Merge branch 'master' of whale.am28.uni-tuebingen.de:scientificComputing

bootstrap/exercises/bootstraptymus-datahist.pdf

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bootstrap/exercises/correlationsignificance.m

@@ -50,7 +50,7 @@ hold on;
 bar(b, h, 'facecolor', 'b');
 bar(b(b>=rq), h(b>=rq), 'facecolor', 'r');
 plot( [rd rd], [0 4], 'r', 'linewidth', 2 );
-xlim([-0.2 0.2])
+xlim([-0.25 0.25])
 xlabel('Correlation coefficient');
 ylabel('Probability density of H0');
 hold off;

bootstrap/exercises/exercises01.tex

@@ -15,7 +15,7 @@
 \else
 \newcommand{\stitle}{}
 \fi
-\header{{\bfseries\large \"Ubung 3\stitle}}{{\bfseries\large Statistik}}{{\bfseries\large 21. Oktober, 2015}}
+\header{{\bfseries\large \"Ubung\stitle}}{{\bfseries\large Bootstrap}}{{\bfseries\large 17. Januar, 2017}}
 \firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email:
 jan.benda@uni-tuebingen.de}
 \runningfooter{}{\thepage}{}
@@ -84,10 +84,13 @@ jan.benda@uni-tuebingen.de}
 
 \input{instructions}
 
-
 \begin{questions}
 
 \question \qt{Bootstrap des Standardfehlers}
+Wir wollen den Standardfehler, die Standardabweichung des Mittelwerts,
+eines Datensatze mit Hilfe der Bootstrapmethode berechnen und mit der
+Formel ``Standardabweichung geteilt durch Wurzel aus $n$''
+vergleichen.
 \begin{parts}
   \part Lade von Ilias die Datei \code{thymusglandweights.dat} herunter.
   Darin befindet sich ein Datensatz vom Gewicht der Thymus Dr\"use in 14-Tage alten
@@ -112,8 +115,11 @@ jan.benda@uni-tuebingen.de}
 \end{solution}
 
 
-\continue
 \question \qt{Student t-Verteilung}
+Durch Standardabweichungen normierte Mittelwerte sind nicht Gaussverteilt,
+wenn beide aus Normalverteilten Daten abgesch\"atzt werden.
+Die Verteilung von $t=\bar x/(\sigma_x/\sqrt{m})$ folgt vielmehr
+der Student t-Verteilung.
 \begin{parts}
 \part Erzeuge 100000 normalverteilte Zufallszahlen.
 \part Ziehe daraus 1000 Stichproben vom Umfang $m=3$, 5, 10, oder 50.
@@ -123,6 +129,7 @@ dieser Mittelwerte.
 \part Berechne ausserdem die Gr\"o{\ss}e $t=\bar x/(\sigma_x/\sqrt{m})$
 (Standardabweichung $\sigma_x$) und vergleiche diese mit der Normalverteilung mit Standardabweichung Eins. Ist $t$ normalverteilt, bzw. unter welchen Bedingungen ist $t$ normalverteilt?
 \end{parts}
+\newsolutionpage
 \begin{solution}
   \lstinputlisting{tdistribution.m}
   \includegraphics[width=1\textwidth]{tdistribution-n03}\\
@@ -132,7 +139,10 @@ dieser Mittelwerte.
 \end{solution}
 
 
-\question \qt{Korrelationen}
+\continue
+\question \qt{Permutationstest}
+Wir wollen die Signifikanz einer Korrelation durch einen
+Permutationstest bestimmen.
 \begin{parts}
 \part Erzeuge 1000 korrelierte Zufallszahlen $x$, $y$ durch
 \begin{verbatim}

