Updated bayesRecon documentation, added index.md, yml and yaml files …

…for workflow.

.github/workflows/pkgdown.yaml

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+# Workflow derived from https://github.com/r-lib/actions/tree/v2/examples
+# Need help debugging build failures? Start at https://github.com/r-lib/actions#where-to-find-help
+on:
+  push:
+    branches: [main, master]
+  pull_request:
+  release:
+    types: [published]
+  workflow_dispatch:
+
+name: pkgdown.yaml
+
+permissions: read-all
+
+jobs:
+  pkgdown:
+    runs-on: ubuntu-latest
+    # Only restrict concurrency for non-PR jobs
+    concurrency:
+      group: pkgdown-${{ github.event_name != 'pull_request' || github.run_id }}
+    env:
+      GITHUB_PAT: ${{ secrets.GITHUB_TOKEN }}
+    permissions:
+      contents: write
+    steps:
+      - uses: actions/checkout@v4
+
+      - uses: r-lib/actions/setup-pandoc@v2
+
+      - uses: r-lib/actions/setup-r@v2
+        with:
+          use-public-rspm: true
+
+      - uses: r-lib/actions/setup-r-dependencies@v2
+        with:
+          extra-packages: any::pkgdown, local::.
+          needs: website
+
+      - name: Build site
+        run: pkgdown::build_site_github_pages(new_process = FALSE, install = FALSE)
+        shell: Rscript {0}
+
+      - name: Deploy to GitHub pages 🚀
+        if: github.event_name != 'pull_request'
+        uses: JamesIves/[email protected]
+        with:
+          clean: false
+          branch: gh-pages
+          folder: docs

_pkgdown.yml

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+url: https://idsia.github.io/bayesRecon/
+template:
+  bootstrap: 5
+

