cond_logLik: Conditional log likelihood

In pomp: Statistical Inference for Partially Observed Markov Processes

Conditional log likelihood

Description

The estimated conditional log likelihood from a fitted model.

Usage

## S4 method for signature 'kalmand_pomp'
cond_logLik(object, ..., format = c("numeric", "data.frame"))

## S4 method for signature 'pfilterd_pomp'
cond_logLik(object, ..., format = c("numeric", "data.frame"))

## S4 method for signature 'wpfilterd_pomp'
cond_logLik(object, ..., format = c("numeric", "data.frame"))

## S4 method for signature 'bsmcd_pomp'
cond_logLik(object, ..., format = c("numeric", "data.frame"))

## S4 method for signature 'pfilterList'
cond_logLik(object, ..., format = c("numeric", "data.frame"))

Arguments

object	result of a filtering computation
...	ignored
format	format of the returned object

Details

The conditional likelihood is defined to be the value of the density of

Y(t_k) | Y(t_1),\dots,Y(t_{k-1})

evaluated at Y(t_k) = y^*_k. Here, Y(t_k) is the observable process, and y^*_k the data, at time t_k.

Thus the conditional log likelihood at time t_k is

\ell_k(\theta) = \log f[Y(t_k)=y^*_k \vert Y(t_1)=y^*_1, \dots, Y(t_{k-1})=y^*_{k-1}],

where f is the probability density above.

Value

The numerical value of the conditional log likelihood. Note that some methods compute not the log likelihood itself but instead a related quantity. To keep the code simple, the cond_logLik function is nevertheless used to extract this quantity.

When object is of class ‘bsmcd_pomp’ (i.e., the result of a bsmc2 computation), cond_logLik returns the conditional log “evidence” (see bsmc2).

See Also

More on sequential Monte Carlo methods: bsmc2(), eff_sample_size(), filter_mean(), filter_traj(), kalman, mif2(), pfilter(), pmcmc(), pred_mean(), pred_var(), saved_states(), wpfilter()

Other extraction methods: coef(), covmat(), eff_sample_size(), filter_mean(), filter_traj(), forecast(), logLik, obs(), pred_mean(), pred_var(), saved_states(), spy(), states(), summary(), timezero(), time(), traces()

pomp documentation built on Aug. 8, 2023, 1:08 a.m.