bootstrap/exercises/instructions.tex

@@ -4,38 +4,3 @@
 {\large Jan Grewe, Jan Benda}\\[-3ex]
 Abteilung Neuroethologie \hfill --- \hfill Institut f\"ur Neurobiologie \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\
 \end{center}
-
-\ifprintanswers%
-\else
-
-% Die folgenden Aufgaben dienen der Wiederholung, \"Ubung und
-% Selbstkontrolle und sollten eigenst\"andig bearbeitet und gel\"ost
-% werden. Die L\"osung soll in Form eines einzelnen Skriptes (m-files)
-% im ILIAS hochgeladen werden. Jede Aufgabe sollte in einer eigenen
-% ``Zelle'' gel\"ost sein. Die Zellen \textbf{m\"ussen} unabh\"angig
-% voneinander ausf\"uhrbar sein. Das Skript sollte nach dem Muster:
-% ``variablen\_datentypen\_\{nachname\}.m'' benannt werden
-% (z.B. variablen\_datentypen\_mueller.m).
-
-\begin{itemize}
-\item \"Uberzeuge dich von jeder einzelnen Zeile deines Codes, dass
-  sie auch wirklich das macht, was sie machen soll! Teste dies mit
-  kleinen Beispielen direkt in der Kommandozeile.
-\item Versuche die L\"osungen der Aufgaben m\"oglichst in
-  sinnvolle kleine Funktionen herunterzubrechen.
-  Sobald etwas \"ahnliches mehr als einmal berechnet werden soll,
-  lohnt es sich eine Funktion daraus zu schreiben!
-\item Teste rechenintensive \code{for} Schleifen, Vektoren, Matrizen
-  zuerst mit einer kleinen Anzahl von Wiederholungen oder kleiner
-  Gr\"o{\ss}e, und benutze erst am Ende, wenn alles \"uberpr\"uft
-  ist, eine gro{\ss}e Anzahl von Wiederholungen oder Elementen, um eine gute
-  Statistik zu bekommen.
-\item Benutze die Hilfsfunktion von \code{matlab} (\code{help
-    commando} oder \code{doc commando}) und das Internet, um
-  herauszufinden, wie bestimmte \code{matlab} Funktionen zu verwenden
-  sind und was f\"ur M\"oglichkeiten sie bieten.
-  Auch zu inhaltlichen Konzepten bietet das Internet oft viele
-  Antworten!
-\end{itemize}
-
-\fi

bootstrap/lecture/Makefile

@@ -4,10 +4,13 @@ all : pdf
 
 include ../../chapter.mk
 
-# script:
+include ../../slides.mk
-pdf : chapter
 
-clean : cleanchapter
+# script and slides:
+pdf : chapter slides
+
+clean : cleanchapter cleanslides
+
+cleanall : clean cleanallchapter cleanallslides
 
-cleanall : clean cleanchapter
 

bootstrap/lecture/beamercolorthemetuebingen.sty

@@ -0,0 +1,61 @@
+% Copyright 2007 by Till Tantau
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/licenses/LICENSE for more details.
+
+\usepackage{color} 
+\definecolor{karminrot}{RGB}{165,30,55}
+\definecolor{gold}{RGB}{180,160,105}
+\definecolor{anthrazit}{RGB}{50 ,65 ,75 }
+
+\mode<presentation>
+
+\setbeamercolor*{normal text}{fg=anthrazit,bg=white}
+\setbeamercolor*{alerted text}{fg=anthrazit}
+\setbeamercolor*{example text}{fg=anthrazit}
+\setbeamercolor*{structure}{fg=gold,bg=karminrot}
+
+\providecommand*{\beamer@bftext@only}{%
+  \relax
+  \ifmmode
+    \expandafter\beamer@bftext@warning
+  \else
+    \expandafter\bfseries
+  \fi
+}
+\providecommand*{\beamer@bftext@warning}{%
+  \ClassWarning{beamer}
+    {Cannot use bold for alerted text in math mode}%
+}
+
+\setbeamerfont{alerted text}{series=\beamer@bftext@only}
+
+\setbeamercolor{palette primary}{fg=karminrot,bg=white}
+\setbeamercolor{palette secondary}{fg=gold,bg=white}
+\setbeamercolor{palette tertiary}{fg=anthrazit,bg=white}
+\setbeamercolor{palette quaternary}{fg=black,bg=white}
+
+\setbeamercolor{sidebar}{bg=karminrot!100}
+
+\setbeamercolor{palette sidebar primary}{fg=karminrot}
+\setbeamercolor{palette sidebar secondary}{fg=karminrot}
+\setbeamercolor{palette sidebar tertiary}{fg=karminrot}
+\setbeamercolor{palette sidebar quaternary}{fg=karminrot}
+
+\setbeamercolor{item projected}{fg=black,bg=black!20}
+
+\setbeamercolor*{block body}{}
+\setbeamercolor*{block body alerted}{}
+\setbeamercolor*{block body example}{}
+\setbeamercolor*{block title}{parent=structure}
+\setbeamercolor*{block title alerted}{parent=alerted text}
+\setbeamercolor*{block title example}{parent=example text}
+
+\setbeamercolor*{titlelike}{parent=structure}
+
+\mode
+<all>

