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pbox Package Vignette

Ahmed T. Hammad

2024-05-16

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.


library(pbox)
#> Loading required package: gamlss.dist
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.

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.

# Set pbox
pbx <- set_pbox(SEAex)
#> All features are continuous.
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#>   Lapack routine dgesv: system is exactly singular: U[1,1] = 0
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#>   Lapack routine dgesv: system is exactly singular: U[1,1] = 0
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#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#>   |                                                                              |=================================                                     |  47%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#>   |                                                                              |==================================                                    |  49%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
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#>   Lapack routine dgesv: system is exactly singular: U[1,1] = 0
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#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#>   |                                                                              |=================================                                     |  47%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#>   |                                                                              |==================================                                    |  49%  |                                                                              |====================================                                  |  51%  |                                                                              |=====================================                                 |  53%  |                                                                              |======================================                                |  55%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  59%  |                                                                              |===========================================                           |  61%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  65%  |                                                                              |===============================================                       |  67%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  71%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[1,1] = 0
#>   |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  75%  |                                                                              |======================================================                |  76%  |                                                                              |=======================================================               |  78%  |                                                                              |========================================================              |  80%  |                                                                              |==========================================================            |  82%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  86%  |                                                                              |==============================================================        |  88%  |                                                                              |===============================================================       |  90%  |                                                                              |=================================================================     |  92%  |                                                                              |==================================================================    |  94%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#>   |                                                                              |===================================================================   |  96%  |                                                                              |===================================================================== |  98%  |                                                                              |======================================================================| 100%
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#>   Lapack routine dgesv: system is exactly singular: U[3,3] = 0
#>   |                                                                              |==========                                                            |  14%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  18%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  24%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[3,3] = 0
#>   |                                                                              |==================                                                    |  25%  |                                                                              |===================                                                   |  27%  |                                                                              |=====================                                                 |  29%  |                                                                              |======================                                                |  31%  |                                                                              |=======================                                               |  33%  |                                                                              |=========================                                             |  35%  |                                                                              |==========================                                            |  37%  |                                                                              |===========================                                           |  39%  |                                                                              |=============================                                         |  41%  |                                                                              |==============================                                        |  43%  |                                                                              |================================                                      |  45%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#>   |                                                                              |=================================                                     |  47%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#>   |                                                                              |==================================                                    |  49%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#>   |                                                                              |====================================                                  |  51%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[3,3] = 0
#>   |                                                                              |=====================================                                 |  53%Error in solve.default(oout$hessian) : 
#>   system is computationally singular: reciprocal condition number = 1.61756e-16
#>   |                                                                              |======================================                                |  55%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  59%  |                                                                              |===========================================                           |  61%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  65%  |                                                                              |===============================================                       |  67%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  71%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[1,1] = 0
#>   |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  75%  |                                                                              |======================================================                |  76%  |                                                                              |=======================================================               |  78%  |                                                                              |========================================================              |  80%  |                                                                              |==========================================================            |  82%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  86%  |                                                                              |==============================================================        |  88%  |                                                                              |===============================================================       |  90%  |                                                                              |=================================================================     |  92%Error in solve.default(oout$hessian) : 
#>   Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#>   |                                                                              |==================================================================    |  94%  |                                                                              |===================================================================   |  96%  |                                                                              |===================================================================== |  98%  |                                                                              |======================================================================| 100%
#> 
#> 
#> ---Final fitted copula---
#> Copula Type: ellipCopula 
#> Family: normal 
#> parameter: 0.4568983 
#> --------------------------
#> pbox object generated!
print(pbx)
#> Probabilistic Box Object of class pbox
#> 
#> ||--General Overview--||
#> ----------------
#> 1)Data Structure
#> Number of Rows:  122 
#> Number of Columns:  5 
#> 
#> 1.1)Variable Statistics:
#>          var     min     max       mean  median
#>       <char>   <num>   <num>      <num>   <num>
#> 1:  Malaysia   30.50   32.30   31.24344   31.20
#> 2:  Thailand   33.20   37.30   35.10656   35.10
#> 3:   Vietnam   30.90   32.90   31.63934   31.60
#> 4: avgRegion   25.21   26.66   25.78951   25.73
#> 5:      Year 1901.00 2022.00 1961.50000 1961.50
#> 
#> ----------------
#> 2)Copula Summary:
#> Type: ellipCopula 
#> Normal copula, dim. d = 5 
#> Dimension:  5 
#> Parameters:
#>   rho.1   = 0.4568983
#> dispstr:  ex 
#> 
#> 2.1)Copula margins:
#> [1] "RG"     "SN1"    "RG"     "RG"     "SHASHo"
#> 2.1)Kendall correlation:
#>            Malaysia    Thailand   Vietnam avgRegion        Year
#> Malaysia  1.0000000 0.175537766 0.3864290 0.5751234 0.377308066
#> Thailand  0.1755378 1.000000000 0.2246915 0.2472509 0.001384308
#> Vietnam   0.3864290 0.224691517 1.0000000 0.4424894 0.280789004
#> avgRegion 0.5751234 0.247250903 0.4424894 1.0000000 0.422692241
#> Year      0.3773081 0.001384308 0.2807890 0.4226922 1.000000000
#> 
#> -------------------------------

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.

# Marginal Distribution

qpbox(pbx, mj = "Malaysia:33")
#>         P 
#> 0.9986981

# Joint Distribution

qpbox(pbx, mj = "Malaysia:33 & Vietnam:34")
#>         P 
#> 0.9981035

# Conditional Distribution

qpbox(pbx, mj = "Vietnam:31", co = "avgRegion:26")
#>          P 
#> 0.03647037

#Conditional Distribution with Fixed Conditions

qpbox(pbx, mj = "Malaysia:33 & Vietnam:31", co = "avgRegion:26", fixed = TRUE)
#>         P 
#> 0.9688897

#Joint Distribution with Mean Values

qpbox(pbx, mj = "mean:c(Vietnam, Thailand)", lower.tail = TRUE)
#>         P 
#> 0.3740338

# Joint Distribution with Median Values

qpbox(pbx, mj = "median:c(Vietnam, Thailand)", lower.tail = TRUE)
#>        P 
#> 0.353339

# Joint Distribution with Specific Values

qpbox(pbx, mj = "Malaysia:33 & mean:c(Vietnam, Thailand)", lower.tail = TRUE)
#>         P 
#> 0.3740201

# Conditional Distribution with Mean Conditions

qpbox(pbx, mj = "Malaysia:33 & median:c(Vietnam,Thailand)", co = "mean:c(avgRegion)")
#>         P 
#> 0.6217401

Confidence Intervals

qpbox(pbx, mj = "Malaysia:33 & median:c(Vietnam,Thailand)", co = "mean:c(avgRegion)", CI = TRUE, fixed = TRUE)
#>         P      2.5%     97.5% 
#> 0.6505089 0.5493915 0.7573722

Scenario Analysis

We perform scenario analysis by modifying underlying parameters of the pbox object.

scenario_results <- scenario_pbox(pbx, mj = "Vietnam:31 & avgRegion:26", param_list = list(Vietnam = "mu"))
print(scenario_results)
#> $`SD-3`
#>          P 
#> 0.09561431 
#> 
#> $`SD-2`
#>          P 
#> 0.06737206 
#> 
#> $`SD-1`
#>          P 
#> 0.04488868 
#> 
#> $SD0
#>          P 
#> 0.02803826 
#> 
#> $SD1
#>        P 
#> 0.016256 
#> 
#> $SD2
#>           P 
#> 0.008648929 
#> 
#> $SD3
#>           P 
#> 0.004167532

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.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.