pypfda.resampling

Particle resampling schemes.

Each scheme takes a vector of normalized weights and a random generator and returns an integer index array of the same length whose values are in [0, n_members). The expected number of times particle \(i\) is selected equals \(N w_i\). Variance differs across schemes; systematic resampling has the lowest variance and is the recommended default for most applications.

References

Douc, R., Cappé, O. & Moulines, E. (2005). Comparison of resampling schemes for particle filtering. ISPA 2005.

Functions

multinomial(weights[, rng])

Plain multinomial resampling.

resample(weights[, method, rng])

Dispatch by name to one of the resampling routines.

residual(weights[, rng])

Residual resampling.

stratified(weights[, rng])

Stratified resampling.

systematic(weights[, rng])

Systematic resampling.
pypfda.resampling.systematic(weights, rng=None)[source]

Systematic resampling.

Draws a single uniform random offset and walks through the inverse cumulative distribution function with deterministic, evenly-spaced strides. Lowest variance among standard schemes; preserves the expected count exactly when weights are rationals with a common denominator that divides N.

Parameters:

  • weights (array_like, shape (n_members,)) – Normalized weights.

  • rng (numpy.random.Generator, optional) – Random number generator. If None, np.random.default_rng() is used.

Returns:

indices – Indices into the input weight vector.

Return type:

ndarray of int, shape (n_members,)

pypfda.resampling.stratified(weights, rng=None)[source]

Stratified resampling.

Like systematic() but draws an independent uniform offset inside each of the N equal-width strata. Slightly higher variance than systematic, but eliminates the (theoretical) failure mode where systematic resampling can be sensitive to particle ordering.

Parameters:
Return type:

ndarray[tuple[Any, …], dtype[int64]]

pypfda.resampling.residual(weights, rng=None)[source]

Residual resampling.

Allocates floor(N * w_i) deterministic copies of each particle and resamples the remainder multinomially with normalized residual weights. Often the lowest variance for small ensembles where many weights are close to the uniform value.

Parameters:
Return type:

ndarray[tuple[Any, …], dtype[int64]]

pypfda.resampling.multinomial(weights, rng=None)[source]

Plain multinomial resampling.

Draws N independent samples from the categorical distribution defined by the weights. Highest variance of the standard schemes; included mainly as a baseline.

Parameters:
Return type:

ndarray[tuple[Any, …], dtype[int64]]

pypfda.resampling.resample(weights, method='systematic', rng=None)[source]

Dispatch by name to one of the resampling routines.

Parameters:

  • weights (array_like, shape (n_members,)) – Normalized weights.

  • method ({'systematic', 'stratified', 'residual', 'multinomial'}, default 'systematic') – Resampling scheme.

  • rng (numpy.random.Generator, optional) – Random generator.

Returns:

indices

Return type:

ndarray of int, shape (n_members,)