diff --git a/R/epinowcast.R b/R/epinowcast.R
index e7ed8048b..359189fc8 100644
--- a/R/epinowcast.R
+++ b/R/epinowcast.R
@@ -111,8 +111,10 @@ epinowcast <- function(data,
                          data = data
                        ),
                        expectation = epinowcast::enw_expectation(
-                         formula = ~ rw(day, .group),
+                         r = ~ rw(day, .group),
                          generation_time = 1,
+                         observation = ~1,
+                         latent_reporting_delay = 1,
                          data = data
                        ),
                        missing = epinowcast::enw_missing(
diff --git a/R/model-modules.R b/R/model-modules.R
index 681cf50ee..710be6c3b 100644
--- a/R/model-modules.R
+++ b/R/model-modules.R
@@ -219,48 +219,76 @@ enw_report <- function(non_parametric = ~0, structural = ~0, data) {
 
 #' Expectation model module
 #'
-#' @param formula A formula (as implemented in [enw_formula()]) describing
+#' @param r A formula (as implemented in [enw_formula()]) describing
 #' the generative process used for expected incidence. This can use features
 #' defined by reference date as defined in `metareference` as produced by
 #' [enw_preprocess_data()]. By default this is set to use a daily group
-#' specific random walk. Note that the daily group specific random walk is
-#' currently the only option supported by [epinowcast()].
+#' specific random walk.
 #'
 #' @param generation_time A numeric vector that sums to 1 and defaults to 1.
 #' Describes the weighting to apply to previous generations (i.e as part of a
 #' renewal equation). When set to 1 (the default) this corresponds to modelling
 #' the daily growth rate.
 #'
+#' @param observation A formula (as implemented in [enw_formula()]) describing
+#' the modifiers used to adjust expected observations. This can use features
+#' defined by reference date as defined in `metareference` as produced by
+#' [enw_preprocess_data()]. By default no modifiers are used but a common choice
+#' might be to adjust for the day of the week. Note as the baseline is no
+#' modification an intercept is always used and it is set to 0.
+#'
+#' @param latent_reporting_delay A numeric vector that defaults to 1.
+#' Describes the weighting to apply to past and current latent expected
+#' observations (from most recent to least). This can be used both to convolve
+#' based on some assumed reporting delay and to rescale obserations (by
+#' multiplying a probability mass function by some fraction) to account
+#' ascertainment etc.
+#'
+#' @param ... Additional parameters passed to [enw_add_metaobs_features()]. The
+#' same arguments as passed to `enw_preprocess_data()` should be used here.
 #' @inherit enw_report return
 #' @inheritParams enw_obs
 #' @family modelmodules
 #' @export
 #' @examples
 #' enw_expectation(data = enw_example("preprocessed"))
-enw_expectation <- function(formula = ~ rw(day, by = .group),
-                            generation_time = 1, data) {
-  if (as_string_formula(formula) %in% "~0") {
-    stop("An expectation model formula must be specified")
+enw_expectation <- function(r = ~ rw(day, by = .group), generation_time = 1,
+                            observation = ~1, latent_reporting_delay = 1,
+                            data, ...) {
+  if (as_string_formula(r) %in% "~0") {
+    stop("An expectation model formula for r must be specified")
+  }
+  if (as_string_formula(observation) %in% "~0") {
+    observation <- ~1
   }
-
   if (sum(generation_time) != 1) {
     stop("The generation time must sum to 1")
   }
 
-  features <- data$metareference[[1]]
-  features <- features[
+  # Set up growth rate features
+  r_features <- data$metareference[[1]]
+  if (length(latent_reporting_delay) > 1) {
+    r_features <- enw_extend_date(
+      r_features,
+      days = length(latent_reporting_delay) - 1, direction = "start"
+    )
+    enw_add_metaobs_features(r_features, ...)
+  }
+  r_features <- r_features[
     date >= (min(date) + length(generation_time))
   ]
 
