e">\(t_0\)</span> up til the previous time-point <span class="math inline">\(t_{k-1}\)</span>. The <em>posterior</em> estimates
are conditioned also on the observations available at the “current”
time-point <span class="math inline">\(t_{k}\)</span>. These are denoted
respectively by <span class="math display">\[
\text{Prior:} \quad \mathrm{E}\left[ x_{t_k} \mid y_{t_{k-1}},
y_{t_{k-2}},...,y_{t_0} \right]
\]</span> <span class="math display">\[
\text{Posterior:} \quad \mathrm{E}\left[ x_{t_k} \mid y_{t