toy example with leaky accumulator models

ou-model.R

# illustrate that the temporally-accrued evidence in an Ornstein-
# Uhlenbeck model of perceptual decision-making is bounded

t <- 500     # length of time to run the process
drift <- .2  # drift rate measures the perceptual signal strength
leak <- .9   # evidence leakage rate 

# momentary samples are presumed to generate normally distributed 
# evidence with mean corresponding to drift rate, and (for reasons
# known but to Roger) standard deviation .1
samples <- rnorm(t, mean = drift, sd = .1)

# discrete-time approximation to the Ornstein-Uhlenbeck model
evidence <- purrr::accumulate(
  .x = samples,            # <-- my idiot brain REALLY wants this to be .y = samples 
  .f = ~ (leak * .x) + .y    
)

# plot
plot(1:t, evidence, type = "l", xlab = "time")