propagation: Propagate particles forward in time

Description

This function propagates particles forward in time. Assuming that the particles have been propagated to a given time slice \(t\), the aim is to propagate them to a later time slice \(t + k\) according to the Gaussian mixture graphical model and to the evidence collected over time. At first, a renewal step is performed if the effective sample size (ESS) is below a given threshold (Doucet and Johansen, 2009). This step consists in randomly selecting new particles among the old ones proportionately to their current weights. Upon receiving the data (the evidence) of \(t + 1\), each particle is used to generate samples for the unknown values. Its weight is then updated to the likelihood for the observed values. The higher this likelihood, the more likely the particle is selected at the next renewal step for propagation to \(t + 2\), and so on (Koller and Friedman, 2009).

Usage

propagation(
  part,
  gmgm,
  evid = NULL,
  col_seq = NULL,
  col_weight = "weight",
  n_times = 1,
  min_ess = 1
)

Value

A data frame (tibble) containing the particles supplemented with the samples of time slices \(t + 1, \dots , t + k\).

Arguments

part: A data frame containing the particles propagated to time slice \(t\), as obtained from function particles or propagation.
gmgm: An object of class gmbn or gmdbn. For a gmdbn object, the gmbn elements used for propagation are selected according to the temporal depth of the particles, assuming that the particles contain all the samples since the first time slice (this depth is thus considered as the current time slice).
evid: A data frame containing the evidence of time slices \(t + 1, \dots , t + k\). Its columns must explicitly be named after nodes of gmgm and can contain missing values (columns with no value can be removed). If NULL (the default), no evidence is taken into account.
col_seq: A character vector containing the column names of part and evid that describe the observation sequence. If NULL (the default), all the particles and observations belong to a single sequence. In evid, the observations of a same sequence must be ordered such that the \(k\)th one is related to time slice \(t + k\) (note that the sequences can have different lengths).
col_weight: A character string corresponding to the column name of part that describes the particle weight.
n_times: A non-negative integer corresponding to the number of time slices \(k\) over which the particles are propagated.
min_ess: A numeric value in [0, 1] corresponding to the minimum ESS (expressed as a proportion of the number of particles) under which the renewal step is performed. If 1 (the default), this step is performed at each time slice.

References

Doucet, A. and Johansen, A. M. (2009). A Tutorial on Particle Filtering and Smoothing: Fifteen years later. Handbook of nonlinear filtering, 12:656--704.

Koller, D. and Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques. The MIT Press.

Examples

Run this code

# \donttest{
library(dplyr)
set.seed(0)
data(gmdbn_air, data_air)
evid <- data_air %>%
  group_by(DATE) %>%
  slice(1:3) %>%
  ungroup()
evid$NO2[sample.int(150, 30)] <- NA
evid$O3[sample.int(150, 30)] <- NA
evid$TEMP[sample.int(150, 30)] <- NA
evid$WIND[sample.int(150, 30)] <- NA
part <- particles(data.frame(DATE = unique(evid$DATE))) %>%
  propagation(gmdbn_air, evid, col_seq = "DATE", n_times = 3)# }