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

latex/environments.tex

@@ -25,6 +25,12 @@
 \definecolor{sec22}{RGB}{210,150,0} 
 \definecolor{sec23}{RGB}{145,105,70} 
 
+\newcommand{\source}[1]{    
+  \begin{flushright}
+    \color{gray}\scriptsize \url{#1}
+  \end{flushright}
+}
+
 \newenvironment<>{emphasize}[1]{%
   \begin{actionenv}#2%
       \def\insertblocktitle{#1}%

statistics/Makefile

@@ -3,12 +3,9 @@ DOTSOURCES = $(wildcard figs/*.dot)
 
 
 all: $(DOTSOURCES:dot=pdf) 
-	python figs/generate.py
+	pdflatex lecture_statistics*.tex
-	python figs/generate03.py
+	pdflatex lecture_statistics*.tex
-	python figs/generateTPlots.py
+	pdflatex lecture_statistics*.tex
-	pdflatex talk*.tex
-	pdflatex talk*.tex
-	pdflatex talk*.tex
 
 
 figs/prob%.pdf : figs/prob%.dot

statistics/certificate.lyx

@@ -1,218 +0,0 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass g-brief2
-\begin_preamble
-\fenstermarken % prints address window marks
-\faltmarken % prints folding marks
-%\lochermarke % prints puncher marks 
-\trennlinien % prints striplines
-%\unserzeichen % prints "our ref" instead of "my ref"
-\end_preamble
-\use_default_options false
-\maintain_unincluded_children false
-\language english
-\language_package default
-\inputencoding auto
-\fontencoding global
-\font_roman palatino
-\font_sans default
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-\font_sf_scale 100
-\font_tt_scale 100
-
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-\output_sync 0
-\bibtex_command default
-\index_command default
-\paperfontsize 12
-\spacing onehalf
-\use_hyperref false
-\papersize default
-\use_geometry false
-\use_amsmath 1
-\use_esint 1
-\use_mhchem 1
-\use_mathdots 1
-\cite_engine basic
-\use_bibtopic false
-\use_indices false
-\paperorientation portrait
-\suppress_date false
-\use_refstyle 0
-\index Index
-\shortcut idx
-\color #008000
-\end_index
-\secnumdepth 4
-\tocdepth 4
-\paragraph_separation skip
-\defskip medskip
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle empty
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-Note also the document preamble settings.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout NameRowA
-Dr.
- rer.
- nat.
- Fabian Sinz
-\end_layout
-
-\begin_layout NameRowB
-
-\end_layout
-
-\begin_layout NameRowC
-
-\end_layout
-
-\begin_layout NameRowD
-
-\end_layout
-
-\begin_layout NameRowE
-
-\end_layout
-
-\begin_layout NameRowF
-
-\end_layout
-
-\begin_layout NameRowG
-
-\end_layout
-
-\begin_layout AddressRowA
-University Tübingen
-\end_layout
-
-\begin_layout AddressRowB
-
-\end_layout
-
-\begin_layout AddressRowC
-Auf der Morgenstelle 28
-\end_layout
-
-\begin_layout AddressRowD
-72076 Tübingen
-\end_layout
-
-\begin_layout InternetRowA
-http:/
-\begin_inset Formula $\!$
-\end_inset
-
-/www.epagoge.de
-\end_layout
-
-\begin_layout InternetRowB
-fabian.sinz@epagoge.de
-\end_layout
-
-\begin_layout ReturnAddress
-University Tübingen 
-\begin_inset Formula $\cdot$
-\end_inset
-
- Auf der Morgenstelle 28 
-\begin_inset Formula $\cdot$
-\end_inset
-
- 72076 Tübingen
-\end_layout
-
-\begin_layout Date
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-today
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Reference
-
-\end_layout
-
-\begin_layout Opening
-To whom it may concern,
-\end_layout
-
-\begin_layout Closing
-Best regards
-\end_layout
-
-\begin_layout Signature
-Dr.
- Fabian Sinz
-\end_layout
-
-\begin_layout Encl.
-
-\end_layout
-
-\begin_layout Letter
-this letter certifies that 
-\emph on
-Lakshmi Channappa
-\emph default
- attended the course 
-\emph on
-Statistics in a Nutshell
-\emph default
- held at the Neurochip research group at the 
-\emph on
-Naturwissenschaftliches und Medizinisches Institut Reutlingen 
-\emph default
-in 2013
-\emph on
-.
- 
-\emph default
-The course was organized in two lectures of four hours each and covered
- topics such as basics of probability theory, errorbars and confidence intervals
-, statistical tests, p-values, multiple hypothesis testing, basics of study
- design, and basics of ANOVA.
- Small calculation and programming exercises were used to clarify selected
- material.
-\end_layout
-
-\end_body
-\end_document

