---
title: "pbox Package Vignette"
author: "Ahmed T. Hammad"
date: "2024-05-16"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{pbox Package Vignette}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

```
# Introduction

The `pbox` package is designed for probabilistic modeling and scenario analysis using Probability Boxes (p-boxes). This vignette demonstrates the main functions of the `pbox` package, from loading and visualizing data to creating and querying a `pbox` object.

# Load and Prepare Data
First, we load the `SEAex` dataset included in the `pbox` package. We add a Year column and then reshape the data for plotting.

```{r}

library(pbox)
library(data.table)
library(ggplot2)

data("SEAex", package = "pbox")
SEAex$Year <- 1901:2022
SEAex_long <- melt(SEAex, id.vars = "Year", variable.name = "Country")
```

# Visualize Data
We use `ggplot2` to create a time series plot of the temperature data for each country.

```{r}
ggplot(SEAex_long, aes(x = Year, y = value, color = Country)) +
  geom_line(color = "black") +  # Set all lines to black
  labs(x = "Year", y = "Temperature °C") +
  ggtitle("") +
  facet_grid(Country ~ ., scales = "free_y") +
  theme(legend.position = "none", panel.spacing.y = unit(10, "pt")) +
  theme_bw()

```



# Create PBOX Object
We create a `pbox` object from the `SEAex` dataset using the `set_pbox` function.

```{r}
# Set pbox
pbx <- set_pbox(SEAex)
print(pbx)
```


# Explore Probability Space
We can query the probabilistic space of the pbox object using the qpbox function. Below are examples of different types of queries.

```{r}
# Marginal Distribution

qpbox(pbx, mj = "Malaysia:33")

# Joint Distribution

qpbox(pbx, mj = "Malaysia:33 & Vietnam:34")

# Conditional Distribution

qpbox(pbx, mj = "Vietnam:31", co = "avgRegion:26")

#Conditional Distribution with Fixed Conditions

qpbox(pbx, mj = "Malaysia:33 & Vietnam:31", co = "avgRegion:26", fixed = TRUE)

#Joint Distribution with Mean Values

qpbox(pbx, mj = "mean:c(Vietnam, Thailand)", lower.tail = TRUE)

# Joint Distribution with Median Values

qpbox(pbx, mj = "median:c(Vietnam, Thailand)", lower.tail = TRUE)

# Joint Distribution with Specific Values

qpbox(pbx, mj = "Malaysia:33 & mean:c(Vietnam, Thailand)", lower.tail = TRUE)

# Conditional Distribution with Mean Conditions

qpbox(pbx, mj = "Malaysia:33 & median:c(Vietnam,Thailand)", co = "mean:c(avgRegion)")
```


# Confidence Intervals
```{r}
qpbox(pbx, mj = "Malaysia:33 & median:c(Vietnam,Thailand)", co = "mean:c(avgRegion)", CI = TRUE, fixed = TRUE)
```

## Grid Search
We can perform a grid search to explore the probabilistic space over a grid of values.

```{r}
grid_results <- grid_pbox(pbx, mj = c("Vietnam", "Malaysia"))
print(grid_results)
print(grid_results[which.max(grid_results$probs),])
print(grid_results[which.min(grid_results$probs),])

```

# Scenario Analysis
We perform scenario analysis by modifying underlying parameters of the pbox object.
```{r}
scenario_results <- scenario_pbox(pbx, mj = "Vietnam:31 & avgRegion:26", param_list = list(Vietnam = "mu"))
print(scenario_results)
```


This vignette demonstrates the main functionalities of the `pbox` package, including data preparation, visualization, probabilistic querying, and scenario analysis. The `pbox` package provides powerful tools for probabilistic modeling and analysis, making it a valuable asset for risk assessment and decision-making applications.