $\hat{u}$      30.0     30.0    30.5    32.0    35.0    32.0

  : Summary of the MU-number posterior mass functions and required numerical resource for 200 simulated data sets.[]{data-label="tab:SimSummary"}

Table \[tab:SimSummary\] presents summaries of the mass functions of the number of MUs and descriptions of the resource required as functions of the true number of MUs. The MAP estimate corresponded to the true number of MUs for all data sets generated from five or fewer MUs, and for most of these datasets the HPCS contained only the true model. For true sizes of greater than five the MAP estimate was correct for $81$ of the $100$ data sets and the HPCS contained the truth for all but two data sets.

It is unsurprising that the uncertainty in the MU-number increases with the true number of MUs; this is visible both as an increase in the average size of the HPCS and a reduction in the average posterior probability for the true number. In addition, both the number of particles required to control Monte Car