bootstrap/lecture/bootstrap-slides.tex

@@ -0,0 +1,110 @@
+\documentclass{beamer}
+
+%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\title[]{Scientific Computing --- Bootstrap methods}
+\author[]{Jan Benda}
+\institute[]{Neuroethology}
+\date[]{WS 16/17}
+\titlegraphic{\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}
+
+%%%%% beamer %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>
+{
+  \usetheme{Singapore}
+  \setbeamercovered{opaque}
+  \usecolortheme{tuebingen}
+  \setbeamertemplate{navigation symbols}{}
+  \usefonttheme{default}
+  \useoutertheme{infolines}
+  % \useoutertheme{miniframes}
+}
+
+%\AtBeginSection[]
+%{
+%  \begin{frame}<beamer>
+%    \begin{center}
+%      \Huge \insertsectionhead
+%    \end{center}
+%  \end{frame}
+%}
+
+\setbeamertemplate{blocks}[rounded][shadow=true]
+\setcounter{tocdepth}{1}
+
+%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{bm} 
+\usepackage{pslatex}   % nice font for pdf file
+%\usepackage{multimedia}
+
+\usepackage{dsfont}
+\newcommand{\naZ}{\mathds{N}}
+\newcommand{\gaZ}{\mathds{Z}}
+\newcommand{\raZ}{\mathds{Q}}
+\newcommand{\reZ}{\mathds{R}}
+\newcommand{\reZp}{\mathds{R^+}}
+\newcommand{\reZpN}{\mathds{R^+_0}}
+\newcommand{\koZ}{\mathds{C}}
+
+%%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{graphicx}
+\newcommand{\texpicture}[1]{{\sffamily\small\input{#1.tex}}}
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ commentstyle=\itshape\color{darkgray},
+ keywordstyle=\color{blue},
+ stringstyle=\color{green},
+ backgroundcolor=\color{blue!10},
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+ captionpos=b,
+ xleftmargin=1em,
+ xrightmargin=1em,
+ aboveskip=10pt
+ }
+
+\graphicspath{{figures/}}
+
+ 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document} 
+
+\begin{frame}[plain]
+  \frametitle{}
+  \vspace{-1cm}
+  \titlepage % erzeugt Titelseite
+\end{frame}
+
+\subsection{Bootstrap distribution}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+  \frametitle{Sampling distribution}
+  \includegraphics[width=1\textwidth]{srs1}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Theoretical sampling distribution}
+  \includegraphics[width=1\textwidth]{srs2}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Bootstrap distribution}
+  \includegraphics[width=1\textwidth]{srs3}\\[1ex]
+  \begin{itemize}
+  \item Resampling with replacement.
+  \item Size of resample equals size of original sample.
+  \end{itemize}
+\end{frame}
+
+\end{document}
+

programming/exercises/factorialscriptb.m

@@ -1 +1 @@
-printfaculty(5);
+printfactorial(5);

programming/exercises/myfactorial.m

@@ -1,4 +1,4 @@
-function x = mufactorial(n)
+function x = myfactorial(n)
 % return the factorial of n
 x = 1;
 for i = 1:n

programming/exercises/printfactorial.m

@@ -1,5 +1,5 @@
-function printfaculty(n)
+function printfactorial(n)
-% compute the faculty of n and print it
+% compute the factorial of n and print it
 x = 1;
 for i = 1:n
     x = x * i;

programming/lecture/programming-chapter.tex

@@ -26,6 +26,7 @@
 \item Matrizen erstmal 2-D und nur kurz n-D
 \item Zusammenfassung von Fehlermeldungen bezueglich Matrizen und Vektoren
 \item Random-walk behutsam mit einer Schleife, dann zwei Schleifen. Plus Bildchen.
+\item Random-Walk with drift is model for decision making! See resoures/GoldShadlen2007 paper, Figure 2. Das wird auch in Systems Neurosciene \texttt{9 - Kognitive Kontrolle II.pdf} behandelt.
 \item Doppelte for-Schleife
 \item File output and input (load, save, fprintf, scanf) (extra chapter?)
 \item help() und doc()

projects/project_fano_time/solution/counthist.m

@@ -0,0 +1,11 @@
+function [counts, cbins] = counthist(spikes, tmin, tmax, T, cmax)
+tbins = tmin+T/2:T:tmax;
+cbins = 0.5:cmax;
+counts = zeros(1, length(cbins));
+for k = 1:length(spikes)
+    times = spikes{k};
+    n = hist(times((times>=tmin)&(times<=tmax)), tbins);
+    counts = counts + hist(n, cbins);
+end
+counts = counts / sum(counts);
+end

