Usage.md

In elizabethriddle/BFF: Sequential Adaptive Parameter Estimation and Change Point Detection

devtools::install_github("elizabethriddle/BFF")

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## Downloading GitHub repo elizabethriddle/BFF@master

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#devtools::install("~/Documents/PhD Year 1/RCode/Bayesian Forgetting Factor/BFF")
library(BFF)

## Loading required package: Matrix

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## Successfully loaded changepoint package version 2.2.2
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Illustrative Batch Example

This simulation is found in the thesis with a single change point and a trend period.

set.seed(10)
noisy_lambda_illustrative_data <- c(rnorm(200,0,1),rnorm(100,5,1),rnorm(50,seq(5,-5,length.out = 50),1),rnorm(150,-5,1))
results_BFF_post_param_illus <- BFF_gaussian_predictive_paramest(noisy_lambda_illustrative_data,threshold_val = c(0.05),burnin=100,grace_period = 10,alpha=39,beta=1.8,sw=100)


g1<-ggplot()+ theme_bw()+geom_line(data=data.frame(x=c(1:500),y=noisy_lambda_illustrative_data),aes(x,y))+geom_point(data=data.frame(x=c(200),y=min(noisy_lambda_illustrative_data[101:500])-0.1),shape=4,size=4,aes(x,y))+geom_point(data=data.frame(x=300,y=min(noisy_lambda_illustrative_data[101:500])-0.1),shape=1,size=4,aes(x,y))+xlab("Observation")+ylim(min(noisy_lambda_illustrative_data[101:500])-0.1,max(noisy_lambda_illustrative_data[101:500]))+ylab("Value")+scale_x_continuous(limits=c(101,500),minor_breaks = seq(150,500,by=50))+theme(text = element_text(size=15))
g2<-ggplot()+ theme_bw()+geom_line(data=data.frame(x=c(1:500),y=results_BFF_post_param_illus$lambda_values),aes(x,y))+geom_point(data=data.frame(x=c(200),y=min(results_BFF_post_param_illus$lambda_values[101:500])-0.01),shape=4,size=4,aes(x,y))+geom_point(data=data.frame(x=300,y=min(results_BFF_post_param_illus$lambda_values[101:500])-0.01),shape=1,size=4,aes(x,y))+xlab("Observation")+ylim(min(results_BFF_post_param_illus$lambda_values[101:500])-0.01,max(results_BFF_post_param_illus$lambda_values[101:500]))+ylab(expression(lambda~Estimate))+scale_x_continuous(limits=c(101,500),minor_breaks = seq(150,500,by=50))+theme(text = element_text(size=15))
grid.arrange(g1,g2,ncol=1)

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Sequential Example

Will now apply sequentially to larger data example.

Data Generation:

n<-250000

# Implementing same data as thesis large scale examples:

mean_signal_vals <- 0
mean_signal <- c()


bkp <- sort(c(sample(c(2:(n-2)),n/200)))
if((n/200)>1){
  possible_values <- setdiff(c(2:n-2),(rep(bkp,each=31)+rep(c(0:30),times=length(bkp))))
  while(any(diff(c(0,bkp))<30)){
    not_valid <- which(diff(c(0,bkp))<30)
    bkp<-bkp[-not_valid]
    bkp<-sort(c(bkp,sample(possible_values,n/200-length(bkp))))
    possible_values <- setdiff(possible_values,(rep(bkp,each=31)+rep(c(0:30),times=length(bkp))))
  }
}
lg <- diff(c(0, bkp, n)) ### rep(n/K, K)
trend_points <- sample(which((lg[-1]>81) &  (lg[-1]<300)),n/1000)+1

for(k in 1:length(lg)){
  if(k>1){
    mean_signal_vals <- c(mean_signal_vals,mean_signal_vals[k-1]+(sample(c(-1,1),1)*runif(1,3,6)))
  }
  if((k) %in% trend_points){
    # Randomly choose trend length
    trend_length <- sample(c(50:(lg[k]-30)),1)
    # Randomly choose gradient
    chosen_grad <- sample(c(0.05,0.06,0.07,0.08),1)
    mean_signal <- c(mean_signal,seq(from=(mean_signal_vals[k-1]),by=(sample(c(-1,1),1)*chosen_grad),length.out=trend_length))
    mean_signal <- c(mean_signal,rep(tail(mean_signal,1),lg[k]-trend_length))
    mean_signal_vals[k] <- tail(mean_signal,1)
  }
  else{
    mean_signal <- c(mean_signal,rep(mean_signal_vals[k],lg[k]))
  }

