Knot placement details, cross referencing etc.

assets/library.bib

@@ -169,3 +169,19 @@
   issn      = {2666-5468},
   keywords  = {Electricity peak load, Generalized additive models, Artificial neural networks, Prediction, Combination, Weather effects, Seasonality}
 }
+@book{johnson1995continuous,
+  title     = {Continuous univariate distributions, volume 2},
+  author    = {Johnson, Norman L and Kotz, Samuel and Balakrishnan, Narayanaswamy},
+  year      = {1995},
+  publisher = {John wiley \& sons},
+  volume    = {289}
+}
+@article{li2022general,
+  title     = {General P-splines for non-uniform B-splines},
+  author    = {Li, Zheyuan and Cao, Jiguo},
+  year      = {2022},
+  journal   = {arXiv preprint},
+  publisher = {Cornell University},
+  doi       = {10.48550/arXiv.2201.06808},
+  url       = {https://arxiv.org/abs/2201.06808}
+}

index.qmd

@@ -36,7 +36,7 @@ revealjs-plugins:
   - pointer
 ---
 
-## Outline
+## Outline {.center}
 
 <!--
 Render with: quarto preview /home/jonathan/git/PHD-Presentation/25_07_phd_defense/index.qmd --no-browser --port 6074
@@ -48,20 +48,17 @@ $$
 $$
 :::
 
-<br/>
-
 :::: {style="font-size: 150%;"}
 
 <i class="fa fa-fw fa-rocket" style="color:var(--col_grey_9);"></i> &ensp; [Research Motivation](#motivation)
 
-<i class="fa fa-fw fa-book" style="color:var(--col_grey_9);"></i> &ensp; Overview of the Thesis
+<i class="fa fa-fw fa-book" style="color:var(--col_grey_9);"></i> &ensp; [Overview of the Thesis](#sec-overview)
 
-<i class="fa fa-fw fa-code-merge" style="color:var(--col_grey_9);"></i> &ensp; Online Aggregation
+<i class="fa fa-fw fa-layer-group" style="color:var(--col_grey_9);"></i> &ensp; [Online Aggregation](#sec-crps-learning)
 
-<i class="fa fa-fw fa-fire-flame-simple" style="color:var(--col_grey_9);"></i> &ensp; Probabilistic Forecasting of European Carbon and Energy Prices
+<i class="fa fa-fw fa-chart-line" style="color:var(--col_grey_9);"></i> &ensp; [Probabilistic Forecasting of European Carbon and Energy Prices](#sec-voldep)
-
-<i class="fa fa-fw fa-newspaper" style="color:var(--col_grey_9);"></i> &ensp; Contributions & Outlook
 
+<i class="fa fa-fw fa-newspaper" style="color:var(--col_grey_9);"></i> &ensp; [Contributions & Outlook](#sec-conclusion)
 
 :::
 
@@ -101,7 +98,7 @@ col_yellow <- "#FCE135"
 ## Motivation
 
 
-## Overview of the Thesis {transition="fade" transition-speed="slow"}
+## Overview of the Thesis {transition="fade" transition-speed="slow" #sec-overview}
 
 <table style="width: 100%; border-collapse: separate; border-spacing: 0 1em; border: none;">
   <tr style="border: none;">
@@ -589,7 +586,7 @@ ggplot() +
 ::::
 
 
-# CRPS Learning
+# CRPS Learning {#sec-crps-learning}
 
 Berrisch, J., & Ziel, F. [-@BERRISCH2023105221]. *Journal of Econometrics*, 237(2), 105221.
 
@@ -2627,27 +2624,21 @@ chart = {
 
 ::: {.column width="48%"}
 
-Basis specification `b_smooth_pr` is internally passed to `make_basis_mats()`:
+Non-central beta distribution @johnson1995continuous:
 
-```{r, echo = TRUE, eval = FALSE, cache = TRUE}
+::: {style="font-size: 70%;"}
-mod <- online(
+
-  y = Y,
+\begin{equation*}
-  experts = experts,
+  \mathcal{B}(x, a, b, c) = \sum_{j=0}^{\infty} e^{-c/2} \frac{\left( \frac{c}{2} \right)^j}{j!} I_x \left( a + j , b \right)
-  tau = 1:99 / 100,
+\end{equation*}
-  b_smooth_pr = list(
+
-    knots = 9,
+::::
-    mu = 0.3, # NEW
+
-    sigma = 1,
+```{r, fig.align="center", echo=FALSE, out.width = "1000px", cache = TRUE}
-    nonc = 0,
+knitr::include_graphics("assets/mcrps_learning/knot_placement.svg")
-    tailweight = 1,
-    deg = 3
-  )
-)
 ```
 
-Knots are distributed using the generalized beta distribution.
+<i class="fa fa-fw fa-triangle-exclamation" style="color:var(--col_orange_9);"></i> Penalty and $\lambda$ need to be adjusted accordingly @li2022general
-
-TODO: Add actual algorithm to backup slides
 
 :::
 
@@ -2657,6 +2648,27 @@ TODO: Add actual algorithm to backup slides
 
 ::: {.column width="48%"}
 
+Using non equidistant knots in `profoc` is straightforward:
+
+```{r, echo = TRUE, eval = FALSE, cache = TRUE}
+mod <- online(
+  y = Y,
+  experts = experts,
+  tau = 1:99 / 100,
+  b_smooth_pr = list(
+    knots = 9,
+    mu = 0.3,
+    sigma = 1,
+    nonc = 0,
+    tailweight = 1,
+    deg = 3
+  )
+)
+```
+
+Basis specification `b_smooth_pr` is internally passed to `make_basis_mats()`.
+
+<i class="fa fa-fw fa-check" style="color:var(--col_green_9);"></i> Profoc adjusts penatly and $\lambda$
 
 :::
 
@@ -2716,7 +2728,7 @@ Pubications:
 
 ::::
 
-# Modeling Volatility and Dependence of European Carbon and Energy Prices
+# Modeling Volatility and Dependence of European Carbon and Energy Prices {#sec-voldep}
 
 Berrisch, J., Pappert, S., Ziel, F., & Arsova, A. (2023). *Finance Research Letters*, 52, 103503.
 
@@ -3482,6 +3494,10 @@ Accounting for heteroscedasticity or stabilizing the variance via log transforma
 
 ::::
 
-## Conclusion
+## Contributions and Outlook {#sec-conclusion}
+
+
+
+
 
 ## References