parabola_tv.md

Regression and Other Stories: Parabola

Andrew Gelman, Jennifer Hill, Aki Vehtari 2021-04-20

• A Computing in R
  • A.7 Some R programming
    • Opimization

Tidyverse version by Bill Behrman.

Demonstration of using Stan for optimization. See Appendix A in Regression and Other Stories.

---

# Packages
library(tidyverse)
library(rstan)

# Parameters
  # Common code
file_common <- here::here("_common.R")

#===============================================================================

# Run common code
source(file_common)

A Computing in R

A.7 Some R programming

Opimization

Finding the peak of a parabola

Plot of y = 15 + 10x − 2x².

v <- 
  tibble(
    x = seq_range(c(-2, 5)),
    y = 15 + 10 * x - 2 * x^2
  )

v %>% 
  ggplot(aes(x, y)) +
  geom_line() +
  geom_point(data = tibble(x = 2.5, y = 27.5)) +
  labs(
    title = expression(paste("Plot of ", y == 15 + 10 * x - 2 * x^2)),
    subtitle = "Maximum is at x = 2.5, y = 27.5"
  )

Stan model for function 15 + 10x − 2x².

model_code =
"
parameters {
  real x;
}
model {
  target += 15 + 10 * x - 2 * x^2;
}
"

Compile the Stan function and optimize it.

set.seed(245)

fit <- 
  stan_model(model_code = model_code) %>% 
  optimizing()

fit

#> $par
#>   x 
#> 2.5 
#> 
#> $value
#> [1] 27.5
#> 
#> $return_code
#> [1] 0
#> 
#> $theta_tilde
#>        x
#> [1,] 2.5

The output labeled par is the value of x at which the function is optimized, and the output labeled value is the target function at the optimum. A return_code of 0 corresponds to the optimizer running with no problem, and you can ignore theta_tilde.