}
trend_points <- trend_points-1
bkp_wo_trend <- bkp[-trend_points]
noisy_signal <- rnorm(length(mean_signal),mean_signal,sqrt(1))

Apply initial model:

# Apply initial model first to 10,000 of data:

initial_BFF_results <- BFF_gaussian_seq_initial(noisy_signal[1:10000],threshold_val = c(0.005),burnin=100,grace_period=20,sw=2000,alpha=39,beta=1.8,post_p = TRUE,pred_p = TRUE)

Update Model:

current_BFF_results <- initial_BFF_results 
for (i in c(10001:250000)) {
  new_BFF_results <- BFF_gaussian_seq_update(noisy_signal[i],noisy_signal[i-1],i,threshold_val = c(0.005),grace_period=20,sw=2000,alpha=39,beta=1.8,post_p = TRUE,pred_p = TRUE,
                                             current_BFF_results$current_mu,
                                             current_BFF_results$current_sigma2,
                                             current_BFF_results$N_values_old_old,
                                             current_BFF_results$D_values_old_old,
                                             current_BFF_results$M_values_old_old,
                                             current_BFF_results$N_values_old,
                                             current_BFF_results$D_values_old,
                                             current_BFF_results$M_values_old,
                                             current_BFF_results$mu_0_prior_value_old,
                                             current_BFF_results$sigma2_0_prior_value_old,
                                             current_BFF_results$sigma2_alpha_0_prior_value_old,
                                             current_BFF_results$sigma2_beta_0_prior_value_old,
                                             current_BFF_results$mu_0_prior_value,
                                             current_BFF_results$sigma2_alpha_0_prior_value,
                                             current_BFF_results$sigma2_beta_0_prior_value,
                                             current_BFF_results$anomalous_mu_threshold_sw,
                                             current_BFF_results$anomalous_lambda_threshold_sw,
                                             current_BFF_results$p_values_change_mu,
                                             current_BFF_results$p_values_change_lambda,
                                             current_BFF_results$anomalous_predictive_threshold_cal,
                                             current_BFF_results$p_values_predictive)
  # Do something here with estimates if desired such as store them
  current_BFF_results <- new_BFF_results 
}


# Performance measures
bff_results_post_lambda_cal_fast_0.005 <- c(unlist(performance_large_changepoint(current_BFF_results$anomalous_lambda_threshold_sw[[1]][-1]-1,bkp_wo_trend[bkp_wo_trend>2000],length(noisy_signal),20)))

bff_results_predictive_cal_fast_0.005 <- c(unlist(performance_large_changepoint(current_BFF_results$anomalous_predictive_threshold_cal[[1]][-1]-1,bkp_wo_trend[bkp_wo_trend>2000],length(noisy_signal),20)))

results_df <- rbind(bff_results_post_lambda_cal_fast_0.005,bff_results_predictive_cal_fast_0.005)
colnames(results_df) <- c("F1","ARL0","ARL1","CCD","DNF","FP","Positives")
rownames(results_df) <- c("BFF Post Lambda","BFF Pred")
results_df

##                        F1      ARL0      ARL1       CCD       DNF  FP Positives
## BFF Post Lambda 0.8350056 4818.4314 1.0280374 0.7542800 0.9350811  52       801
## BFF Pred        0.7348148  862.0174 0.1209677 0.7492447 0.7209302 288      1032

elizabethriddle/BFF documentation built on April 4, 2022, 11:51 a.m.