chapter_four_scripts.R

source("manifesto_functions.R")


##################
### Get Small Data

#Engineer One and Two Remediation Rate Beliefs
eng_one <- c(4,7) #Median and 90% Stretch
eng_two <- c(2,4)

# 4 fix, 7 stretch fix, out of 10 
GetBeliefsHits(eng_one[1], eng_one[2],10)

MakeBetaGraph(1.96,2.78,"Vuln Fix Rate","Plausibility",
              "Sec Eng Beliefs","4 Fix, 7 Max, out of 10")

# 2 Fixes, 4 Stretch Fixes, out of 10
GetBeliefsHits(eng_two[1], eng_two[2],10)

MakeBetaGraph(2.07,7.32,"Vuln Fix Rate","Plausibility",
                "Sec Eng 2's Beliefs","2 Fix, 4 Max, out of 10")

### Data Functions for MakeBetaGraph() ###

# Generate prior distribution data using SME shape parameters
prior <- distribution_beta(1000,2.07,7.32)

# Look at first 20 results
head(prior, 20)

# Get 89% Credible Interval
ci(prior, method="HDI")

# Add density for graphing
prior <- prior %>% estimate_density()

# Print out some results
head(prior, 5)

#############################
### Scoring Beliefs With Data
opened_dates <- c("2020-07-25","2020-08-01","2020-08-03","2020-08-03",
                  "2020-08-03","2020-08-05","2020-08-05","2020-08-30",
                  "2020-09-12","2020-09-20","2020-09-23")

closed_dates <- c("2020-07-29","2020-08-05","2020-08-06","2020-08-06",
                  "2020-09-03","2020-09-13","2020-09-25")

#Get Shape Parameters For Each Engineer
eng_one <- GetBeliefsHits(4,7,10)
eng_two <- GetBeliefsHits(2,4,10)

#Get counts of opened and closed dates and their delta
opened <- length(opened_dates)
closed <- length(closed_dates)
delta <- opened - closed

# Compare each engineer's belief to the vulnerability data – no bias
raw_score <- ScoreBetaBeliefs(bias = c(.5,.5), first_belief = eng_one,    
                              second_belief = eng_two, hits = closed, misses = delta )

# Compare again, but bias the data toward the second engineer: .3, .7
favor_eng2_score <- ScoreBetaBeliefs(bias = c(.3,.7), 
                                     first_belief = eng_one, second_belief = eng_two, 
                                     hits = closed, misses = delta )

# Print out the unbiased Score
raw_score

# Print out the biased score
favor_eng2_score

# Vuln Data Central Tendency – date ratios
closed/opened

###########################
### Graph The Updated Model
# Bayesian Updating - Data + Beliefs
updated_hits <- eng_one[1] + closed   #update
updated_misses <- eng_one[2] + delta  #update
MakeBetaGraph(hit = updated_hits, miss = updated_misses,
              "Vuln Fix Rate","Plausibility","Bayesian Updating Example",
              "Eng 1 Beliefs + Data")


#########################
### Predicting The Future

# What’s A Plausible Remediation Rate For 22 Extreme Vulns?
future_count <- 22
vpred <- GetVulnPredictions(updated_hits, updated_misses, future_count)


### Code Inside GetVulnPredictions
# Priors + Data
beta_vals <- c(updated_hits, updated_misses)

# Store as list from 0 to 22
future_list = 0:future_count

# LearnBayes predictive function: uses beta prior and binomial data output
prob_future = pbetap(beta_vals, future_count, future_list)

# This call produces the list seen below.
round(cbind(future_list, prob_future), digits=3)

### 90% Most Probable Results
discint(cbind(vpred[,1], vpred[,2]), .9)

beta_probs = rbeta(n=1000, updated_hits, updated_misses)
closed_counts = rbinom(n=1000, size=future_count, prob=beta_probs)
table(closed_counts)

closed_freq = table(closed_counts)
closed_props = closed_freq/sum(closed_freq)
plot(closed_props, type="h", xlab="Number Closed",
     las=1, lwd=3, ylab="Probability Closed")

##############################
### Wrapping Up Basic Burndown

# Get prior beliefs in shape parameter form
eng_one <- GetBeliefsHits(4,7,10)

# Raw Data
opened_dates <- c("2020-07-25","2020-08-01","2020-08-03","2020-08-03",
                  "2020-08-03","2020-08-05","2020-08-05","2020-08-30",
                  "2020-09-12","2020-09-20","2020-09-23")

closed_dates <- c("2020-07-29","2020-08-05","2020-08-06","2020-08-06",
                  "2020-09-03","2020-09-13","2020-09-25")

