Sample from posterior distributions using the No U-turn Sampler (NUTS). For details see the original NUTS paper and the more recent introduction.
This crate was developed as a faster replacement of the sampler in PyMC, to be used with the new numba backend of aesara. The python wrapper for this sampler is nutpie.
use nuts_rs::{CpuLogpFunc, LogpError, new_sampler, SamplerArgs, Chain, SampleStats};
use thiserror::Error;
use rand::thread_rng;
// Define a function that computes the unnormalized posterior density
// and its gradient.
struct PosteriorDensity {}
// The density might fail in a recoverable or non-recoverable manner...
#[derive(Debug, Error)]
enum PosteriorLogpError {}
impl LogpError for PosteriorLogpError {
fn is_recoverable(&self) -> bool { false }
}
impl CpuLogpFunc for PosteriorDensity {
type Err = PosteriorLogpError;
// We define a 10 dimensional normal distribution
fn dim(&self) -> usize { 10 }
// The normal likelihood with mean 3 and its gradient.
fn logp(&mut self, position: &[f64], grad: &mut [f64]) -> Result<f64, Self::Err> {
let mu = 3f64;
let logp = position
.iter()
.copied()
.zip(grad.iter_mut())
.map(|(x, grad)| {
let diff = x - mu;
*grad = -diff;
-diff * diff / 2f64
})
.sum();
return Ok(logp)
}
}
// We get the default sampler arguments
let mut sampler_args = SamplerArgs::default();
// and modify as we like
sampler_args.num_tune = 1000;
sampler_args.maxdepth = 3; // small value just for testing...
// We instanciate our posterior density function
let logp_func = PosteriorDensity {};
let chain = 0;
let mut rng = thread_rng();
let mut sampler = new_sampler(logp_func, sampler_args, chain, &mut rng);
// Set to some initial position and start drawing samples.
sampler.set_position(&vec![0f64; 10]).expect("Unrecoverable error during init");
let mut trace = vec![]; // Collection of all draws
for _ in 0..2000 {
let (draw, info) = sampler.draw().expect("Unrecoverable error during sampling");
trace.push(draw);
// Or get more detailed information about divergences
if let Some(div_info) = info.divergence_info() {
println!("Divergence at position {:?}", div_info.start_location);
}
dbg!(&info);
}
Sampling several chains in parallel so that samples are accessable as they are generated
is implemented in [sample_parallel
].
This crate mostly follows the implementation of NUTS in Stan and PyMC, only tuning of mass matrix and step size differs somewhat.