pbox Package Vignette
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
#> Registered S3 method overwritten by 'quantmod':
#> method from
#> as.zoo.data.frame zoo
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)
#> It seems your data might not be stationary!
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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
#> | |=================================================== | 73% | |==================================================== | 75% | |====================================================== | 76% | |======================================================= | 78% | |======================================================== | 80% | |========================================================== | 82% | |=========================================================== | 84% | |============================================================ | 86% | |============================================================== | 88% | |=============================================================== | 90% | |================================================================= | 92% | |================================================================== | 94% | |=================================================================== | 96% | |===================================================================== | 98% | |======================================================================| 100%
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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$hessian) :
#> Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#> | |==================================== | 51% | |===================================== | 53% | |====================================== | 55% | |======================================== | 57% | |========================================= | 59% | |=========================================== | 61% | |============================================ | 63% | |============================================= | 65% | |=============================================== | 67% | |================================================ | 69% | |================================================= | 71%Error in solve.default(oout$hessian) :
#> Lapack routine dgesv: system is exactly singular: U[1,1] = 0
#> | |=================================================== | 73% | |==================================================== | 75% | |====================================================== | 76% | |======================================================= | 78% | |======================================================== | 80% | |========================================================== | 82% | |=========================================================== | 84% | |============================================================ | 86% | |============================================================== | 88% | |=============================================================== | 90% | |================================================================= | 92%Error in solve.default(oout$hessian) :
#> Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#> | |================================================================== | 94% | |=================================================================== | 96% | |===================================================================== | 98% | |======================================================================| 100%
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#> Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#> | |================================= | 47%Error in solve.default(oout$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$hessian) :
#> Lapack routine dgesv: system is exactly singular: U[1,1] = 0
#> | |=================================================== | 73% | |==================================================== | 75% | |====================================================== | 76% | |======================================================= | 78% | |======================================================== | 80% | |========================================================== | 82% | |=========================================================== | 84% | |============================================================ | 86% | |============================================================== | 88% | |=============================================================== | 90% | |================================================================= | 92% | |================================================================== | 94% | |=================================================================== | 96% | |===================================================================== | 98% | |======================================================================| 100%
#> | | | 0% | |= | 2% | |=== | 4% | |==== | 6% | |===== | 8% | |======= | 10% | |======== | 12%Error in solve.default(oout$hessian) :
#> 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$hessian) :
#> Lapack routine dgesv: system is exactly singular: U[3,3] = 0
#> | |===================================== | 53% | |====================================== | 55% | |======================================== | 57% | |========================================= | 59% | |=========================================== | 61% | |============================================ | 63% | |============================================= | 65% | |=============================================== | 67% | |================================================ | 69% | |================================================= | 71%Error in solve.default(oout$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$hessian) :
#> Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#> | |================================================================== | 94%Error in solve.default(oout$hessian) :
#> Lapack routine dgesv: system is exactly singular: U[4,4] = 0
#> | |=================================================================== | 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"
#> 2.2)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
#> 0.6217401Confidence Intervals
Grid Search
We can perform a grid search to explore the probabilistic space over a grid of values.
grid_results <- grid_pbox(pbx, mj = c("Vietnam", "Malaysia"))
print(grid_results)
#> Vietnam Malaysia probs
#> <num> <num> <list>
#> 1: 30.9 30.5 0.0001235705
#> 2: 31.2 30.5 0.0004576423
#> 3: 31.3 30.5 0.0005318575
#> 4: 31.4 30.5 0.0005801543
#> 5: 31.5 30.5 0.0006092625
#> ---
#> 117: 31.7 32.3 0.620192
#> 118: 31.8 32.3 0.6975326
#> 119: 32.0 32.3 0.8132672
#> 120: 32.3 32.3 0.9104411
#> 121: 32.9 32.3 0.9725093
print(grid_results[which.max(grid_results$probs),])
#> Vietnam Malaysia probs
#> <num> <num> <list>
#> 1: 32.9 32.3 0.9725093
print(grid_results[which.min(grid_results$probs),])
#> Vietnam Malaysia probs
#> <num> <num> <list>
#> 1: 30.9 30.5 0.0001235705Scenario 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
#> 0.004167532This 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.