I am currently using Approximate Bayesian Computation to parameterize uncertain parameters of a model to reproduce observed patterns of disease outbreak presence and absence. To do this, I am using the abc package.
However, when I run the abc function to estimate the posterior distributions of the parameters from neural network regression, I obtain negative values even though all parameters are positive. I don't know if this is related, but I have this warning:
Warning messages:
1: In density.default(x, weights = weights) :
Selecting bandwidth *not* using 'weights'
Initially, I used the True Skill Statistic (TSS; difference between True Presence Rate and False Presence Rate) as summary statistics (range: -1 to 1), and in a second step, I used the root mean squared error (RMSE) between the simulated TSS and the observed TSS (value of 1) as summary statistics. In both cases, I have negative estimates. So any help would be greatly appreciated to understand what is causing these negative estimates.
Here is the output:
> summary(abc_neuralnet)
Call:
abc::abc(target = observed_summary_statistics, param = simulated_parameters,
sumstat = simulated_summary_statistics, tol = 1, method = "neuralnet")
Data:
abc.out$adj.values (10000 posterior samples)
Weights:
abc.out$weights
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16
Min.: 14.0275 -5.5947 475.6561 -2004.7401 -3410.4807 -0.0041 -0.2877 -0.4942 -0.0403 -0.6970 -0.0524 -0.3172 -0.1729 -0.2109 0.4302 0.0319
Weighted 2.5 % Perc.: 21.0431 1.5006 879.1652 2940.7780 -255.8276 0.2331 -0.1156 -0.1222 -0.0179 0.3437 0.0189 -0.1189 0.0248 -0.1586 0.4668 0.0605
Weighted Median: 130.9660 10.4621 5857.8215 18011.2848 2652.1901 0.4609 0.2799 0.5944 0.3044 0.7649 0.5835 0.5960 0.5098 0.5346 0.7495 0.1958
Weighted Mean: 138.2207 10.6428 5880.5932 18186.6218 2798.3743 0.5053 0.2919 0.5823 0.3040 0.7255 0.5612 0.5943 0.5130 0.5410 0.7519 0.1986
Weighted Mode: 41.2750 15.1685 2046.0809 7565.2865 473.4871 0.2850 0.0511 0.6869 0.3914 0.8491 0.9260 0.8935 0.2530 0.4488 0.5668 0.0947
Weighted 97.5 % Perc.: 283.2321 20.3251 10985.0459 34015.6282 6562.8585 0.9261 0.7165 1.2972 0.6245 0.9763 1.0293 1.2934 1.0046 1.2514 1.0480 0.3448
Max.: 307.9988 20.4851 14114.8565 45242.1735 7852.7231 1.0047 1.1997 1.4287 0.6768 1.0072 1.1691 1.3752 1.0913 1.3801 1.0690 0.4321
V17 V18
Min.: -0.0444 -0.7655
Weighted 2.5 % Perc.: 0.1018 -0.2778
Weighted Median: 0.5202 0.4043
Weighted Mean: 0.5449 0.4108
Weighted Mode: 0.1790 -0.0694
Weighted 97.5 % Perc.: 1.0907 1.1251
Max.: 1.2888 2.0197
Here are the data: https://www.dropbox.com/scl/fi/cdse5nhbo60tnv47yjear/Test_abc.csv?rlkey=59umwgnk5juv392te51016t6u&st=924wq05k&dl=0
Here is the code:
library(Metrics)
library(abc)
data <- read.csv("C:/Users/Test_abc.csv")
## Define the observed summary statistics
## observed_TSS <- 1
observed_summary_statistics <- c(RMSE_TSS_C1 = 0, RMSE_TSS_C2 = 0)
## Compute the root mean squared error (RMSE) between simulated and observed variables
data$RMSE_TSS_C1 <- sapply(data$TSS_C1, FUN = function(x){Metrics::rmse(1, x)})
data$RMSE_TSS_C2 <- sapply(data$TSS_C2, FUN = function(x){Metrics::rmse(1, x)})
## summary(data)
## Retrieve the simulated summary statistics
simulated_summary_statistics <- data[, c("RMSE_TSS_C1", "RMSE_TSS_C2")]
## summary(simulated_summary_statistics)
## Retrieve the simulated parameters
simulated_parameters <- data[, c("V1", "V2", "V3", "V4", "V5", "V6", "V7", "V8", "V9", "V10", "V11", "V12", "V13", "V14", "V15", "V16", "V17", "V18")]
## summary(simulated_parameters)
## Run the "cv4abc" function
cv_rejection <- abc::cv4abc(param = simulated_parameters, sumstat = simulated_summary_statistics, nval = 5, tols = c(0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 1), method = "rejection", transf = "none")
## Run the "abc" function
abc_neuralnet <- abc::abc(target = observed_summary_statistics, param = simulated_parameters, sumstat = simulated_summary_statistics, tol = 1, method = "neuralnet")