index.md

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+# bayesRecon: BAyesian reCONciliation of hierarchical forecasts
+
+<!-- 
+<img src="./man/figures/logo.png" align="right" />
+-->
+<!-- badges: start -->
+
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+<!-- badges: end -->
+
+The package `bayesRecon` implements several methods for probabilistic
+reconciliation of hierarchical time series forecasts.
+
+The main functions are:
+
+- `reconc_gaussian`: reconciliation via conditioning of multivariate
+  Gaussian base forecasts; this is done analytically;
+- `reconc_BUIS`: reconciliation via conditioning of any probabilistic
+  forecast via importance sampling; this is the recommended option for
+  non-Gaussian base forecasts;
+- `reconc_MCMC`: reconciliation via conditioning of discrete
+  probabilistic forecasts via Markov Chain Monte Carlo;
+- `reconc_MixCond`: reconciliation via conditioning of mixed
+  hierarchies, where the upper forecasts are multivariate Gaussian and
+  the bottom forecasts are discrete distributions;
+- `reconc_TDcond`: reconciliation via top-down conditioning of mixed
+  hierarchies, where the upper forecasts are multivariate Gaussian and
+  the bottom forecasts are discrete distributions.
+
+## Getting started 
+
+The starting point for `bayesRecon` functions is the vignette in the "Get Started"
+section of the website. Moreover you can find the documentation in the 
+Reference section and additional vignettes in the Articles section. 
+Finally a short example is provided below. 
+
+
+## Installation
+
+You can install the **stable** version on [R
+CRAN](https://cran.r-project.org/package=bayesRecon)
+
+``` r
+install.packages("bayesRecon", dependencies = TRUE)
+```
+
+You can also install the **development** version from
+[Github](https://github.com/IDSIA/bayesRecon)
+
+``` r
+# install.packages("devtools")
+devtools::install_github("IDSIA/bayesRecon", build_vignettes = TRUE, dependencies = TRUE)
+```
+
+## Getting help
+
+If you encounter a clear bug, please file a minimal reproducible example
+on [GitHub](https://github.com/IDSIA/bayesRecon/issues).
+
+
+## Examples
+
+Let us consider the minimal temporal hierarchy in the figure, where the
+bottom variables are the two 6-monthly forecasts and the upper variable
+is the yearly forecast. We denote the variables for the two semesters
+and the year by $S_1, S_2, Y$ respectively.
+
+<img src="./man/figures/minimal_hierarchy.png" alt="Graph of a minimal hierarchy with two bottom and one upper variable." width="50%" style="display: block; margin: auto;" />
+
+The hierarchy is described by the *aggregation matrix* A, which can be
+obtained using the function `get_reconc_matrices`.
+
+``` r
+library(bayesRecon)
+
+rec_mat <- get_reconc_matrices(agg_levels = c(1, 2), h = 2)
+A <- rec_mat$A
+print(A)
+#>      [,1] [,2]
+#> [1,]    1    1
+```
+
+### Example 1: Poisson base forecasts
+
+We assume that the base forecasts are Poisson distributed, with
+parameters given by $\lambda_{Y} = 9$, $\lambda_{S_1} = 2$, and
+$\lambda_{S_2} = 4$.
+
+``` r
+lambdaS1 <- 2
+lambdaS2 <- 4
+lambdaY <- 9
+lambdas <- c(lambdaY, lambdaS1, lambdaS2)
+n_tot = length(lambdas)
+
+base_forecasts = list()
+for (i in 1:n_tot) {
+  base_forecasts[[i]] = list(lambda = lambdas[i])
+}
+```
+
+We recommend using the BUIS algorithm (Zambon et al., 2024) to sample
+from the reconciled distribution.
+
+``` r
+buis <- reconc_BUIS(
+  A,
+  base_forecasts,
+  in_type = "params",
+  distr = "poisson",
+  num_samples = 100000,
+  seed = 42
+)
+
+samples_buis <- buis$reconciled_samples
+```
+
+Since there is a positive incoherence in the forecasts
+($\lambda_Y > \lambda_{S_1}+\lambda_{S_2}$), the mean of the bottom
+reconciled forecast increases. We show below this behavior for $S_1$.
+
+``` r
+reconciled_forecast_S1 <- buis$bottom_reconciled_samples[1,]
+range_forecats <- range(reconciled_forecast_S1)
+hist(
+  reconciled_forecast_S1,
+  breaks = seq(range_forecats[1] - 0.5, range_forecats[2] + 0.5),
+  freq = F,
+  xlab = "S_1",
+  ylab = NULL,
+  main = "base vs reconciled"
+)
+points(
+  seq(range_forecats[1], range_forecats[2]),
+  stats::dpois(seq(range_forecats[1], range_forecats[2]), lambda =
+                 lambdaS1),
+  pch = 16,