# Count Closed
closed <- length(closed_dates)

# Count left opened
delta <- length(opened_dates) - closed

# Bayesian Update, beliefs + data
updated_hits <- eng_one[1] + closed
updated_misses <- eng_one[2] + delta

# Create a graph that is a mesh of the above
MakeBetaGraph(hit = updated_hits, miss = updated_misses,
              "Vuln Fix Rate","Plausibility","Bayesian Updating Example",
              "Eng 1 Beliefs + Data")

### Bayes Burndown Curves
# Bayes Burndown Curve (black): Eng1 Beliefs + Data 
curve(dbeta(x, closed + eng_one[1], delta + eng_one[2]), from=0, to=1,
      xlab="Burndown Rate", ylab="Plausibility",col=1, lwd=4, las=1)

# Actual Vuln Data (Dates) Curve (red)    
curve(dbeta(x, closed + 1, delta + 1), add=TRUE, col=2,lwd=4)

# Engineer 1 Beliefs (green) 
curve(dbeta(x, eng_one[1], eng_one[2]), add=TRUE, col=3, lwd=4)

# Engineer 2 Beliefs (blue) 
curve(dbeta(x, eng_two[1], eng_two[2]), add=TRUE, col=4, lwd=4)

#Legend
legend("topright", c("Engineer 2","Engineer 1", "Real Data",
                     "Bayesian Update"), col=c(4,3, 2, 1), lwd=c(3,3, 3, 3))

######################################
### Building A Bayesian Burndown Chart
# Jan includes Prior + first months data.
vulnData <- tibble(
  yaxis = c("Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", 
            "Oct", "Nov", "Dec"),
  hits   = c( 2, 4, 13, 4, 5, 12, 17, 7, 4, 3, 2, 4),
  misses = c(12, 11, 10, 9, 8, 7, 6, 5, 14, 13, 12, 16)
)

# Encode Prior Beliefs
eng_one_prior <- GetBeliefsHits(eng_one[1], eng_one[2],10)

# Build Tidy Data Frame for Visualization
eng_risk <- MakeVulnData(vulnData, eng_one_prior)

# Make Visualization
MakeRidgeChart(eng_risk, 
               "Extreme Vulnerability Burndown Rates - One Week SLA", 
               "One Team Baselining Month By Month", 
               "Baseline Rate", 
               "Months", 
               "Time Frame")

### MakeVulnData() and MakeBurnData() Availble in manifesto_functions.R

# Get beta shape parameters from eng_ris for january
jan <- eng_risk %>% filter(yaxis == "Jan") %>% 
  select(closed, misses) %>% distinct()

# Generate 1,000 random probabilities constrained by shape params
jan_dist <- rbeta(10000, jan$closed, jan$misses)

# Get the 89% Highest Density Interval
jan_hdi <- ci(jan_dist, method = "HDI")
jan_hdi

# Get the shape parameters for Dec
dec <- eng_risk %>% filter(yaxis == "Dec") %>% 
  select(closed, misses) %>% distinct()

# Generate 1000 probabilities constrained by shape parameters
dec_dist <- rbeta(1000, dec$closed, dec$misses)

# Get the HDI
dec_hdi <- ci(dec_dist, method = "HDI")
dec_hdi

# Get Diff Between Months
diff_dist <- dec_dist - jan_dist

# How much of Dec is credibly within Jan?
rope(diff_dist)

#####################
### Are We Improving?
# Best central tendency point estimates
map_estimate(jan_dist)

map_estimate(dec_dist)

# Simple/Quick Plots
plot(density(jan_dist))

plot(density(dec_dist))

GetRope(eng_risk, "Jun", "Dec")

##########################
### Final: Comparing Teams

# Build Team One Data Frame
teamOneData <- tibble(yaxis = "Team 1", 
                      hits = c(10,24,46, 160),   
                      misses = c(20,20,20,5), 
                      legend = c("Q1", "Q2", "Q3", "Q4"))


# Codify Eng One Beliefs
prior <- GetBeliefsHits(eng_one[1], eng_one[2],10)


# Create Posterior Distribution
team1 <- MakeVulnData(teamOneData, prior)


# Build TEam Two Data Frame
teamTwoData <- tibble(yaxis = "Team 2", 
                      hits = c(10,15,20, 40), 
                      misses = c(20,30,40,80), 
                      legend = c("Q1", "Q2", "Q3", "Q4"))

# Codify Eng Two Beliefs
prior <- GetBeliefsHits(eng_two[1], eng_two[2],10)

# Create Posterior Distribution
team2 <- MakeVulnData(teamTwoData, prior)


# Combine Posteriors Into One Data Frame row by row
eng_risk <- rbind(team1, team2)

# Make Combined Chart
MakeRidgeChart2(eng_risk, 
                "Extreme Vulnerability Burndown Rates - One Week SLA", 
                "Q1 To Q4 Difference", 
                "Baseline Rate", "Teams", 
                "Time Frame")