statistics/figs/fig0.dot

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statistics/figs/fig01.dot

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statistics/figs/fig02.dot

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statistics/figs/fig03.dot

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statistics/figs/fig04.dot

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statistics/figs/fig05.dot

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statistics/figs/fig06.dot

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statistics/figs/generate.py

@@ -1,106 +0,0 @@
-from __future__ import division
-import seaborn as sns
-import sys
-sys.path.append('/home/fabee/code/')
-from matplotlib.pyplot import *
-from fabee.Plotting import *
-from scipy import stats
-from numpy import *
-
-sns.set_context("talk", font_scale=1.5, rc={"lines.linewidth": 2.5})
-
-# ---------------------------------------------------------------------------
-fig, ax = subplots()
-fig.subplots_adjust(bottom=.3, left=.3)
-n = 50
-x = loadtxt('scripts/thymusglandweights.dat')[:n]
-ax.bar([0,1],[mean(x),mean(x)],yerr = [std(x,ddof=1), std(x,ddof=1)/sqrt(n)],
-       facecolor='dodgerblue', alpha=.8,width=.7, align='center',
-       error_kw={'color':'k','lw':2}, capsize=10, ecolor='k')
-ax.set_title('standard deviation or standard error?',fontsize=14, fontweight='bold')
-
-ax.set_xlim([-.5,1.5])
-box_off(ax)
-#disjoint_axes(ax)
-ax.set_xticks([0,1])
-ax.set_xticklabels([r'$\hat\sigma$', r'$\frac{\hat\sigma}{\sqrt{n}}$'], fontsize=30)
-
-ax.set_ylabel(r'$\frac{1}{n}\sum_{i=1}^n x_i$',fontsize=30, fontweight='bold')
-
-fig.savefig('figs/StandardErrorOrStandardDeviation.pdf')
-
-# ---------------------------------------------------------------------------
-fig, ax = subplots()
-
-t = linspace(-5,5,1000)
-t2 = linspace(stats.laplace.ppf(0.025),stats.laplace.ppf(1-0.025),1000)
-
-ax.fill_between(t,stats.laplace.pdf(t),color='dodgerblue')
-ax.set_xticks([])
-ax.text(5,-0.05, r'$\hat m$',fontsize=30)
-ax.text(0,0.7, r'$m$',fontsize=30)
-ax.set_yticks([])
-#disjoint_axes(ax)
-box_off(ax)
-
-ax.set_title('putative sampling distribution of the median',fontsize=14, fontweight='bold')
-ax.axis([-5,5,0,.8])
-ax.plot([0,0],[0,.7],'--k',lw=2)
-
-fig.savefig('figs/samplingDistributionMedian00.pdf')
-
-ax.fill_between(t2,stats.laplace.pdf(t2),color='crimson')
-
-fig.savefig('figs/samplingDistributionMedian01.pdf')
-
-# ---------------------------------------------------------------------------
-fig, ax = subplots()
-k = 7
-N = 21
-F = stats.f
-t = linspace(1e-6,8,1000)
-t2= linspace(F.ppf(0.95,k-1,N-k),8,1000)
-
-ax.fill_between(t,F.pdf(t,k-1,N-k),color='dodgerblue')
-ax.fill_between(t2,F.pdf(t2,k-1,N-k),color='crimson')
-ax.set_xlabel('group MS/ error MS')
-ax.set_ylabel(r'p(group MS/ error MS| $H_0$)')
-ax.set_title('F-distribution',fontsize=14, fontweight='bold')
-ax.set_ylim((0,0.8))
-box_off(ax)
-fig.savefig('figs/Fdistribution00.pdf')
-
-# ---------------------------------------------------------------------------
-fig, ax = subplots()
-n = 5
-p = stats.t.pdf
-t = linspace(-5,8,1000)
-t0 = 1.5
-t00 = 1.
-
-mu0 = 3
-t1 = linspace(-5,t00,1000)
-t2 = linspace(t0,8,1000)
-t3 = linspace(-5,-t0,1000)
-ax.fill_between(t,p(t,n-1),color='dodgerblue',alpha=1)
-ax.fill_between(t2,p(t2,n-1),color='indigo',alpha=1)
-ax.fill_between(t3,p(t3,n-1),color='indigo',alpha=1)
-ax.set_xlabel('t')
-ax.set_ylabel(r'sampling distribution')
-ax.set_ylim((0,0.8))
-box_off(ax)
-fig.savefig('figs/experimentalDesign00.pdf')
-
-
-ax.fill_between(t,p(t,n-1,loc=mu0),color='lime',alpha=.5)
-ax.fill_between(t1,p(t1,n-1,loc=mu0),color='magenta',alpha=1)
-ax.arrow(0,.4,mu0,0,head_width=0.05)
-ax.arrow(mu0,.4,-mu0,0,head_width=0.05)
-ax.text(mu0/2,.45,r'$\delta$',fontsize=20)
-ax.set_xlabel('t')
-ax.set_ylabel(r'sampling distribution')
-ax.set_ylim((0,0.8))
-box_off(ax)
-fig.savefig('figs/experimentalDesign01.pdf')
-
-

