No-U-Turn Sampler (NUTS)

class sampyl.NUTS(logp, start, step_size=0.25, adapt_steps=100, Emax=1000.0, target_accept=0.65, gamma=0.05, k=0.75, t0=10.0, **kwargs)

No-U-Turn sampler (Hoffman & Gelman, 2014) for sampling from a probability distribution defined by a log P(theta) function.

For technical details, see the paper: http://www.stat.columbia.edu/~gelman/research/published/nuts.pdf

Parameters:
  • logp – log P(X) function for sampling distribution
  • start – Dictionary of starting state for the sampler. Should have one element for each argument of logp.
  • grad_logp –

    (optional) Function or list of functions that calculate grad log P(theta). Pass functions here if you don’t want to use autograd for the gradients. If logp has multiple parameters, grad_logp must be a list of gradient functions w.r.t. each parameter in logp.

    If you wish to use a logp function that returns both the logp value and the gradient, set grad_logp = True.

  • scale – (optional) Dictionary with same format as start. Scaling for initial momentum in Hamiltonian step.
  • step_size – (optional) float. Initial step size for the deterministic proposals.
  • adapt_steps – (optional) int. Integer number of steps used for adapting the step size to achieve a target acceptance rate.
  • Emax – (optional) float. Maximum energy.
  • target_accept – (optional) float. Target acceptance rate.
  • gamma – (optional) float.
  • k – (optional) float. Scales the speed of step size adaptation.
  • t0 – (optional) float. Slows initial step size adaptation.

Example

def logp(x, y):
    ...

start = {'x': x_start, 'y': y_start}
nuts = sampyl.NUTS(logp, start)
chain = nuts.sample(1000)
sample(num, burn=0, thin=1, n_chains=1, progress_bar=True)

Sample from \(P(X)\)

Parameters:
  • num – int. Number of samples to draw from \(P(X)\).
  • burn – (optional) int. Number of samples to discard from the beginning of the chain.
  • thin – (optional) float. Thin the samples by this factor.
  • n_chains – (optional) int. Number of chains to return. Each chain is given its own process and the OS decides how to distribute the processes.
  • progress_bar – (optional) boolean. Show the progress bar, default = True.
Returns:

Record array with fields taken from arguments of logp function.
step()

Perform one NUTS step.