.gitignore

 *.pdf
 
 tex/auto
+tex/slides.vrb
 
 model/+fs2000/
 model/fs2000/

matlab/plot_all_distributions.m

@@ -18,6 +18,7 @@ function densities = plot_all_distributions(modelname, nparticles, idparam)
     plot3(densities{1,1}, ones(512,1), densities{1,2}, '-k')
     hold on
     for i=2:25, plot3(densities{i,1}, i*ones(512,1), densities{i,2}, '-k'), end
+    view(axes1,[-31.1204379546341 14.8026428177991]);
     axis tight
     grid on
     hold off

tex/slides.tex

@@ -39,6 +39,7 @@
 \addbibresource{slides.bib}
 
 \usepackage{verbatimbox}
+\usepackage{pgfplots}
 
 \newcommand{\trace}{\mathrm{tr}}
 \newcommand{\vect}{\mathrm{vec}}
@@ -125,7 +126,7 @@
 
     \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 +148,7 @@
 
   \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 +162,7 @@
     % ⇒ 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 +185,14 @@
 
   \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).
 
@@ -292,13 +293,25 @@ posterior_sampling_options = ('particles', 20000,
 
 \begin{frame}
   \frametitle{Sequential importance sampling, V}
+
+  \begin{center}
+    \resizebox{\textwidth}{!}{\input{../model/distributions.tex}}
+  \end{center}
+
+\end{frame}
+
+
+
+
+\begin{frame}
+  \frametitle{Sequential importance sampling, VI}
   \framesubtitle{TODO}
 
   \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