statistics/figs/generate03.py

@@ -1,265 +0,0 @@
-import sys
-import seaborn as sns
-sys.path.append('/home/fabee/code/')
-from matplotlib.pyplot import *
-from fabee.Plotting import *
-from scipy import stats
-from numpy import *
-
-sns.set_context("talk", font_scale=1.5, rc={"lines.linewidth": 2.5})
-
-def hinton(matrix, max_weight=None, ax=None):
-    """Draw Hinton diagram for visualizing a weight matrix."""
-    ax = ax if ax is not None else gca()
-
-    if not max_weight:
-        max_weight = 2**np.ceil(np.log(np.abs(matrix).max())/np.log(2))
-
-    ax.patch.set_facecolor('gray')
-    ax.set_aspect('equal', 'box')
-    ax.xaxis.set_major_locator(NullLocator())
-    ax.yaxis.set_major_locator(NullLocator())
-
-    for (x,y),w in np.ndenumerate(matrix):
-        color = 'white' if w > 0 else 'black'
-        size = np.sqrt(np.abs(w))
-        rect = Rectangle([x - size / 2, y - size / 2], size, size,
-                             facecolor=color, edgecolor=color)
-        ax.add_patch(rect)
-
-    ax.autoscale_view()
-    ax.invert_yaxis()
-
-# ---------------------------------------------------------------------------
-fig, ax = subplots()
-fig.subplots_adjust(bottom=.2)
-
-ax.bar([0,1],[.2,.8],facecolor='dodgerblue', alpha=.8,width=.7, align='center')
-ax.set_title('Bernoulli distribution',fontsize=16, fontweight='bold')
-
-ax.set_xlim([-.5,1.5])
-box_off(ax)
-#disjoint_axes(ax)
-ax.set_xlabel('outcomes',fontsize=14, fontweight='bold')
-ax.set_ylabel('P(outcome)',fontsize=14, fontweight='bold')
-ax.set_xticks([0,1])
-ax.set_xticklabels([0,1])
-ax.set_ylim((0,1))
-
-fig.savefig('figs/Bernoulli.pdf')
-
-# ---------------------------------------------------------------------------
-fig, ax = subplots()
-fig.subplots_adjust(bottom=.2)
-n = 5
-k = arange(0,n)
-ax.bar(k,0*k+1./n,facecolor='dodgerblue', alpha=.8,width=.7, align='center')
-ax.set_title('uniform distribution',fontsize=16, fontweight='bold')
-
-box_off(ax)
-#disjoint_axes(ax)
-ax.set_xlabel('k',fontsize=14, fontweight='bold')
-ax.set_ylabel('P(X=k)',fontsize=14, fontweight='bold')
-ax.set_xticks(k)
-ax.set_xticklabels(k+1)
-ax.set_ylim((0,1))
-fig.savefig('figs/Uniform.pdf')
-
-# ---------------------------------------------------------------------------
-
-for i,(n,p) in enumerate(zip([10,20],[.5,.8])):
-    fig, ax = subplots()
-
-    fig.subplots_adjust(bottom=.2)
-    k = arange(n+1)
-    
-    ax.bar(k,stats.binom.pmf(k,n,p),facecolor='dodgerblue', alpha=.8,width=.7, align='center')
-    ax.set_title(r'binomial distribution $B\left(%.2f, %i\right)$' % (p,n),fontsize=16, fontweight='bold')
-    
-    box_off(ax)
-    #disjoint_axes(ax)
-    ax.set_xlabel('k',fontsize=14, fontweight='bold')
-    ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
-    ax.set_xticks(k)
-    ax.set_xticklabels(k)
-    ax.set_xlim((-1,n+1))
-    ax.set_ylim((0,1))
-    fig.savefig('figs/Binomial%02i.pdf' % (i,))
-
-
-# ---------------------------------------------------------------------------
-n = 20
-for i, lam in enumerate([5, 0.05]):
-    fig, ax = subplots()
-
-    fig.subplots_adjust(bottom=.2)
-    k = arange(n+1)
-    
-    ax.bar(k,stats.poisson.pmf(k,lam),facecolor='dodgerblue', alpha=.8,width=.7, align='center')
-    ax.set_title(r'Poisson distribution $\lambda=%.2f$' % (lam,),fontsize=16, fontweight='bold')
-    
-    box_off(ax)
-    #disjoint_axes(ax)
-    ax.set_xlabel('k',fontsize=14, fontweight='bold')
-    ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
-    ax.set_xticks(k)
-    ax.set_xticklabels(k)
-    ax.set_xlim((-1,n+1))
-    ax.set_ylim((0,1))
-    fig.savefig('figs/Poisson%02i.pdf' % (i,))
-
-# ---------------------------------------------------------------------------
-fig, ax = subplots()
-
-fig.subplots_adjust(bottom=.2)
-t = linspace(-3,3,200)
-ax.fill_between(t,stats.norm.pdf(t),facecolor='dodgerblue', alpha=.8)
-ax.set_title(r'Gaussian/Normal distribution $N(\mu,\sigma)$',fontsize=16, fontweight='bold')
-    
-box_off(ax)
-#disjoint_axes(ax)
-ax.set_xlabel('x',fontsize=14, fontweight='bold')
-ax.set_ylabel('p(x)',fontsize=14, fontweight='bold')
-fig.savefig('figs/Gaussian00.pdf')
-
-# ---------------------------------------------------------------------------
