diff --git a/tex/slides.tex b/tex/slides.tex
index d07c51d1e6d79acdbcd0511a08371fab109a10d2..ee73817f2c189388e30ac9fb66b6af8698347f8b 100644
--- a/tex/slides.tex
+++ b/tex/slides.tex
@@ -125,7 +125,7 @@
 
     \medskip
 
-  \item If we obtain $\{x_i\}_{i=1}^N$ from another distribution $q(x)$:
+  \item If we obtain $\{x_i\}_{i=1}^N$ from another distribution with density $q(x)$:
     \[
       \mathbb E_p\left[ \varphi(X) \right] = \int q(x)\frac{p(x)}{q(x)}\varphi(x)\mathrm d x = \int q(x)\tilde{\omega}(x)\varphi(x)\mathrm d x = \mathbb E_q\left[ \tilde{\omega}(X)\varphi(X) \right]
     \]
@@ -147,7 +147,7 @@
 
   \begin{itemize}
 
-  \item IS works as long as the support of the targetted distribution ($p$) is included in the support of the instrumental distribution ($q$).\newline
+  \item IS works as long as the support of the targeted distribution ($p$) is included in the support of the instrumental distribution ($q$).\newline
 
   \item How do we choose distribution $q(x)$?\newline
 
@@ -161,7 +161,7 @@
     % ⇒ We are better off if the unormalized weight variance is low, i.e. if f/g is approximately constant.
     % The closer g is to f, the better we are.
 
-  \item Is it possible to find a reasonable intrumental distribution for a posterior distribution?\newline
+  \item Is it possible to find a reasonable intrumental distribution for a posterior distribution? The prior?\newline
 
   \item Probably better not to ``jump'' directly to the posterior distribution...
 
@@ -184,14 +184,14 @@
 
   \item[Target] $p\left(\theta|\mathcal Y_T\right) \propto p(\theta) p(\mathcal Y_T| \theta)$\newline
 
-  \item Consider the ''simplified`` object $p\left(\theta\right)p\left(\mathcal Y_T\right)^{\phi}$\newline
+  \item Consider the ''simplified`` object $p\left(\theta\right)p\left(\mathcal Y_T| \theta\right)^{\phi}$\newline
 
-  \item $p\left(\theta\right)$ is a good instrumental distribution for $p\left(\theta\right)p\left(\mathcal Y_T\right)^{\phi}$ for small values of $\phi$.\newline
+  \item $p\left(\theta\right)$ is a good instrumental distribution for $p\left(\theta\right)p\left(\mathcal Y_T| \theta\right)^{\phi}$ for small values of $\phi$.\newline
 
   \item Consider a sequence of $\{\phi_i\}_{i=1}^M$ with $\phi_i<\phi_j$ for all $j>i$ and $\phi_M = 1$.\newline
 
-  \item Use $p\left(\theta\right)$ as an intrumental distribution for $p\left(\theta\right)p\left(\mathcal Y_T\right)^{\phi_1}$ and $p\left(\theta\right)p\left(\mathcal Y_T\right)^{\phi_i}$
-    as an instrumental distribution for $p\left(\theta\right)p\left(\mathcal Y_T\right)^{\phi_{i+1}}$.\newline
+  \item Use $p\left(\theta\right)$ as an intrumental distribution for $p\left(\theta\right)p\left(\mathcal Y_T| \theta\right)^{\phi_1}$ and $p\left(\theta\right)p\left(\mathcal Y_T| \theta\right)^{\phi_i}$
+    as an instrumental distribution for $p\left(\theta\right)p\left(\mathcal Y_T| \theta\right)^{\phi_{i+1}}$.\newline
 
   \item Herbst and Schofheide consider $\phi_n = \left( \frac{n}{M} \right)^\lambda$ with $\lambda>1$ (convexity).
 
@@ -296,9 +296,9 @@ posterior_sampling_options = ('particles', 20000,
 
   \begin{itemize}
 
-  \item More options.\newline
+  \item More options (number of mutation MH steps, resampling algorithm, ...).\newline
 
-  \item Complete posterior computations.\newline
+  \item Complete posterior computations (bayesian IRFs, forectasts, ...).\newline
 
   \item No reason to start from the prior distribution.\newline