Untitled notebook

Mix.install(
  [
    {:ulam, path: Path.join(__DIR__, ".."), env: :dev}
  ],
  config_path: :ulam,
  lockfile: :ulam
)

Section

require Ulam.UlamModel, as: UlamModel
alias Ulam.ProgressMonitors.KinoProgressMonitor

require Explorer.DataFrame, as: DataFrame
alias Explorer.Series

alias Statistics.Distributions.Normal

non_vectorized_model_file = "examples/linear_regression_vectorization/non_vectorized.stan"

non_vectorized_model =
    UlamModel.new stan_file: non_vectorized_model_file do
      data do
        n :: int(lower: 0)
        x :: vector(n)
        y :: vector(n)
      end

      parameters do
        # Parameters for the linear regression
        intercept :: real()
        slope :: real()
        error :: real(lower: 0)
        # Prior on x
        mu_x :: real()
        sigma_x :: real(lower: 0)
      end

      model do
        for i <- 1..n do
          x[i] <~> normal(mu_x, sigma_x)
          y[i] <~> normal(x[i] * slope + intercept, error)
        end
      end
    end

compiled_model = UlamModel.compile(non_vectorized_model)

params = %{
  mu_x: 1.2,
  sigma_x: 0.7,
  slope: 0.7,
  intercept: 2.8,
  error: 0.15
}

# Simulate some data
n = 160
x = for _i <- 1..n, do: Normal.rand(params.mu_x, params.sigma_x)
y = for x_i <- x, do: Normal.rand(x_i * params.slope + params.intercept, params.error)

data = %{x: x, y: y, n: n}

:ok

:ok

# Sample from the precompiled model
dataframe =
  UlamModel.sample(compiled_model, data,
    nr_of_samples: 10_000,
    nr_of_warmup_samples: 100_000,
    nr_of_chains: 4,
    progress_monitor: KinoProgressMonitor
  )

#Explorer.DataFrame<
  Polars[40000 x 13]
  lp__ f64 [216.438, 216.321, 215.388, 214.367, 215.433, ...]
  accept_stat__ f64 [0.937126, 0.999769, 0.978436, 0.871591, 0.993678, ...]
  stepsize__ f64 [0.309385, 0.309385, 0.309385, 0.309385, 0.309385, ...]
  treedepth__ s64 [3, 4, 3, 2, 4, ...]
  n_leapfrog__ s64 [7, 15, 7, 3, 15, ...]
  divergent__ s64 [0, 0, 0, 0, 0, ...]
  energy__ f64 [-212.891, -215.788, -213.813, -213.3, -211.814, ...]
  intercept f64 [2.79727, 2.80188, 2.82414, 2.82774, 2.81214, ...]
  slope f64 [0.692079, 0.688404, 0.673604, 0.675499, 0.67917, ...]
  error f64 [0.158438, 0.157599, 0.166397, 0.169968, 0.138837, ...]
  mu_x f64 [1.36237, 1.37116, 1.35812, 1.35515, 1.29617, ...]
  sigma_x f64 [0.59416, 0.59675, 0.615252, 0.595205, 0.673599, ...]
  chain__ s64 [1, 1, 1, 1, 1, ...]
>