-
-fig, ax = subplots()
-n = 10
-kk = 5
-p = .5
-fig.subplots_adjust(bottom=.2)
-k = arange(n+1)
-    
-ax.bar(k,stats.binom.pmf(k,n,p),facecolor='dodgerblue', alpha=.8,width=.7, align='center')
-ax.bar(k[:kk+1],stats.binom.pmf(k[:kk+1],n,p),facecolor='crimson', alpha=.5,width=.7, align='center')
-ax.set_title(r'binomial distribution $B\left(\frac{1}{2}, %i\right)$' % (n,), fontsize=16, fontweight='bold')
-
-box_off(ax)
-#disjoint_axes(ax)
-ax.set_xlabel('k',fontsize=14, fontweight='bold')
-ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
-ax.set_xticks(k)
-ax.set_xticklabels(k)
-ax.set_xlim((-1,n+1))
-ax.set_ylim((0,1))
-fig.savefig('figs/BinomialCdf00.pdf' )
-
-
-fig, ax = subplots()
-n = 10
-kk = 5
-p = .5
-fig.subplots_adjust(bottom=.2)
-k = arange(n+1)
-    
-ax.bar(k,stats.binom.pmf(k,n,p),facecolor='dodgerblue', alpha=.8,width=.7, align='center',label='p.m.f.')
-ax.bar(k[:kk+1],stats.binom.pmf(k[:kk+1],n,p),facecolor='crimson', alpha=.5,width=.7, align='center')
-ax.plot(k,stats.binom.cdf(k,n,p),'ok',mfc='crimson', alpha=1.,label='c.d.f.', ms=15)
-
-ax.set_title(r'binomial distribution $B\left(\frac{1}{2}, %i\right)$' % (n,), fontsize=16, fontweight='bold')
-ax.legend(frameon=False, loc='best')
-box_off(ax)
-#disjoint_axes(ax)
-ax.set_xlabel('k',fontsize=14, fontweight='bold')
-ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
-ax.set_xticks(k)
-ax.set_xticklabels(k)
-ax.set_xlim((-1,n+1))
-ax.set_ylim((0,1.1))
-fig.savefig('figs/BinomialCdf01.pdf' )
-
-fig, ax = subplots()
-n = 10
-kk = 2
-p = .5
-fig.subplots_adjust(bottom=.2)
-k = arange(n+1)
-    
-ax.bar(k,stats.binom.pmf(k,n,p),facecolor='dodgerblue', alpha=.8,width=.7, align='center',label='p.m.f.')
-ax.bar(k[:kk+1],stats.binom.pmf(k[:kk+1],n,p),facecolor='crimson', alpha=.5,width=.7, align='center')
-ax.bar(k[-kk-1:],stats.binom.pmf(k[-kk-1:],n,p),facecolor='crimson', alpha=.5,width=.7, align='center')
-
-ax.set_title(r'binomial distribution $B\left(\frac{1}{2}, %i\right)$' % (n,), fontsize=16, fontweight='bold')
-ax.legend(frameon=False, loc='best')
-box_off(ax)
-#disjoint_axes(ax)
-ax.set_xlabel('k',fontsize=14, fontweight='bold')
-ax.set_ylabel('P(k)',fontsize=14, fontweight='bold')
-ax.set_xticks(k)
-ax.set_xticklabels(k)
-ax.set_xlim((-1,n+1))
-ax.set_ylim((0,1.1))
-fig.savefig('figs/BinomialExample00.pdf' )
-
-
-#------------------------------------------------------
-fig = figure(figsize=(10,3.5))
-ax = fig.add_axes([.1,.13,.6,.3])
-
-n = 10
-p = [.5,.8]
-q = [.7, .3]
-fig.subplots_adjust(bottom=0.2)
-k = arange(n+1)
-P = vstack((stats.binom.pmf(k,n,p[0])*q[0], stats.binom.pmf(k,n,p[1])*q[1])).T
-
-hinton(P, ax = None)
-
-#disjoint_axes(ax)
-ax.set_xticks(k)
-ax.set_xticklabels(k)
-ax.set_yticks([0,1])
-ax.set_ylim((-.5,1.5))
-ax.set_xlim((-.5,n+.5))
-ax.set_yticklabels(['subject #1', 'subject #2'])
-fig.savefig('figs/Joint00.pdf' )
-
-ax = fig.add_axes([.75,.13,.2,.3])
-ax.barh([0,1],q, facecolor='dodgerblue',alpha=.8, align='center')
-box_off(ax)
-#disjoint_axes(ax)
-ax.set_xticks([0,.5,1.])
-ax.set_yticks([])
-ax.set_ylim((-.5,1.5))
-fig.savefig('figs/Joint01.pdf' )
-
-ax = fig.add_axes([.1,.6,.6,.2])
-ax.bar(k,sum(P,axis=1), facecolor='dodgerblue',alpha=.8, align='center')
-a = .7
-ax.axis([-a,n-a+1.5,0,1])
-box_off(ax)
-#disjoint_axes(ax)
-ax.set_xticks([])
-ax.set_yticks([0,.3])
-ax.set_ylim((0,.3))
-fig.savefig('figs/Joint02.pdf' )
-
-
-#------------------------------------------------------
-n = 10
-k = arange(n+1)
-p = [.5,.8]
-q = [.7, .3]
-P = vstack((stats.binom.pmf(k,n,p[0])*q[0], stats.binom.pmf(k,n,p[1])*q[1]))
-Pk = sum(P,axis=0)
-
-fig = figure()
-for i,kk in enumerate(k):
-    ax = fig.add_subplot(3,4,i+1)
-    fig.subplots_adjust(bottom=0.2)
-
-    ax.bar([0,1],P[:,i]/Pk[i], facecolor='dodgerblue',alpha=.8, align='center')
-
-    
-    #disjoint_axes(ax)
-    ax.set_xticks([0,1])
-    ax.set_xticklabels(['#1','#2'], fontsize=8)
-    ax.set_yticks([0,.5,1])
-    ax.set_yticklabels([0,.5,1],fontsize=8)
-    ax.set_xlim((-.5,1.5))
-    ax.set_ylim((0,1))
-    ax.set_title('P({#1,#2}| %i successes)'  % (i,), fontsize=8)
-
-fig.subplots_adjust(wspace=.8, hspace=.8)
-fig.savefig('figs/Posterior00.pdf')