+  # Growth rate indicator variables
   r_list <- list(
     r_seed = length(generation_time),
     gt_n = length(generation_time),
     lrgt = log(rev(generation_time)),
-    t = nrow(features),
+    t = nrow(r_features),
     obs = 0
   )
 
   r_list$g <- cumsum(rep(r_list$t, data$groups[[1]])) - r_list$t
+  r_list$ft <- r_list$t + r_list$r_seed
 
   # Initial prior for seeding observations
   latest_matrix <- latest_obs_as_matrix(data$latest[[1]])
@@ -268,33 +296,60 @@ enw_expectation <- function(formula = ~ rw(day, by = .group),
   seed_obs <- purrr::map(seed_obs, ~ rep(log(.), r_list$gt_n))
   seed_obs <- round(unlist(seed_obs), 1)
 
-  form <- enw_formula(formula, features, sparse = FALSE)
-  data <- enw_formula_as_data_list(
-    form,
+  # Growth rate model formula
+  r_form <- enw_formula(r, r_features, sparse = FALSE)
+  r_data <- enw_formula_as_data_list(
+    r_form,
     prefix = "expr", drop_intercept = TRUE
   )
 
+  # Observation indicator variables
+  obs_list <- list(
+    lrd_n = length(latent_reporting_delay),
+    lrlrd = log(rev(latent_reporting_delay))
+  )
+  obs_list$obs <- ifelse(
+    sum(latent_reporting_delay) == 1 && obs_list$lrd_n == 1 &&
+      as_string_formula(observation) %in% "~1",
+    0, 1
+  )
+  # Observation formula
+  obs_form <- enw_formula(observation, data$metareference[[1]], sparse = FALSE)
+  obs_data <- enw_formula_as_data_list(
+    obs_form,
+    prefix = "expo", drop_intercept = TRUE
+  )
+
   out <- list()
-  out$formula$expectation <- form$formula
+  out$formula$r <- r_form$formula
+  out$formula$observation <- obs_form$formula
+  out$data_raw$r <- r_features
+  out$data_raw$observation <- data$metareference[[1]]
+
   names(r_list) <- paste0("expr_", names(r_list))
-  out$data <- c(r_list, data)
+  names(obs_list) <- paste0("expo_", names(obs_list))
+  out$data <- c(r_list, r_data, obs_list, obs_data)
+
   out$priors <- data.table::data.table(
     variable = c(
       "expr_r_int", "expr_beta_sd",
-      rep("expr_leobs_int", length(seed_obs))
+      rep("expr_leobs_int", length(seed_obs)),
+      "expo_beta_sd"
     ),
-    dimension = c(1, 1, seq_along(seed_obs)),
+    dimension = c(1, 1, seq_along(seed_obs), 1),
     description = c(
       "Intercept of the log growth rate",
-      "Standard deviation of scaled pooled expectation effects",
+      "Standard deviation of scaled pooled log growth rate effects",
       rep("Intercept for initial log observations (ordered by group and then
-          time)", length(seed_obs))
+          time)", length(seed_obs)),
+      "Standard deviation of scaled pooled log growth rate effects"
     ),
     distribution = c(
-      "Normal", "Zero truncated normal", rep("Normal", length(seed_obs))
+      "Normal", "Zero truncated normal", rep("Normal", length(seed_obs)),
+      "Zero truncated normal"
     ),
-    mean = c(0, 0, seed_obs),
-    sd = c(0.2, 0.1, rep(1, length(seed_obs)))
+    mean = c(0, 0, seed_obs, 0),
+    sd = c(0.2, 1, rep(1, length(seed_obs)), 1)
   )
   out$inits <- function(data, priors) {
     priors <- enw_priors_as_data_list(priors)
@@ -312,17 +367,28 @@ enw_expectation <- function(formula = ~ rw(day, by = .group),
         )),
         expr_r_int = rnorm(
           1, priors$expr_r_int[1], priors$expr_r_int[2] * 0.1
-        )
+        ),
+        expo_beta = numeric(0),
+        expo_beta_sd = numeric(0)
       )
       if (data$expr_fncol > 0) {
         init$expr_beta <- rnorm(data$expr_fncol, 0, 0.01)
       }
-      if (data$ expr_rncol > 0) {
+      if (data$expr_rncol > 0) {
         init$expr_beta_sd <- abs(rnorm(
           data$expr_rncol, priors$expr_beta_sd_p[1],
           priors$expr_beta_sd_p[2] / 10
         ))
       }
+      if (data$expo_fncol > 0) {
+        init$expo_beta <- rnorm(data$expo_fncol, 0, 0.01)
+      }
+      if (data$expo_rncol > 0) {
+        init$expo_beta_sd <- abs(rnorm(
+          data$expo_rncol, priors$expo_beta_sd_p[1],
+          priors$expo_beta_sd_p[2] / 10
+        ))
+      }
       return(init)
     }
     return(fn)
diff --git a/R/preprocess.R b/R/preprocess.R
index 62e401f70..57456f50c 100644
--- a/R/preprocess.R
+++ b/R/preprocess.R
@@ -165,20 +165,31 @@ enw_add_metaobs_features <- function(metaobs,
 #' @title FUNCTION_TITLE
 #' @description FUNCTION_DESCRIPTION
 #' @param metaobs PARAM_DESCRIPTION
-#' @param max_delay PARAM_DESCRIPTION, Default: 20
+#' @param days
+#' @param direction Should new dates be added at the begining or end of
+#' the data. Default is "end" with "start" also available
 #' @return OUTPUT_DESCRIPTION
 #' @family preprocess
 #' @export
 #' @importFrom data.table copy data.table rbindlist setkeyv
 #' @importFrom purrr map
-enw_extend_date <- function(metaobs, max_delay = 20) {
+enw_extend_date <- function(metaobs, days = 20, direction = "end") {
+  direction <- match.arg(direction, choices = c("start", "end"))
+
+  new_days <- 1:days
+  if (direction %in% "start") {
+    new_days <- -new_days
+    filt_fn <- min
+  } else {
+    filt_fn <- max
+  }
   exts <- data.table::copy(metaobs)
-  exts <- exts[, .SD[date == max(date)], by = .group]
+  exts <- exts[, .SD[date == filt_fn(date)], by = .group]
   exts <- split(exts, by = ".group")
   exts <- purrr::map(
     exts,
     ~ data.table::data.table(
-      extend_date = .$date + 1:(max_delay - 1),
+      extend_date = .$date + new_days,
       .
     )
   )
@@ -920,7 +931,10 @@ enw_preprocess_data <- function(obs, by = c(), max_delay = 20,
 