+  col = 4,
+  cex = 2
+)
+```
+
+<img src="man/figures/README-unnamed-chunk-6-1.png" alt="PMF of base versus reconciled forecasts." width="80%" style="display: block; margin: auto;" />
+
+The blue circles represent the probability mass function of a Poisson
+with parameter $\lambda_{S_1}$ plotted on top of the histogram of the
+reconciled bottom forecasts for $S_1$. Note how the histogram is shifted
+to the right.
+
+Moreover, while the base bottom forecast were assumed independent, the
+operation of reconciliation introduced a negative correlation between
+$S_1$ and $S_2$. We can visualize it with the plot below which shows the
+empirical correlations between the reconciled samples of $S_1$ and the
+reconciled samples of $S_2$.
+
+``` r
+AA <-
+  xyTable(buis$bottom_reconciled_samples[1, ],
+          buis$bottom_reconciled_samples[2, ])
+plot(
+  AA$x ,
+  AA$y ,
+  cex = AA$number * 0.001  ,
+  pch = 16 ,
+  col = rgb(0, 0, 1, 0.4) ,
+  xlab = "S_1" ,
+  ylab = "S_2" ,
+  xlim = range(buis$bottom_reconciled_samples[1, ]) ,
+  ylim = range(buis$bottom_reconciled_samples[2, ])
+)
+```
+
+<img src="man/figures/README-unnamed-chunk-7-1.png" alt="Bubble plot of correlations between S1 and S2." width="80%" style="display: block; margin: auto;" />
+
+We also provide a function for sampling using Markov Chain Monte Carlo
+(Corani et al., 2023).
+
+``` r
+mcmc = reconc_MCMC(
+  A,
+  base_forecasts,
+  distr = "poisson",
+  num_samples = 30000,
+  seed = 42
+)
+
+samples_mcmc <- mcmc$reconciled_samples
+```
+
+### Example 2: Gaussian base forecasts
+
+We now assume that the base forecasts are Gaussian distributed, with
+parameters given by
+
+- $\mu_{Y} = 9$, $\mu_{S_1} = 2$, and $\mu_{S_2} = 4$;
+- $\sigma_{Y} = 2$, $\sigma_{S_1} = 2$, and $\sigma_{S_2} = 3$.
+
+``` r
+muS1 <- 2
+muS2 <- 4
+muY <- 9
+mus <- c(muY, muS1, muS2)
+
+sigmaS1 <- 2
+sigmaS2 <- 2
+sigmaY <- 3
+sigmas <- c(sigmaY, sigmaS1, sigmaS2)
+
+base_forecasts = list()
+for (i in 1:n_tot) {
+  base_forecasts[[i]] = list(mean = mus[[i]], sd = sigmas[[i]])
+}
+```
+
+We use the BUIS algorithm to sample from the reconciled distribution:
+
+``` r
+buis <- reconc_BUIS(
+  A,
+  base_forecasts,
+  in_type = "params",
+  distr = "gaussian",
+  num_samples = 100000,
+  seed = 42
+)
+samples_buis <- buis$reconciled_samples
+buis_means <- rowMeans(samples_buis)
+```
+
+If the base forecasts are Gaussian, the reconciled distribution is still
+Gaussian and can be computed in closed form:
+
+``` r
+Sigma <- diag(sigmas ^ 2)  #transform into covariance matrix
+analytic_rec <- reconc_gaussian(A,
+                                base_forecasts.mu = mus,
+                                base_forecasts.Sigma = Sigma)
+analytic_means_bottom <- analytic_rec$bottom_reconciled_mean
+analytic_means_upper <- A %*% analytic_means_bottom
+analytic_means <- rbind(analytic_means_upper,analytic_means_bottom)
+```
+
+The base means of $Y$, $S_1$, and $S_2$ are 9, 2, 4.
+
+The reconciled means obtained analytically are 7.41, 2.71, 4.71, while
+the reconciled means obtained via BUIS are 7.41, 2.71, 4.71.
+
+## References
+
+Corani, G., Azzimonti, D., Augusto, J.P.S.C., Zaffalon, M. (2021).
+*Probabilistic Reconciliation of Hierarchical Forecast via Bayes’ Rule*.
+ECML PKDD 2020. Lecture Notes in Computer Science, vol 12459.
+[DOI](https://doi.org/10.1007/978-3-030-67664-3_13)
+
+Corani, G., Azzimonti, D., Rubattu, N. (2024). *Probabilistic
+reconciliation of count time series*. International Journal of
+Forecasting 40 (2), 457-469.
+[DOI](https://doi.org/10.1016/j.ijforecast.2023.04.003)
+
+Zambon, L., Azzimonti, D. & Corani, G. (2024). *Efficient probabilistic
+reconciliation of forecasts for real-valued and count time series*.
+Statistics and Computing 34 (1), 21.
+[DOI](https://doi.org/10.1007/s11222-023-10343-y)
+
+Zambon, L., Agosto, A., Giudici, P., Corani, G. (2024). *Properties of
+the reconciled distributions for Gaussian and count forecasts*.
+International Journal of Forecasting (in press).
+[DOI](https://doi.org/10.1016/j.ijforecast.2023.12.004)
+
+Zambon, L., Azzimonti, D., Rubattu, N., Corani, G. (2024).
+*Probabilistic reconciliation of mixed-type hierarchical time series*.
+The 40th Conference on Uncertainty in Artificial Intelligence, accepted.