projects/project_fano_time/solution/discriminability.m

@@ -0,0 +1,23 @@
+function [d, thresholds, true1s, false1s, true2s, false2s, pratio] = discriminability(spikes1, spikes2, tmax, T, cmax)
+[c1, b1] = counthist(spikes1, 0.0, tmax, T, cmax);
+[c2, b2] = counthist(spikes2, 0.0, tmax, T, cmax);
+thresholds = 0:cmax;
+true1s = zeros(length(thresholds), 1);
+true2s = zeros(length(thresholds), 1);
+false1s = zeros(length(thresholds), 1);
+false2s = zeros(length(thresholds), 1);
+for k = 1:length(thresholds)
+    th = thresholds(k);
+    t1 = sum(c1(b1<=th));
+    f1 = sum(c1(b1>th));
+    t2 = sum(c2(b2>=th));
+    f2 = sum(c2(b2<th));
+    true1s(k) = t1;
+    true2s(k) = t2;
+    false1s(k) = f1;
+    false2s(k) = f2;
+end
+%pratio = (true1s + true2s)./(false1s+false2s);
+pratio = (true1s + true2s)/2;
+d = max(pratio);
+end

projects/project_fano_time/solution/fanotime.m

@@ -0,0 +1,71 @@
+%% general settings for the model neuron:
+trials = 10;
+tmax = 50.0;
+D = 0.01;
+
+%% generate and plot spiketrains for two inputs:
+I1 = 14.0;
+I2 = 15.0;
+spikes1 = lifspikes(trials, I1, tmax, D);
+spikes2 = lifspikes(trials, I2, tmax, D);
+subplot(1, 2, 1);
+tmin = 10.0;
+spikeraster(spikes1, tmin, tmin+2.0);
+title(sprintf('I_1=%g', I1))
+subplot(1, 2, 2);
+spikeraster(spikes2, tmin, tmin+2.0);
+title(sprintf('I_2=%g', I2))
+%savefigpdf(gcf(), 'spikeraster.pdf')
+
+%% spike count histograms:
+Ts = [0.01 0.1 0.5 1.0];
+cmax = 100;
+figure()
+for k = 1:length(Ts)
+    T = Ts(k);
+    [c1, b1] = counthist(spikes1, 0.0, tmax, T, cmax);
+    [c2, b2] = counthist(spikes2, 0.0, tmax, T, cmax);
+    subplot(2, 2, k)
+    bar(b1, c1, 'r');
+    hold on;
+    bar(b2, c2, 'b');
+    xlim([0 cmax])
+    title(sprintf('T=%gms', 1000.0*T))
+    hold off;
+end
+
+%% discrimination measure:
+T = 0.1;
+cmax = 20;
+[d, thresholds, true1s, false1s, true2s, false2s, pratio] = discriminability(spikes1, spikes2, tmax, T, cmax);
+figure()
+subplot(1, 3, 1);
+plot(thresholds, true1s, 'b');
+hold on;
+plot(thresholds, true2s, 'b');
+plot(thresholds, false1s, 'r');
+plot(thresholds, false2s, 'r');
+hold off;
+% Ratio:
+subplot(1, 3, 2);
+fprintf('discriminability = %g\n', d);
+plot(thresholds, pratio);
+% ROC:
+subplot(1, 3, 3);
+plot(false2s, true1s);
+
+%% discriminability:
+Ts = 0.01:0.01:1.0;
+cmax = 100;
+ds = zeros(length(Ts), 1)
+for k = 1:length(Ts)
+    T = Ts(k);
+    [c1, b1] = counthist(spikes1, 0.0, tmax, T, cmax);
+    [c2, b2] = counthist(spikes2, 0.0, tmax, T, cmax);
+    [d, thresholds, true1s, false1s, true2s, false2s, pratio] = discriminability(spikes1, spikes2, tmax, T, cmax);
+    ds(k) = d;
+end
+figure()
+plot(Ts, ds)
+
+

