Bootstrap particle filter

The bootstrap filtering algorithm. Systematic resampling is performed at each observation.

Usage

pfilter(model, obs_process, data, n_particles, init_model = NULL)

# S4 method for class 'SimInf_model'
pfilter(model, obs_process, data, n_particles, init_model = NULL)

Arguments

model

The SimInf_model object to simulate data from.

obs_process

Specification of the stochastic observation process. The obs_process can be specified as a formula if the model contains only one node and there is only one data point for each time in data. The left hand side of the formula must match a column name in the data data.frame and the right hand side of the formula is a character specifying the distribution of the observation process, for example, Iobs ~ poisson(I). The following distributions are supported: x ~ binomial(size, prob), x ~ poisson(rate) and x ~ uniform(min, max). The observation process can also be a function to evaluate the probability density of the observations given the simulated states. The first argument passed to the obs_process function is the result from a run of the model and it contains one trajectory with simulated data for a time-point. The second argument to the obs_process function is a data.frame containing the rows for the specific time-point that the function is called for. Note that the function must return the log of the density.

data

A data.frame holding the time series data.

n_particles

An integer with the number of particles (> 1) to use at each timestep.

init_model

An optional function that, if non-NULL, is applied before running each proposal. The function must accept one argument of type SimInf_model with the current model of the fitting process. This function can be useful to specify the initial state of u0 or v0 of the model before running a trajectory with proposed parameters.

Value

A SimInf_pfilter object.

References

1993

Examples

if (FALSE) { # \dontrun{
## Let us consider an SIR model in a closed population with N = 100
## individuals of whom one is initially infectious and the rest are
## susceptible. First, generate one realisation (with a specified
## seed) from the model with known parameters 'beta = 0.16' and
## 'gamma = 0.077'. Then, use 'pfilter' to apply the bootstrap
## particle algorithm on the simulated data.
model <- SIR(u0 = data.frame(S = 99, I = 1, R = 0),
             tspan = seq(1, 100, by = 3),
             beta = 0.16,
             gamma = 0.077)

## Run the SIR model to generate simulated observed data for the
## number of infected individuals.
set.seed(22)
infected <- trajectory(run(model), "I")[, c("time", "I")]
colnames(infected) <- c("time", "Iobs")

## Use a Poison observation process for the infected individuals, such
## that 'Iobs ~ poison(I + 1e-6)'. A small constant '1e-6' is added to
## prevent numerical errors, since the simulated counts 'I' could be
## zero, which would result in the Poisson rate parameter being zero,
## which violates the conditions of the Poisson distribution. Use 1000
## particles.
pf <- pfilter(model,
              obs_process = Iobs ~ poisson(I + 1e-6),
              data = infected,
              npart = 1000)

## Print a brief summary.
pf

## Compare the number infected 'I' in the filtered trajectory with the
## infected 'Iobs' in the observed data.
plot(pf, ~I)
lines(Iobs ~ time, infected, col = "blue", lwd = 2, type = "s")
} # }