Overview of the package

The samplr package is an R package available on CRAN. With it, you can:

• use MCMC algorithms
• use the Autocorrelated Bayesian Sampler model (Zhu et al., 2024)
• calculate some useful statistics that help with model inference.

Prerequisites

install.packages("samplr")

library(samplr)

Metropolis Hastings

sampler_mh(
  start = 1,
  distr_name = "norm",
  distr_params = c(0, 1),
  sigma_prop = .1,
  iterations = 1e4
)

Sampling from Metropolis Hastings

1. Use sampler_mh() to generate samples from a Normal distribution \(\mu=3; \sigma^2=5\)
2. Same as above, but with a large proposal width (\(\sigma^2_{prop} = 10\)). How does the acceptance rate change?
3. Use sampler_mh() to generate samples from a Beta distribution \(\alpha = 4, \beta = 4\)

Sampling from Metropolis Hastings (my solutions #1)

sampler_mh(
  start = 0, 
  distr_name = "norm", 
  distr_params = c(3, sqrt(5))
)

Sampling from Metropolis Hastings (my solutions #2)

Same as above, but with a large proposal width (\(\sigma^2_{prop} = 10\)). How does the acceptance rate change?

set.seed(1)
sampler_mh(
  start = 0, 
  distr_name = "norm", 
  distr_params = c(3, sqrt(5)), 
  sigma_prop = 1
)$`Acceptance Ratio`

[1] 0.8631476

set.seed(1)
sampler_mh(
  start = 0, 
  distr_name = "norm", 
  distr_params = c(3, sqrt(5)), 
  sigma_prop = 10
)$`Acceptance Ratio`

[1] 0.5845552

Sampling from Metropolis Hastings (my solutions #2)

Sampling from Metropolis Hastings (my solutions #2)

Clarifying sigma..

sampler_mh(
  start = 0, 
  distr_name = "norm",
  distr_params = c(0, 2), 
  sigma_prop = 4
)

Sampling from Metropolis Hastings (my solutions #3)

Use sampler_mh() to generate samples from a Beta distribution \(\alpha = 4, \beta = 4\)

sampler_mh(
  start = 0, 
  distr_name = "beta", 
  distr_params = c(4,4)
)

From samples to responses – Anchoring

Lieder et al. (2018) use MCMC to provide an explanation of anchoring as resource-rational allocation of resources.

From samples to responses – Anchoring

From samples to responses – Anchoring (my solution)

set.seed(1)
starts <- c(60, 320)

target_sd <- 30
proposal_variance <- 20
n.max <- 200 # maximum number of samples we're going to test

# Initialise vector
responses <- c()

# Loop over starting points
for (start in starts){
  # loop over possible n values
  for (n in 1:n.max){
    samples <- sampler_mh(
      start = start, 
      distr_name = "norm", 
      distr_params = c(157, target_sd), 
      sigma_prop = proposal_variance, 
      iterations = n
    )$Samples[n] # choose the nth sample
    
    # add samples to vector
    responses <- c(responses, samples)
  }
}