pfjax.models.base_model

Module Contents

Classes

BaseModel

Base model for particle filters.
class pfjax.models.base_model.BaseModel(bootstrap)[source]

Bases: object

Base model for particle filters.

This class sets up a PF model from small set of methods:

  • The derived class should provide methods state_lpdf(), meas_lpdf(), state_sample() and meas_sample() in order calculate the complete data likelihood pfjax.loglik_full() and simulate data from the model via pfjax.simulate().

  • To use the “basic” particle filter pfjax.particle_filter(), the derived class must provide methods pf_init() and pf_step().

  • To use the Rao-Blackwellized particle filter pfjax.particle_filter_rb(), the derived class must provide methods pf_init(), step_sample(), and step_lpdf().

  • If pf_init() is missing, the base class will automatically construct it from prior_lpdf(), init_sample(), and init_lpdf().

  • if pf_step() is missing, the base class will automatically construct it from state_lpdf(), meas_lpdf(), step_sample(), and step_lpdf().

  • If in either of the above step_sample() and step_lpdf() are missing, the base class assumes a bootstrap particle filter and sets step_sample = state_sample and step_lpdf = state_lpdf.

  • If in either of the above init_sample() and init_lpdf() are missing, the base calss sets init_sample = prior_sample and init_lpdf = prior_lpdf.

Notes:

  • pf_step() and pf_init() could be computed more efficiently for bootstrap sampling. Perhaps this could be specified with an argument bootstrap to the constructor.

  • In general, nothing is stopping the user from creating e.g., pf_step() which is inconsistent with step_sample(), etc.

Parameters

bootstrap – Boolean for whether or not to create a bootstrap particle filter.

step_sample(key, x_prev, y_curr, theta)[source]

Sample from default proposal distribution

q(x_curr | x_prev, y_curr, theta) = p(x_curr | x_prev, theta)
Parameters

  • key – PRNG key.

  • x_prev – State variable at previous time t-1.

  • y_curr – Measurement variable at current time t.

  • theta – Parameter value.

Returns

Sample of the state variable x_curr at current time t.

step_lpdf(x_curr, x_prev, y_curr, theta)[source]

Calculate log-density of the default proposal distribution

q(x_curr | x_prev, y_curr, theta) = p(x_curr | x_prev, theta)
Parameters

  • x_curr – State variable at current time t.

  • x_prev – State variable at previous time t-1.

  • y_curr – Measurement variable at current time t.

  • theta – Parameter value.

Returns

Log-density of the state variable x_curr at current time t.

init_sample(key, y_init, theta)[source]

Sample from default initial proposal distribution

q(x_init | y_init, theta) = p(x_init | theta)
Parameters

  • key – PRNG key.

  • y_init – Measurement variable at initial time t = 0.

  • theta – Parameter value.

Returns

Sample of the state variable x_init at initial time t = 0.

init_lpdf(x_init, y_init, theta)[source]

Calculate log-density of the default proposal distribution

q(x_curr | x_prev, y_curr, theta) = p(x_curr | x_prev, theta)
Parameters

  • x_init – State variable at initial time t = 0.

  • y_init – Measurement variable at initial time t = 0.

  • theta – Parameter value.

Returns

Log-density of the state variable x_init at initial time t = 0.

pf_step(key, x_prev, y_curr, theta)[source]

Particle filter update.

Returns a draw from proposal distribution

x_curr ~ q(x_curr) = q(x_curr | x_prev, y_curr, theta)

and the log weight

logw = log p(y_curr | x_curr, theta) + log p(x_curr | x_prev, theta) - log q(x_curr)
Parameters

  • key – PRNG key.

  • x_prev – State variable at previous time t-1.

  • y_curr – Measurement variable at current time t.

  • theta – Parameter value.

Returns

  • x_curr - A sample from the proposal distribution at current time t.

  • logw - The log-weight of x_curr.

Return type

Tuple

pf_init(key, y_init, theta)[source]

Initial step of particle filter.

Returns a draw from the proposal distribution

x_init ~ q(x_init) = q(x_init | y_init, theta)

and calculates the log weight

logw = log p(y_init | x_init, theta) + log p(x_init | theta) - log q(x_init)
Parameters

  • key – PRNG key.

  • y_init – Measurement variable at initial time t = 0.

  • theta – Parameter value.

Returns

  • x_init - A sample from the proposal distribution at initial tme t = 0.

  • logw - The log-weight of x_init.

Return type

Tuple