This package provides a common interface for a bunch of “reference-table” estimation methods to estimate simulation models.

Reference table methods (i.e. run the model a bunch of times at random then figure out how the real data matches the original parameters) are very inefficient but they have three big advantages:

1. They quickly produce *confidence intervals* for estimated parameters
2. They are **easily testable** by cross-validation
3. They can all be ranked using the same random samples of input-outputs from the model

Install from github with the devtools package

##Might need to uncomment this line on windows/mac
##if you don't build packages from sources:
##Sys.setenv("R_REMOTES_NO_ERRORS_FROM_WARNINGS" = "true")

devtools::install_github("carrknight/freelunch")

This package has a lot of dependecies, so the installation will take a while. Sorry!

Imagine a simple 2 parameters (paramone,paramtwo) simulation model with two summary statistics (ssone and sstwo). Let’s run it 5,000 times with random inputs:

set.seed(0)
library(tidyverse)
#> ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──
#> ✓ ggplot2 3.3.2     ✓ purrr   0.3.4
#> ✓ tibble  3.0.4     ✓ dplyr   1.0.2
#> ✓ tidyr   1.1.2     ✓ stringr 1.4.0
#> ✓ readr   1.4.0     ✓ forcats 0.5.0
#> ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
#> x dplyr::filter() masks stats::filter()
#> x dplyr::lag()    masks stats::lag()

paramone<-rnorm(n=5000)
paramtwo<-runif(n=5000,min=2,max=5)
ssone<-2*paramone + rnorm(n=5000)
sstwo<- paramone/paramtwo  + rnorm(n=5000)
training_data<-
  data.frame(
    paramone,
    paramtwo,
    ssone,
    sstwo
  )
glimpse(training_data)
#> Rows: 5,000
#> Columns: 4
#> $ paramone <dbl> 1.262954285, -0.326233361, 1.329799263, 1.272429321, 0.41464…
#> $ paramtwo <dbl> 3.958031, 2.194137, 4.029837, 4.206115, 2.333899, 2.139964, …
#> $ ssone    <dbl> 3.359710942, 1.218960188, 2.257928728, 1.458035651, 1.009250…
#> $ sstwo    <dbl> 0.62009255, -1.35464108, 1.12005078, 0.22611970, 0.16063519,…

Let’s also assume that we have some real data that says that ssone is 2 and sstwo is 0.25

The library freelunch comes with a bunch of regression/abc facades (calling other packages made by better people). In this package the methods to estimate parameters all start with fit_* and they all have the same interface requiring 4 arguments:

fit_rejection_abc(training_runs = ...,
                  target_runs =  ...,
                  parameter_colnames =...,
                  summary_statistics_colnames = ...
                  )
fit_loclinear_abc(...)
fit_semiauto_abc(...)
fit_neural_network_abc(...)
fit_linear_regression(...)
fit_gam(...)
fit_quantile_random_forest(...)
fit_random_forest(...)

The four parameters needed are just the training_runs (data-frame), the real data observed target_runs (can be a vector or a data.frame), the column names that refer to the parameter parameter_colnames and the column names that refer to summary_statistics_colnames.

So let’s just try and fit a classic rejection abc (using the abc package) and we quickly get the estimated parameters as well as bounds around them:

library(freelunch)

estimation<-
  fit_rejection_abc(training_runs = training_data,
                  target_runs =  c(2,0.25),
                  parameter_colnames = c("paramone","paramtwo"),
                  summary_statistics_colnames = c("ssone","sstwo")
)

tidy_up_estimation(estimation) %>% knitr::kable()

Looking at these results, you must resist the urge of just looking at the estimate.
If you do, which is unfortunately common, you say: paramone is 0.74 and paramtwo is 3.43.
Once you look at the confidence intervals you get a better picture: paramone can be recovered somewhat (somewhere between -0.2 and 1.7) but paramtwo bounds are basically anything from 2 to 5 which are suspiciously similar to the original bounds.

The key here is never trust estimates without testing, particularly point estimates!. Fortunately the package provides cross-validation helpers for testing.

The testing methods in this package all start with cross_validate_* and have the same interface:

cross_validate_rejection_abc(total_data = ...,
                             parameter_colnames = ...,
                             summary_statistics_colnames = ...
                  )
cross_validate_loclinear_abc(...)
cross_validate_semiauto_abc(...)
cross_validate_neural_network_abc(...)
cross_validate_linear_regression(...)
cross_validate_gam(...)
cross_validate_quantile_random_forest(...)
cross_validate_random_forest(...)

What happens here is that we split the runs into some (5 by default) groups and in turn we pretend not to know the input parameters of one group (we treat it as “real” data) and then see if the estimation method is any good.
The arguments are total_data which is just the training data, and the column names like for fit_* calls.

abc.cv<-
  cross_validate_rejection_abc(total_data = training_data,
                  parameter_colnames = c("paramone","paramtwo"),
                  summary_statistics_colnames = c("ssone","sstwo"),
                  #default parameters:
                  ngroup=5,cv_seed = 0
)

If we look at performance¹ (which goes from 0, our point predictions are awful, to 1, point predictions are perfect) we see that we do okay with paramone but paramtwo predictions are simply useless:

abc.cv$performance 
#>      paramone      paramtwo 
#>  0.4969959391 -0.0005872575

however, coverage (out-of-sample probability that the real parameter is in the 95% CI) is quite accurate (target here is 0.95):

abc.cv$contained 
#> paramone paramtwo 
#>   0.9630   0.9412

Summaries however only get you so far, sometimes it’s better to look at the effect visually

Two plot commands can help understand the quality of our estimations and cross-validation. First, we can look at confidence intervals (black error bars), how wide they are and how often the real parameter (red dots) is contained within them.
Ideally what we want is very small confidence intervals with the red dots in them about 95% of the times.

abc.cv %>% plot_confidence_intervals(limit_number_of_runs_to_plot_to = 120)

This plot shows how paramone tends to have quite large confidence intervals but at least they are usually correct; for paramtwo the abc is very wisely deciding NOT to make a real prediction.

And we can also look narrowly at point predictions and see how well they stack up (best-case scenario all the dots are on the 45 degree line):

abc.cv %>% plot_point_prediction_quality()

And if the second plot doesn’t convince you that paramtwo is NOT IDENTIFIED then nothing else will.

1 Performance is just 1 - (mean square root error of the estimation)/(mean square root of just using the average) ↩