projects/project_fano_time/solution/lifspikes.m

@@ -0,0 +1,39 @@
+function spikes = lifspikes(trials, input, tmaxdt, D)
+% Generate spike times of a leaky integrate-and-fire neuron.
+% trials: the number of trials to be generated
+% input: the stimulus either as a single value or as a vector
+% tmaxdt: in case of a single value stimulus the duration of a trial
+%         in case of a vector as a stimulus the time step
+% D: the strength of additive white noise
+    
+    tau = 0.01;
+    if nargin < 4
+        D = 1e0;
+    end
+    vreset = 0.0;
+    vthresh = 10.0;
+    dt = 5e-5;
+    
+    if max(size(input)) == 1
+        input = input * ones(ceil(tmaxdt/dt), 1);
+    else
+        dt = tmaxdt;
+    end
+    spikes = cell(trials, 1);
+    for k=1:trials
+        times = [];
+        j = 1;
+        v = vreset + (vthresh-vreset)*rand(1);
+        noise = sqrt(2.0*D)*randn(length(input), 1)/sqrt(dt);
+        for i=1:length(noise)
+            v = v + (- v + noise(i) + input(i))*dt/tau;
+            if v >= vthresh
+                v = vreset;
+                spiketime = i*dt;
+                times(j) = spiketime;
+                j = j + 1;
+            end
+        end
+        spikes{k} = times;
+    end
+end

projects/project_fano_time/solution/savefigpdf.m

@@ -0,0 +1,28 @@
+function savefigpdf(fig, name, width, height)
+% Saves figure fig in pdf file name.pdf with appropriately set page size
+% and fonts
+
+% default width:
+if nargin < 3
+    width = 11.7;
+end
+% default height:
+if nargin < 4
+    height = 9.0;
+end
+
+% paper:
+set(fig, 'PaperUnits', 'centimeters');
+set(fig, 'PaperSize', [width height]);
+set(fig, 'PaperPosition', [0.0 0.0 width height]);
+set(fig, 'Color', 'white')
+
+% font:
+set(findall(fig, 'type', 'axes'), 'FontSize', 12)
+set(findall(fig, 'type', 'text'), 'FontSize', 12)
+
+% save:
+saveas(fig, name, 'pdf')
+
+end
+

projects/project_fano_time/solution/spikeraster.m

@@ -0,0 +1,30 @@
+function spikeraster(spikes, tmin, tmax)
+% Display a spike raster of the spike times given in spikes.
+%
+% spikeraster(spikes, tmax)
+%   spikes: a cell array of vectors of spike times in seconds
+%   tmin: plot spike raster starting at tmin seconds
+%   tmax: plot spike raster upto tmax seconds
+
+ntrials = length(spikes);
+for k = 1:ntrials
+    times = spikes{k};
+    times = times((times>=tmin) & (times<=tmax));
+    if tmax < 1.5
+        times = 1000.0*times; % conversion to ms
+    end
+    for i = 1:length( times )
+      line([times(i) times(i)],[k-0.4 k+0.4], 'Color', 'k'); 
+    end
+end
+if (tmax-tmin) < 1.5
+    xlabel('Time [ms]');
+    xlim([1000.0*tmin 1000.0*tmax]);
+else
+    xlabel('Time [s]');
+    xlim([tmin tmax]);
+end
+ylabel('Trials');
+ylim([0.3 ntrials+0.7 ]);
+end
+

slides.mk

@@ -0,0 +1,15 @@
+# slides:
+slides : $(BASENAME)-slides.pdf
+
+$(BASENAME)-slides.pdf : $(BASENAME)-slides.tex $(PYPDFFILES) $(GPTTEXFILES)
+	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
+
+watchslides :
+	while true; do ! make -q slides && make slides; sleep 0.5; done
+
+cleanslides :
+	rm -f *~ 
+	rm -f $(BASENAME)-slides.aux $(BASENAME)-slides.log $(BASENAME)-slides.out $(BASENAME)-slides.idx
+
+cleanallslides : cleanslides
+	rm -f $(BASENAME)-slides.pdf

statistics/exercises/randomwalkfirstpassagetime.py

@@ -0,0 +1,34 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+# first passage time of random walker
+# the average of the first passage time grows
+# the more experiments you average (n)
+# eventually diverges to infinity
+# see https://www.math.ucdavis.edu/~tracy/courses/math135A/UsefullCourseMaterial/firstPassage.pdf last paragraph
+
+p = 0.5
+thresh = 1.0
+rep = 1
+rn = 10000
+n = 2
+meantimes = np.zeros(rep)
+for i in range(rep):
+    times = np.zeros(n)
+    for k in  range(n):
+        xx = 0.0
+        xxinx = 0
+        while True:
+            r = np.random.rand(rn)
+            x = np.zeros(len(r))
+            x[r < p] = 1.0
+            x[r >= p]= -1.0
+            y = xx + np.cumsum(x)
+            inx = np.where(y > thresh)[0]
+            if len(inx) > 0:
+                times[k] = xxinx + inx[0]
+                break
+            xx = y[-1]
+            xxinx += len(x)
+    meantimes[i] = np.mean(times)
+print np.mean(meantimes)