   # extract and extend report date meta data to include unobserved reports
   metareport <- enw_metadata(reference_available, target_date = "report_date")
-  metareport <- enw_extend_date(metareport, max_delay = max_delay)
+  metareport <- enw_extend_date(
+    metareport,
+    days = max_delay - 1, direction = "end"
+  )
   metareport <- enw_add_metaobs_features(metareport, ...)
 
   # extract and add features for reference date
diff --git a/inst/examples/germany_latent_renewal.R b/inst/examples/germany_latent_renewal.R
new file mode 100644
index 000000000..30c9d2a5b
--- /dev/null
+++ b/inst/examples/germany_latent_renewal.R
@@ -0,0 +1,156 @@
+# Load packages
+library(epinowcast)
+library(data.table)
+library(ggplot2)
+
+# Use 2 cores
+options(mc.cores = 2)
+
+# Load and filter germany hospitalisations
+nat_germany_hosp <- germany_covid19_hosp[location == "DE"][age_group %in% "00+"]
+nat_germany_hosp <- enw_filter_report_dates(
+  nat_germany_hosp,
+  latest_date = "2021-10-01"
+)
+
+# Make sure observations are complete
+nat_germany_hosp <- enw_complete_dates(
+  nat_germany_hosp,
+  by = c("location", "age_group")
+)
+# Make a retrospective dataset
+retro_nat_germany <- enw_filter_report_dates(
+  nat_germany_hosp,
+  remove_days = 40
+)
+retro_nat_germany <- enw_filter_reference_dates(
+  retro_nat_germany,
+  include_days = 40
+)
+
+# Get latest observations for the same time period
+latest_obs <- enw_latest_data(nat_germany_hosp)
+latest_obs <- enw_filter_reference_dates(
+  latest_obs,
+  remove_days = 40, include_days = 20
+)
+
+# Preprocess observations (note this maximum delay is likely too short)
+pobs <- enw_preprocess_data(retro_nat_germany, max_delay = 20)
+
+# Compile nowcasting model using multi-threading
+model <- enw_model(threads = TRUE, stanc_options = list("O1"))
+
+# Reference date model: Fixed log-normal distribution
+reference_module <- enw_reference(~1, data = pobs)
+
+# Report date model: Day of week reporting effect
+report_module <- enw_report(~ (1 | day_of_week), data = pobs)
+
+# Expectation model:
+# - Weekly random walk on the growth rate
+# - Generation time with probability mass spread over 4 days
+# - latent reporting delay representing the incubation period and assumed
+# ascertainment
+# - Day of week reporting effect
+expectation_module <- enw_expectation(
+  r = ~ rw(week),
+  generation_time = c(0.1, 0.4, 0.4, 0.1),
+  observation = ~ (1 | day_of_week),
+  latent_reporting_delay = 0.4 * c(0.05, 0.3, 0.6, 0.05),
+  data = pobs
+)
+
+# Fit nowcast model with these modules and produce a nowcast
+nowcast <- epinowcast(pobs,
+  expectation = expectation_module,
+  reference = reference_module,
+  report = report_module,
+  fit = enw_fit_opts(
+    save_warmup = FALSE, pp = TRUE,
+    chains = 2, threads_per_chain = 2,
