<!-- livebook:{"persist_outputs":true} -->
# Untitled notebook
```elixir
Mix.install(
[
{:ulam, path: Path.join(__DIR__, ".."), env: :dev}
],
config_path: :ulam,
lockfile: :ulam
)
```
## Section
```elixir
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
```
<!-- livebook:{"output":true} -->
```
:ok
```
```elixir
# 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
)
```
<!-- livebook:{"output":true} -->
```
#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, ...]
>
```