statistics/figs/generatePlots.py

@@ -1,216 +0,0 @@
-import sys
-sys.path.append('/home/fabee/code/')
-import seaborn as sns
-from matplotlib.pyplot import *
-from scipy import stats
-from numpy import *
-
-from matplotlib.ticker import NullFormatter
-
-sns.set_context("talk", font_scale=1.5, rc={"lines.linewidth": 2.5})
-
-# --------------- PLOT 1 -------------------------
-# the random data
-distr = stats.uniform
-col = '+*0<>v'
-
-for k,distr in enumerate([stats.laplace, stats.norm, stats.expon,stats.uniform]):
-    col = [col[i] for i in random.permutation(6)]
-    x = random.randn(5000)
-
-    nullfmt   = NullFormatter()         # no labels
-
-    # definitions for the axes
-    left, width = 0.1, 0.65
-    bottom, height = 0.1, 0.65
-    bottom_h = left_h = left+width+0.02
-    
-    rect_scatter = [left + 0.22, bottom + 0.22 , width, height]
-    rect_histx = [left + 0.22, bottom, width, 0.2]
-    rect_histy = [left, bottom + 0.22 , 0.2, height]
-    
-    # start with a rectangular Figure
-    fig = figure(figsize=(8,8))
-    
-    axQQ = axes(rect_scatter)
-    axHistx = axes(rect_histx)
-    axHisty = axes(rect_histy)
-    
-    # no labels
-    axHistx.yaxis.set_major_formatter(nullfmt)
-    axHisty.xaxis.set_major_formatter(nullfmt)
-    axQQ.xaxis.set_major_formatter(nullfmt)
-    axQQ.yaxis.set_major_formatter(nullfmt)
-    
-    
-    
-    # the scatter plot:
-    z = distr.ppf(stats.norm.cdf(x))
-    y = linspace(amin(z),amax(z),1000)
-    
-    
-    z = distr.ppf(stats.norm.cdf(x))
-    if distr != stats.norm:
-        if distr == stats.uniform:
-            axQQ.plot(x, z,'ok',marker=col[0],ms=5,label='c.d.f.')
-        else:
-            axQQ.plot(x, z,'ok',marker=col[0],ms=5,label='correct')
-
-        if distr != stats.expon:
-            axQQ.plot((z-amin(z))/(amax(z)-amin(z))*(amax(x)-amin(x)) + amin(x),\
-                      (x-amin(x))/(amax(x)-amin(x))*(amax(z)-amin(z)) + amin(z),'ok',marker=col[1],ms=5)
-            axQQ.plot(x, (x-amin(x))/(amax(x)-amin(x))*(amax(z)-amin(z)) + amin(z),'ok',marker=col[2],ms=5)
-        
-    
-    # now determine nice limits by hand:
-    axHistx.hist(x, bins=100,normed=True)
-    if distr != stats.expon:
-        axHisty.plot(distr.pdf(y),y)
-        z2 = distr.pdf(y)
-        y = hstack((y[0],y,y[-1]))
-        z2 = hstack((0,z2,0))
-        axHisty.fill(z2,y,color=(.0,.0,1.))
-    
-    axQQ.set_xlim(axHistx.get_xlim())
-    axQQ.set_ylim(axHisty.get_ylim())
-
-    if distr == stats.uniform:
-        axQQ.set_ylim((-.1,1.1))
-        axHisty.set_ylim((-.1,1.1))
-        axHisty.set_xlim((.0,1.1))
-    
-    axHistx.set_xlabel('x',fontsize=16)
-    axHistx.set_ylabel('p(x)',fontsize=16)
-    axHisty.set_ylabel('y',fontsize=16)
-    axHisty.set_xlabel('p(y)',fontsize=16)
-
-    fig.savefig('figs/HE%i.png' % (k,))
-    if distr == stats.norm:
-        axQQ.plot(x, z,'ok',marker=col[0],ms=5)
-    elif distr == stats.expon:
-        axHisty.plot(distr.pdf(y),y)
-        z2 = distr.pdf(y)
-        y = hstack((y[0],y,y[-1]))
-        z2 = hstack((0,z2,0))
-        axHisty.fill(z2,y,color=(.0,.0,1.))
-       
-    else:
-        axQQ.legend(loc=2)
-    fig.savefig('figs/HE%iSolution.png' % (k,))
-
-# ####################################################3
-fig = figure()
-
-
-ax = fig.add_subplot(111)
-xx = linspace(-3.,stats.norm.ppf(1-0.2),1000)
-
-x = linspace(-3.,3.,1000)
-y = stats.norm.pdf(x,scale=1)
-yy = stats.norm.pdf(xx,scale=1)
-yy[0] = 0
-yy[-1] = 0
-
-ax.plot(x,y,'k-',lw=2)
-ax.plot(x,stats.norm.pdf(x),'k-',lw=1)
-ax.set_xlabel('x',fontsize=16)
-ax.set_ylabel('pdf',fontsize=16)
-ax.fill(xx,yy,'b')
-
-ax.set_xlim(-3.,3.)
-
-ax.text(xx[-1],-.1,'b');
-
-ax.text(xx[-1],.4,'p(x)',color='k');
-ax.text(xx[0],.3,'F(b) = P(x <= b)',color='b');
-
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-
-fig.savefig('figs/cdf.png')
-
-#-----------------------------
-fig = figure()
-
-
-ax = fig.add_subplot(111)
-xx = linspace(-3.,stats.norm.ppf(1-0.2),1000)
-
-x = linspace(-3.,3.,1000)
-y = stats.norm.pdf(x,scale=1)
-yy = stats.norm.pdf(xx,scale=1)
-yy[0] = 0
-yy[-1] = 0
-
-ax.plot(x,y,'k-',lw=2)
-ax.plot(x,stats.norm.cdf(x),'b-',lw=1)
-ax.set_xlabel('x/b',fontsize=16)
-ax.set_ylabel('pdf/cdf',fontsize=16)
-
-ax.set_xlim(-3.,3.)
-
-ax.text(xx[-1],.4,'p(x)',color='k');
-ax.text(xx[0],.3,'F(b) = P(x <= b)',color='b');
-
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-
-fig.savefig('figs/cdf2.png')
-
-# ####################################################3
-fig = figure()
-
-
-ax = fig.add_subplot(111)
-
-x = hstack((linspace(-3.,stats.norm.ppf(0.13),1000),\
-            linspace(stats.norm.ppf(1-0.13),3.,1000)))
-
-xx = hstack((linspace(-3.,stats.norm.ppf(0.2),1000),\
-            linspace(stats.norm.ppf(1-0.2),3.,1000)))
-
-y = stats.norm.pdf(x,scale=1)
-yy = stats.norm.pdf(xx,scale=1)
-
-y[[0,999,1000,-1]] = 0
-yy[[0,999,1000,-1]] = 0
-
-t = linspace(-3.,3.,1000)
-ax.plot(t,stats.norm.pdf(t),'k-',lw=2)
-
-ax.fill(xx[:1000],yy[:1000],'b')
-ax.fill(xx[1000:],yy[1000:],'b')
-ax.text(xx[1000],-.1,'b')
-ax.text(xx[999],-.1,'-b')
-ax.text(.2,.7,'P(|x|>b) =$\\alpha$',color='b');
-
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-
-fig.savefig('figs/pval0.png')
-
-#---------------------------------------------------
-fig = figure()
-
-ax = fig.add_subplot(111)
-
-t = linspace(-3.,3.,1000)
-ax.plot(t,stats.norm.pdf(t),'k-',lw=2)
-
-
-ax.fill(x[:1000],y[:1000],'r')
-ax.fill(x[1000:],y[1000:],'r')
-
-
-ax.text(x[1000],-.1,'t')
-ax.text(x[999],-.1,'-t')
-
-ax.text(.2,.5,'P(|x| > t) = p-value',color='r');
-
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-
-fig.savefig('figs/ pval1.png')
-
-
-
-# show()
-                      
-
-#-----------------------------