+    iter_warmup = 1000, iter_sampling = 1000,
+    adapt_delta = 0.95, max_treedepth = 12
+  ),
+  model = model
+)
+
+# Plot nowcast of observed values
+plot(nowcast, latest_obs)
+
+# Plot Reproduction number estimates
+rt <- enw_posterior(nowcast$fit[[1]], variables = "r")
+cols <- c("mean", "median", "q5", "q20", "q80", "q95")
+rt[, (cols) := lapply(.SD, exp), .SDcols = cols]
+rt <- cbind(
+  expectation_module$data_raw$r[, .(date)], rt
+)
+
+ggplot(rt) +
+  aes(x = date) +
+  geom_line(aes(y = median), size = 1, alpha = 0.6) +
+  geom_line(aes(y = mean), linetype = 2) +
+  geom_ribbon(aes(ymin = q5, ymax = q95), alpha = 0.2, size = 0.2) +
+  geom_ribbon(aes(ymin = q20, ymax = q80, col = NULL), alpha = 0.2) +
+  geom_hline(yintercept = 1, linetype = 2) +
+  theme_bw() +
+  labs(
+    x = "Reference date",
+    y = "Effective reproduction number"
+  )
+
+# Plot expected latent cases
+latent_exp_cases <- enw_posterior(
+  nowcast$fit[[1]],
+  variables = "exp_latent_lobs"
+)
+latent_exp_cases[, (cols) := lapply(.SD, exp), .SDcols = cols]
+latent_exp_cases <- cbind(
+  enw_extend_date(
+    expectation_module$data_raw$r[, .(date, .group = 1)],
+    days = nowcast$data[[1]]$expo_lrd_n,
+    direction = "start"
+  ),
+  latent_exp_cases
+)
+
+ggplot(latent_exp_cases) +
+  aes(x = date) +
+  geom_line(aes(y = median), size = 1, alpha = 0.6) +
+  geom_line(aes(y = mean), linetype = 2) +
+  geom_ribbon(aes(ymin = q5, ymax = q95), alpha = 0.2, size = 0.2) +
+  geom_ribbon(aes(ymin = q20, ymax = q80, col = NULL), alpha = 0.2) +
+  theme_bw() +
+  labs(
+    x = "Reference date",
+    y = "Expected latent cases"
+  )
+
+# Plot expected reported cases
+exp_cases <- enw_posterior(
+  nowcast$fit[[1]],
+  variables = "exp_lobs"
+)
+exp_cases[, (cols) := lapply(.SD, exp), .SDcols = cols]
+exp_cases <- cbind(
+  expectation_module$data_raw$observation,
+  exp_cases
+)
+
+exp_cases <- enw_latest_data(nat_germany_hosp)[, date := reference_date][
+  exp_cases,
+  on = "date"
+]
+
+ggplot(exp_cases) +
+  aes(x = date) +
+  geom_point(aes(y = confirm)) +
+  geom_line(aes(y = median), size = 1, alpha = 0.6) +
+  geom_line(aes(y = mean), linetype = 2) +
+  geom_ribbon(aes(ymin = q5, ymax = q95), alpha = 0.2, size = 0.2) +
+  geom_ribbon(aes(ymin = q20, ymax = q80, col = NULL), alpha = 0.2) +
+  theme_bw() +
+  labs(
+    x = "Reference date",
+    y = "Expected reported cases"
+  )
diff --git a/inst/examples/germany_simple.R b/inst/examples/germany_simple.R
index b10398b96..bc3dc00b0 100644
--- a/inst/examples/germany_simple.R
+++ b/inst/examples/germany_simple.R
@@ -38,13 +38,13 @@ latest_obs <- enw_filter_reference_dates(
 # Preprocess observations (note this maximum delay is likely too short)
 pobs <- enw_preprocess_data(retro_nat_germany, max_delay = 20)
 
