expected_obs.stan File Reference

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Functions
vector	expected_obs (real tar_obs, vector lh, int l, int ref_as_p, int agg_probs, matrix agg_indicator)

Function Documentation

expected_obs()

vector expected_obs	(	real	tar_obs,
		vector	lh,
		int	l,
		int	ref_as_p,
		int	agg_probs,
		matrix	agg_indicator
	)

Calculate expected observations on the log scale

Computes expected observations over time based on final expected observations and reporting probabilities. It handles both probabilities and logit hazards for reporting on each day.

Parameters

tar_obs	The logarithm of the final expected observations for a given date. It should be a real number representing logged observations.
lh	A vector of conditional log probabilities of a report occurring on a given day. When ref_as_p is 0, this should be the logit hazard instead of probability.
l	Length of the vector lh.
ref_as_p	An integer flag (0 or 1) indicating whether the reference date input should be treated as a logit hazard or probability. Set to 1 when no report date effects are present, otherwise 0.
agg_probs	An integer flag (0 or 1) indicating whether the reporting probabilities should be aggregated. Set to 1 when the probabilities should be aggregated, otherwise 0.
agg_indicator	A matrix of integer flags (0 or 1) representing the aggregation of reporting probabilities, designed to be left-multiplied to a column vector of reporting probabilities. Presence of a 1 in a column indicates that that index in the probability column vector will be aggregated, and presence of a 1 in a row indicates that aggregated probability will be placed on that index in the new probability vector.

Returns

A vector representing the expected observations for each date by date of report. The length of the vector matches the length of lh.

Note

Dependencies:

• inv_logit: Used to convert logit hazards to probabilities.
• hazard_to_log_prob: Used for converting hazards to log probabilities.

# compile function for use in R
source(here::here("R", "utils.R"))
enw_stan_to_r(c("hazard.stan", "expected_obs.stan"),
                "inst/stan/functions")
 
tar_obs <- log(1)
date_p <- log(
  (plnorm(1:30, 1.5, 2) - plnorm(0:29, 1.5, 2)) / plnorm(30, 1.5, 2)
)
rep_lh <- rep(0, 30)
 
Example with no reporting day effect
eobs <- exp(expected_obs(
  tar_obs, date_p + rep(0, 30), 30, 1, 0, matrix(0, nrow = 0, ncol = 0)
))
 
Example with hazard effect only on last date of report
ref_lh <- qlogis(prob_to_hazard(exp(date_p)))
eobs <- exp(
  expected_obs(
    tar_obs, ref_lh, 30, 0, 0,
    matrix(numeric(0), nrow = 0, ncol = 0)
  )
)
 
Example with a single day of additional reporting hazard
rep_lh <- rep(0, 30)
rep_lh[7] <- 2
equal_lh <- plogis(hazard_to_log_prob(rep(1/30, 30), 30))
eobs <- round(exp(
  expected_obs(
    tar_obs, equal_lh + rep_lh, 30, 0, 0,
    matrix(numeric(0), nrow = 0, ncol = 0)
  )
), 3)
expected <- c(0.508, 0.250, 0.123, 0.060, 0.030, 0.015, 0.013, 0.001)
 
Example combining multiple hazards and no differential prob due to reference
date
rep_lh <- rep(0, 30)
rep_lh[c(6, 12, 16)] <- 2
rep_lh[c(2, 20)] <- -2
equal_lh <- plogis(hazard_to_log_prob(rep(1 / 30, 30), 30))
eobs <- round(exp(
  expected_obs(
    tar_obs, equal_lh + rep_lh, 30, 0, 0,
    matrix(numeric(0), nrow = 0, ncol = 0)
  )
), 3)
expected <- c(0.508, 0.060, 0.219, 0.108, 0.053, 0.046, 0.003, 0.002, 0.001,
              rep(0.000, 21))
 
Example with aggregation of probabilities where aggregation occurs on every fifth day
agg_probs <- matrix(c(rep(0, times = 30 * 4),
                      rep(c(rep(1, times = 5),
                            rep(0, times = 6 * 5 + 30 * 4)),
                          times = 5),
                      rep(1, times = 5)), ncol = 30, byrow = TRUE)
eobs <- exp(expected_obs(tar_obs, date_p + rep(0, 30), 30, 1, 1, agg_probs))
# -Inf -Inf -Inf -Inf -0.4630154 -Inf -Inf -Inf -Inf -1.8219081
# -Inf -Inf -Inf -Inf -2.4549990 -Inf -Inf -Inf -Inf -2.8994851
# -Inf -Inf -Inf -Inf -3.2477183 -Inf -Inf -Inf -Inf -3.5362414
# Can visualize what this does to the probabilities with
eobs |> exp() |> plot()

Definition at line 102 of file expected_obs.stan.