From 8fbcd80668445160f68e3b54ee3869ae40042715 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Gi=C3=B9=20Marcer?= Date: Thu, 11 Jun 2020 00:21:44 +0200 Subject: [PATCH] sections: fix and add a lot of things --- slides/sections/2.md | 13 +++++---- slides/sections/4.md | 30 ++++++++++----------- slides/sections/5.md | 63 +++++++++++++++++++++++++++++++++++++------- 3 files changed, 77 insertions(+), 29 deletions(-) diff --git a/slides/sections/2.md b/slides/sections/2.md index 55d75a6..f687ece 100644 --- a/slides/sections/2.md +++ b/slides/sections/2.md @@ -1,4 +1,4 @@ -# Landau PDF +# Landau distribution ## Landau PDF @@ -9,6 +9,13 @@ L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty} dt \, e^{-t \ln(t) -xt} \sin (\pi t) $$ + + . . . + + \vspace{30pt} + + \centering + No closed form for \textcolor{cyclamen}{ANYTHING} ::: ::: {.column width=50%} @@ -16,10 +23,6 @@ ::: :::: -. . . - -No closed form for \textcolor{cyclamen}{ANYTHING} - ## Landau median diff --git a/slides/sections/4.md b/slides/sections/4.md index 9dce7ec..874d5eb 100644 --- a/slides/sections/4.md +++ b/slides/sections/4.md @@ -64,16 +64,16 @@ Half Sample Mode \draw [line width=3, ->, cyclamen] (-5,0) -- (5,0); \node [right] at (5,0) {$x$}; % points - \draw [blue, fill=blue] (-4.6,-0.1) rectangle (-4.8,0.1); - \draw [blue, fill=blue] (-4,-0.1) rectangle (-4.2,0.1); - \draw [blue, fill=blue] (-3.3,-0.1) rectangle (-3.5,0.1); - \draw [blue, fill=blue] (-2.3,-0.1) rectangle (-2.5,0.1); - \draw [blue, fill=blue] (-0.6,-0.1) rectangle (-0.8,0.1); - \draw [blue, fill=blue] (-0.1,-0.1) rectangle (0.1,0.1); - \draw [blue, fill=blue] (1.1,-0.1) rectangle (1.3,0.1); - \draw [blue, fill=blue] (2 ,-0.1) rectangle (2.2,0.1); - \draw [blue, fill=blue] (2.7,-0.1) rectangle (2.9,0.1); - \draw [blue, fill=blue] (4,-0.1) rectangle (4.2,0.1); + \draw [blue!50!black, fill=blue] (-4.6,-0.1) rectangle (-4.8,0.1); + \draw [blue!50!black, fill=blue] (-4,-0.1) rectangle (-4.2,0.1); + \draw [blue!50!black, fill=blue] (-3.3,-0.1) rectangle (-3.5,0.1); + \draw [blue!50!black, fill=blue] (-2.3,-0.1) rectangle (-2.5,0.1); + \draw [blue!50!black, fill=blue] (-0.6,-0.1) rectangle (-0.8,0.1); + \draw [blue!50!black, fill=blue] (-0.1,-0.1) rectangle (0.1,0.1); + \draw [blue!50!black, fill=blue] (1.1,-0.1) rectangle (1.3,0.1); + \draw [blue!50!black, fill=blue] (2 ,-0.1) rectangle (2.2,0.1); + \draw [blue!50!black, fill=blue] (2.7,-0.1) rectangle (2.9,0.1); + \draw [blue!50!black, fill=blue] (4,-0.1) rectangle (4.2,0.1); % future nodes \node at (-1,-0.3) (1a) {}; \node at (3.1,0.3) (1b) {}; @@ -131,7 +131,7 @@ $$ \setbeamercovered{transparent} . . . -Kernel Density Estimation +**Kernel Density Estimation** :::: {.columns} ::: {.column width=50% .c} @@ -150,10 +150,10 @@ Kernel Density Estimation \begin{center} \begin{tikzpicture} % points - \draw [blue, fill=blue] (-2,-0.1) rectangle (-1.8,0.1); - \draw [blue, fill=blue] (-0.1,-0.1) rectangle (0.1,0.1); - \draw [blue, fill=blue] (1.3,-0.1) rectangle (1.5,0.1); - \draw [blue, fill=blue] (0.7,-0.1) rectangle (0.9,0.1); + \draw [blue!50!black, fill=blue] (-2,-0.1) rectangle (-1.8,0.1); + \draw [blue!50!black, fill=blue] (-0.1,-0.1) rectangle (0.1,0.1); + \draw [blue!50!black, fill=blue] (1.3,-0.1) rectangle (1.5,0.1); + \draw [blue!50!black, fill=blue] (0.7,-0.1) rectangle (0.9,0.1); \pause % lines \draw [cyclamen, dashed] (-1.9,0.1) -- (-1.9,1); diff --git a/slides/sections/5.md b/slides/sections/5.md index 8e20a40..d14c55e 100644 --- a/slides/sections/5.md +++ b/slides/sections/5.md @@ -1,4 +1,4 @@ -# Kolmogorov - Smirnov test +# Kolmogorov-Smirnov test ## KS @@ -7,16 +7,61 @@ Quantify distance between expected and observed CDF . . . -KS statistic: +:::: {.columns} +::: {.column width=50% .c} + KS statistic: -$$ - D_N = \text{sup}_x |F_N(x) - F(x)| -$$ + $$ + D_N = \text{sup}_x |F_N(x) - F(x)| + $$ -- $F(x)$ is the expected CDF -- $F_N(x)$ is the empirical CDF of $N$ sampled points - - sort points in ascending order - - number of points preceding the point normalized by $N$ + \vspace{20pt} + + - $F(x)$ is the expected CDF + - $F_N(x)$ is the empirical CDF + - sort points in ascending order + - number of points preceding the point normalized by $N$ + +::: + +::: {.column width=50%} + \setbeamercovered{} + \begin{center} + \begin{tikzpicture} + % axes + \draw [thick, ->] (-2.5,0) -- (0,0) -- (0,4.5); + \draw [thick, ->] (0,0) -- (2.5,0); + % empiric + \draw [cyclamen, fill=cyclamen!20!white] (-2.5,0) rectangle (-1.5,0.5); + \draw [cyclamen, fill=cyclamen!20!white] (-1.5,0) rectangle (-0.9,1); + \draw [cyclamen, fill=cyclamen!20!white] (-0.9,0) rectangle (-0.6,1.5); + \draw [cyclamen, fill=cyclamen!20!white] (-0.6,0) rectangle ( 0.2,2); + \draw [cyclamen, fill=cyclamen!20!white] ( 0.2,0) rectangle ( 0.5,2.5); + \draw [cyclamen, fill=cyclamen!20!white] ( 0.5,0) rectangle ( 0.8,3); + \draw [cyclamen, fill=cyclamen!20!white] ( 0.8,0) rectangle ( 1.6,3.5); + \draw [cyclamen, fill=cyclamen!20!white] ( 1.6,0) rectangle ( 2.3,4); + \draw [cyclamen, fill=cyclamen!20!white] ( 2.3,0) rectangle ( 2.5,4.5); + % points + \draw [blue!50!black, fill=blue] (-2.6,-0.1) rectangle (-2.4,0.1); %-2.5 + \draw [blue!50!black, fill=blue] (-1.6,-0.1) rectangle (-1.4,0.1); %-1.5 + \draw [blue!50!black, fill=blue] (-1,-0.1) rectangle (-0.8,0.1); %-0.9 + \draw [blue!50!black, fill=blue] (-0.7,-0.1) rectangle (-0.5,0.1); %-0.6 + \draw [blue!50!black, fill=blue] (0.1,-0.1) rectangle (0.3,0.1); % 0.2 + \draw [blue!50!black, fill=blue] (0.4,-0.1) rectangle (0.6,0.1); % 0.5 + \draw [blue!50!black, fill=blue] (0.7,-0.1) rectangle (0.9,0.1); % 0.8 + \draw [blue!50!black, fill=blue] (1.5,-0.1) rectangle (1.7,0.1); % 1.6 + \draw [blue!50!black, fill=blue] (2.2,-0.1) rectangle (2.4,0.1); % 2.3 + % expected + \pause + \draw[domain=-2.5:2.5, yscale=5, smooth, variable=\x, blue, very thick] + plot ({\x}, {((atan(\x)*pi/180) + pi/2)/pi}); + \pause + \draw [very thick, cyclamen] (0.8,3.6) -- (0.8,4.05); + \end{tikzpicture} + \end{center} + \setbeamercovered{transparent} +::: +:::: ## KS