statistics/figs/generateTPlots.py

@@ -1,184 +0,0 @@
-import sys
-import seaborn as sns
-sys.path.append('/home/fabee/code')
-from matplotlib.pyplot import *
-from scipy import stats
-from numpy import *
-
-sns.set_context("talk", font_scale=1.5, rc={"lines.linewidth": 2.5})
-
-# define the curves
-x = np.linspace(2, 20, 200)
-n = 16.
-
-
-X =random.randn(n)*4.+12.5
-fig = figure()
-ax = fig.add_subplot(111)
-ax.set_xlim(5, 18)
-#ax.set_ylim(0, .5)
-ax.plot([10,10],[-.2,.2],'k-',lw=2)
-ax.text(10,.3,r'stimulus position',rotation=-30);
-ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
-ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
-
-ax.set_xlabel('x eye position')
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
-fig.savefig('figs/repetition0.png')
-
-# ####################################################3
-fig = figure()
-
-
-ax = fig.add_subplot(111)
-
-ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
-
-
-ax.set_xlim(5, 18)
-# ax.set_ylim(0, .5)
-
-ax.plot([10,10],[-.2,.2],'k-',lw=2)
-ax.text(10,.3,r'stimulus position',rotation=-30);
-ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
-ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
-ax.legend()
-
-ax.set_xlabel('x eye position')
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
-
-fig.savefig('figs/repetition1.png')
-
-
-# ####################################################3
-fig = figure()
-
-
-ax = fig.add_subplot(111)
-
-ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
-ax.plot(x,-stats.t.pdf(x,n-1,loc=10,scale=1),'b',label=r'Null distribution of $t$')
-
-ax.set_xlim(5, 18)
-# ax.set_ylim(0, .5)
-
-ax.plot([10,10],[-.2,.2],'k-',lw=2)
-ax.text(10,.3,r'stimulus position',rotation=-30);
-ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
-ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
-ax.legend()
-
-ax.set_xlabel('x eye position')
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
-
-fig.savefig('figs/repetition2.png')
-
-# ####################################################3
-fig = figure()
-
-
-ax = fig.add_subplot(111)
-xx = linspace(stats.norm.ppf(0.05),stats.norm.ppf(1-0.05),100)
-xx += 10.
-
-yy = -stats.norm.pdf(xx,loc=10.,scale=1)
-xx = hstack((xx[0],xx,xx[-1]))
-yy = hstack((0,yy,0))
-
-ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
-ax.plot(x,-stats.t.pdf(x,n-1,loc=10,scale=1),'b',label=r'Null distribution of $t$')
-
-ax.fill(xx,yy,'c')
-
-ax.set_xlim(5, 18)
-# ax.set_ylim(0, .5)
-
-ax.plot([10,10],[-.2,.2],'k-',lw=2)
-ax.text(10,.3,r'stimulus position',rotation=-30);
-ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
-ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
-ax.legend()
-
-ax.set_xlabel('x eye position')
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
-
-fig.savefig('figs/repetition3.png')
-
-
-# ####################################################3
-fig = figure()
-
-
-ax = fig.add_subplot(111)
-xx = linspace(stats.norm.ppf(0.05),stats.norm.ppf(1-0.05),100)
-xx += 10.
-
-yy = -stats.norm.pdf(xx,loc=10.,scale=1)
-xx = hstack((xx[0],xx,xx[-1]))
-yy = hstack((0,yy,0))
-
-ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
-ax.plot(x,-stats.t.pdf(x,n-1,loc=10,scale=1),'b',label=r'Null distribution of $t$')
-
-ax.fill(xx,yy,'c')
-
-ax.set_xlim(5, 18)
-# ax.set_ylim(0, .5)
-
-ax.plot([10,10],[-.2,.2],'k-',lw=2)
-ax.text(10,.3,r'stimulus position',rotation=-30);
-ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
-ax.text(12.5,.3,r'$\hat\mu$',rotation=-45)
-
-ax.plot([xx[0],xx[-1]],[0,0],'-g',label=r'$H_0$',lw=4)
-ax.plot([0,xx[0]],[0,0],'-r',label=r'$H_1$',lw=4)
-ax.plot([xx[-1],20],[0,0],'-r',lw=4)
-
-ax.legend()
-
-ax.set_xlabel('x eye position')
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
-
-fig.savefig('figs/repetition4.png')
-
-
-# ####################################################3
-fig = figure()
-
-
-ax = fig.add_subplot(111)
-
-ax.plot(x,-stats.norm.pdf(x,loc=10,scale=4),'orange',label=r'Null distribution of x')
-ax.plot(x,-stats.t.pdf(x,n-1,loc=10,scale=1),'b',label=r'Null distribution of $t$')
-
-xx = linspace(0,stats.norm.ppf(0.05)+10.,100)
-yy = -stats.norm.pdf(xx,loc=10.,scale=1)
-xx = hstack((xx[0],xx,xx[-1]))
-yy = hstack((0,yy,0))
-ax.fill(xx,yy,'magenta')
-
-xx = linspace(stats.norm.ppf(1-0.05)+10.,20,100)
-yy = -stats.norm.pdf(xx,loc=10.,scale=1)
-xx = hstack((xx[0],xx,xx[-1]))
-yy = hstack((0,yy,0))
-ax.fill(xx,yy,'magenta')
-
-ax.set_xlim(5, 18)
-# ax.set_ylim(0, .5)
-
-ax.plot([10,10],[-.2,.2],'k-',lw=2)
-ax.text(10,.3,r'stimulus position',rotation=-30);
-ax.plot([12.5,12.5],[-.2,.2],'b-',lw=2)
-ax.text(12.5,.3,r'$\hat\mu$',rotation=-45);
-ax.legend()
-
-ax.set_xlabel('x eye position')
-#XKCDify(ax, expand_axes=True,yaxis_loc=0,xaxis_loc=0)
-ax.plot(X,0*X,'ob',label='fixations',mfc='orange',ms=10)
-
-fig.savefig('figs/repetition5.png')

