diff --git a/slides/sections/0.md b/slides/sections/0.md index f92120e..66f4569 100644 --- a/slides/sections/0.md +++ b/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 diff --git a/slides/sections/2.md b/slides/sections/2.md index ae734af..ac014ef 100644 --- a/slides/sections/2.md +++ b/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} -$$ - m = Q \left( \frac{1}{2} \right) -$$ +:::: {.column width=50%} -. . . +::: 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: $$ L_{\text{max}} = L(\mu_L) $$ - $$ \text{FWHM} = w = x_+ - x_- \with L(x_{\pm}) = \frac{L_{\text{max}}}{2} $$ diff --git a/slides/sections/4.md b/slides/sections/4.md index ee7c95a..e36a998 100644 --- a/slides/sections/4.md +++ b/slides/sections/4.md @@ -18,29 +18,16 @@ How to estimate sample median, mode and FWHM? ## Sample median -:::: {.columns align=bottom} -::: {.column width=50%} - $$ - F(m) = \frac{1}{2} - $$ +\Begin{block}{Algorithm} +::: incremental + 1. Sort sample in ascending order + 2. + Take middle element if odd - \vspace{20pt} - - . . . - - - Sort points in ascending order - - . . . - - - Middle element if odd - - Average of the two central elements if even + Take average of two middle elements if even ::: -::: {.column width=50%} - ![](images/median.pdf) -::: -:::: +\End{block} \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] - -- Find the smallest interval containing half points -- Repeat -- If the sample has less than three points, take average +\Begin{block}{Algorithm} +::: incremental +1. Find the smallest interval containing half points +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