slides: improve median and mode sections

slides/sections/0.md

@@ -10,6 +10,7 @@ institute:
 theme: metropolis
 themeoptions:
   - titleformat=allcaps
+  - block=fill
 aspectratio: 169
 
 fontsize: 12pt
@@ -70,6 +71,10 @@ header-includes: |
   \setbeamerfont{section title}{series=\mdseries}
   \setbeamerfont{frametitle}{series=\mdseries}
 
+  % trick to put markdown inside LaTeX
+  \let\Begin\begin
+  \let\End\end
+
   % workaround issue matze/mtheme#371
   \def\sectionpage{
     \centering

slides/sections/2.md

@@ -19,25 +19,45 @@
   . . .
 
 \begin{center}
-  No closed form for \textcolor{cyclamen}{ANYTHING}
+  No closed form for \alert{ANYTHING}
 \end{center}
 
 
 ## Landau median
 
-The median of a PDF is defined as:
+::::: {.columns}
 
-$$
+:::: {.column width=50%}
-  m = Q \left( \frac{1}{2} \right)
-$$
 
-. . .
+::: incremental
+  - The median of $f$ is defined by
+  $$
+    F(m) = \int_{-\infty}^m fdx = \frac{1}{2}
+  $$
+
+  - Equivalently
+    $$
+    m = F^{-1}\left(\frac{1}{2}\right)
+   $$
+
+  - Numerical integration or QDF is needed
+:::
+
+::::
+
+::: {.column width=50%}
+  ![](images/median.pdf)
+:::
+
+:::::
+
+
+## Landau median
 
 - CDF computed by numerical integration
-- QDF computed by numerical root-finding (Brent)
+- QDF computed by numerical root-finding
 
 \setbeamercovered{}
-
 \begin{center}
   \begin{tikzpicture}[remember picture]
     \node at (0,0) (here) {$m_L\ex = 1.3557804...$};
@@ -77,7 +97,6 @@ We need to compute the maximum:
 $$
   L_{\text{max}} = L(\mu_L)
 $$
-
 $$
   \text{FWHM} = w = x_+ - x_- \with L(x_{\pm}) = \frac{L_{\text{max}}}{2}
 $$

slides/sections/4.md

@@ -18,29 +18,16 @@ How to estimate sample median, mode and FWHM?
 
 ## Sample median
 
-:::: {.columns align=bottom}
+\Begin{block}{Algorithm}
-:::  {.column width=50%}
+::: incremental
-  $$
+  1. Sort sample in ascending order
-    F(m) = \frac{1}{2}
+  2.
-  $$
+    Take middle element if odd
 
-  \vspace{20pt}
+    Take average of two middle elements if even
-
-  . . .
-
-  - Sort points in ascending order
-
-  . . .
-
-  - Middle element if odd
-
-    Average of the two central elements if even
 :::
 
-:::  {.column width=50%}
+\End{block}
-  ![](images/median.pdf)
-:::
-::::
 
 \setbeamercovered{}
 \begin{center}
@@ -80,17 +67,19 @@ How to estimate sample median, mode and FWHM?
 
 ## Sample mode
 
-Half Sample Mode[@robertson74]
+**Half Sample Mode** [@robertson74]
 
-
+\Begin{block}{Algorithm}
-- Find the smallest interval containing half points
+::: incremental
-- Repeat
+1. Find the smallest interval containing half points
-- If the sample has less than three points, take average
+2. Repeat on the new interval (called modal)
+3. If the interval has less than three points, take average
+:::
+\End{block}
 
 . . .
 
 \setbeamercovered{}
-
 \begin{center}
 \begin{tikzpicture}[remember picture, >=Stealth]
   % line