fano factor test

projects/pca_natural_img/Makefile

@@ -1,11 +0,0 @@
-latex:
-	pdflatex *.tex > /dev/null
-	pdflatex *.tex > /dev/null
-	pdflatex *.tex > /dev/null
-
-clean:
-	rm -rf *.log *.aux *.zip *.out auto *.bbl *.blg
-	rm -f `basename *.tex .tex`.pdf
-
-zip: latex
-	zip `basename *.tex .tex`.zip *.pdf *.jpg

projects/pca_natural_img/pca_natural_images.tex

@@ -1,61 +0,0 @@
-\documentclass[addpoints,10pt]{exam}
-\usepackage{url}
-\usepackage{color}
-\usepackage{hyperref}
-
-\pagestyle{headandfoot}
-\runningheadrule
-\firstpageheadrule
-\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
-  -- 11/06/2014}
-%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
-\firstpagefooter{}{}{}
-\runningfooter{}{}{}
-\pointsinmargin
-\bracketedpoints
-
-%\printanswers
-%\shadedsolutions
-
-
-\begin{document}
-%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
-\sffamily
-% \begin{flushright}
-% \gradetable[h][questions]
-% \end{flushright}
-
-\begin{center}
-  \input{../disclaimer.tex}
-\end{center}
-
-%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
-
-In you zip file you find a natural image called {\tt natimg.jpg}. 
-\begin{questions}
-
-  \question Load the image and extract all pixels as three dimensional
-  vectors (red, green, and blue channel). 
-  
-  \question Perform a principal component analysis on these
-  three-dimensional vectors.
-
-  \question Try to find a interpretation of the principal components
-  you find in terms of colors. Find a good way to visualize this. 
-
-  \question What could be the biological significance of that (\cite{BG} can
-  give you a clue)?
-
-\end{questions}
-
-\begin{thebibliography}{1}
-\bibitem{BG} Buchsbaum, G., \& Gottschalk, A. (1983). Trichromacy,
-  opponent colours coding and optimum colour information transmission
-  in the retina. Proceedings of the Royal Society of London. Series B,
-  Containing Papers of a Biological Character. Royal Society (Great
-  Britain), 220(1218), 89–113.
-\end{thebibliography}
-
-
-
-\end{document}

projects/project_fano_test/Makefile

@@ -0,0 +1,10 @@
+latex:
+	pdflatex *.tex > /dev/null
+	pdflatex *.tex > /dev/null
+
+clean:
+	rm -rf *.log *.aux *.zip *.out auto
+	rm -f `basename *.tex .tex`.pdf
+
+zip: latex
+	zip `basename *.tex .tex`.zip *.pdf *.dat *.mat

projects/project_fano_test/fano.tex

@@ -0,0 +1,66 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
+  -- 11/06/2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+  \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\begin{questions}
+  \question The Fano factor $\frac{\sigma^2}{\mu}$ is a common measure
+  in neural coding because a Poisson process---for which each spike is
+  independent of every other---has a Fano factor of one.
+
+  The table contains spike counts from a neuron measured in twelve
+  trials.
+
+  \begin{center}
+    \begin{tabular}{cccc}
+      \multicolumn{4}{c}{\bf number of spikes} \\ \hline\\
+      36.00 & 28.00 & 38.00 & 35.00\\
+      32.00 & 30.00 & 35.00 & 29.00\\
+      29.00 & 24.00 & 26.00 & 34.00
+    \end{tabular}
+  \end{center}
+
+  \begin{parts}
+    \part Use {\em Eden, U. T., \& Kramer, M. (2010). Drawing
+      inferences from Fano factor calculations. Journal of
+      neuroscience methods, 190(1), 149--152} to construct a test that
+    uses the Fano factor as test statistic and tests against the Null
+    hypothesis that the spike counts come from a Poisson process.
+    \part Plot the spike counts appropriately. 
+    \part Implement the test and use that it on the data above.
+  \end{parts}
+
+\end{questions}
+
+
+
+\end{document}