superstats.transition.stochastic.ornstein_uhlenbeck#

Ornstein-Uhlenbeck transition models.

Classes

OrnsteinUhlenbeck([bounds, initial_prior, ...])

Ornstein-Uhlenbeck mean-reverting transition.

class superstats.transition.stochastic.ornstein_uhlenbeck.OrnsteinUhlenbeck(bounds=None, initial_prior=None, sigma=None, mu=None, theta=None)[source]#

Bases: StochasticTransition

Ornstein-Uhlenbeck mean-reverting transition.

Parameters:

boundstuple or None, optional, default: None: Lower and upper bounds for the latent state.
initial_priorPrior or None, optional, default: None: Prior for the initial latent state.
sigmafloat or Prior or None, optional, default: None: Diffusion scale.
mufloat or Prior or None, optional, default: None: Long-run mean to revert towards.
thetafloat or Prior or None, optional, default: None: Mean-reversion speed.

Parameters:

bounds (Tuple[float, float] | None)
initial_prior (Prior | None)
sigma (float | Prior | None)
mu (float | Prior | None)
theta (float | Prior | None)

Notes

Implements an OU process: x_t = x_{t-1} + theta * (mu - x_{t-1}) + sigma * eps_t.

sample(batch_size, num_steps)[source]#

Draw batch_size Ornstein-Uhlenbeck trajectories of length num_steps.

Parameters:

batch_sizeint: Number of independent trajectories to draw.
num_stepsint: Number of time steps per trajectory.

Returns:

resultdict - dictionary with keys local_params,: hyper_params, and fixed_params

Parameters:

batch_size (int)
num_steps (int)

Return type:

Dict[str, Any]

sample_one_step(x, params)[source]#

Advance a single OU step.

Parameters:

xfloat: Previous latent state.
paramsdict: Expected keys: mu, theta, sigma.

Returns:

x_nextfloat - the next latent state

Parameters:

x (float)
params (Dict[str, Any])

Return type:

float