statistics/figs/multipletesting.py

@@ -1,72 +0,0 @@
-from __future__ import division
-from numpy import *
-from scipy import stats
-from matplotlib.pyplot import *
-
-N = random.randn
-
-m = 2000
-n = 20
-
-T = zeros((m,))
-R = zeros((m,))
-pT = zeros((m,))
-pR = zeros((m,))
-
-for k in xrange(m):
-    x = N(n)
-    y = N(n)
-
-    T[k], pT[k] = stats.ttest_ind(x,y)
-    R[k], pR[k] = stats.ranksums(x,y)
-
-a = stats.t.ppf([0.025,1.-0.025], n-1)
-b = stats.norm.ppf([0.025,1.-0.025])
-
-
-fig = figure(figsize=(8,8),dpi=100)
-ax = fig.add_axes([.3,.3,.6,.6])
-axb = fig.add_axes([.3,.1,.6,.2])
-axl = fig.add_axes([.1,.3,.2,.6])
-
-ax.plot(T,R,'ok',mfc=(.7,.7,.7))
-axb.hist(T,bins=50,facecolor=(1.,.7,.7),normed=True)
-axl.hist(R,bins=50,facecolor=(.7,.7,1.),normed=True,orientation='horizontal')
-axl.axis([0,1,-5,5])
-axb.plot([a[0],a[0]],[0,1],'k--',lw=2)
-axb.plot([a[1],a[1]],[0,1],'k--',lw=2)
-
-axl.plot([0,1],[b[0],b[0]],'k--',lw=2)
-axl.plot([0,1],[b[1],b[1]],'k--',lw=2)
-axl.set_ylabel('standardized U statistic', fontsize=16)
-axb.set_xlabel('t statistic', fontsize=16)
-
-# print sum(1.*(T < a[0] ))/m + sum(1.*(T > a[1]))/m
-# print sum(1.*(R < b[0] ))/m + sum(1.*(R > b[1]))/m
-
-ax.fill([-5,a[0],a[0],-5],[-5,-5,5,5],color=(1.,.7,.7),alpha=.5)
-ax.fill([a[1],5,5,a[1]],[-5,-5,5,5],color=(1.,.7,.7),alpha=.5)
-axb.fill([-5,a[0],a[0],-5],[0,0,1,1],color=(1.,.7,.7),alpha=.5)
-axb.fill([a[1],5,5,a[1]],[0,0,1,1],color=(1.,.7,.7),alpha=.5)
-
-
-ax.fill([-5,-5,5,5],[-5,b[0],b[0],-5],color=(.7,.7,1.),alpha=.5)
-ax.fill([-5,-5,5,5],[b[1],5,5,b[1]],color=(.7,.7,1.),alpha=.5)
-axl.fill([0,0,1,1],[-5,b[0],b[0],-5],color=(.7,.7,1.),alpha=.5)
-axl.fill([0,0,1,1],[b[1],5,5,b[1]],color=(.7,.7,1.),alpha=.5)
-
-
-
-axb.axis([-5,5,0,1])
-ax.axis([-5,5,-5,5])
-
-axl.set_xticks([])
-axb.set_yticks([])
-axl = axl.twiny()
-axb = axb.twinx()
-axl.set_xticks([0,.5,1.])
-axb.set_yticks([0,.5,1.])
-
-
-
-fig.savefig('multipletesting.pdf')