-# Fit the default nowcast model and produce a nowcast
-# Note that we have reduced samples for this example to reduce runtimes
+# Fit a simple nowcasting model with fixed growth rate and a
+# log-normal reporting distribution.
 nowcast <- epinowcast(pobs,
-  expectation = enw_expectation(~ rw(week) + (1 | day_of_week), data = pobs),
+  expectation = enw_expectation(~1, data = pobs),
   fit = enw_fit_opts(
     save_warmup = FALSE, pp = TRUE,
-    chains = 2, iter_warmup = 500, iter_sampling = 500
+    chains = 2, iter_warmup = 500, iter_sampling = 500,
   ),
-  obs = enw_obs(family = "poisson", data = pobs)
+  obs = enw_obs(family = "poisson", data = pobs),
 )
diff --git a/inst/stan/epinowcast.stan b/inst/stan/epinowcast.stan
index 9ef1e4c97..4bc538163 100644
--- a/inst/stan/epinowcast.stan
+++ b/inst/stan/epinowcast.stan
@@ -2,6 +2,7 @@ functions {
 #include functions/zero_truncated_normal.stan
 #include functions/regression.stan
 #include functions/log_expected_obs_from_r.stan
+#include functions/log_expected_obs_from_latent_obs.stan
 #include functions/discretised_logit_hazard.stan
 #include functions/hazard.stan
 #include functions/expected_obs.stan
@@ -37,9 +38,11 @@ data {
   array[t, g] int latest_obs; // latest obs for each snapshot group
 
   // Expectation model
+    // Growth rate submodule
   int expr_r_seed; // How many seeding initial intercepts to use?
   int expr_gt_n; // Length of the generation time
   int expr_t; // Time span for r
+  int expr_ft; // Sum of expr_t + expr_r_seed
   // PMF describing the generation time (reversed and logged)
   vector[expr_gt_n] expr_lrgt; 
   // Observation model to use for the latent process. Currently 0 = none
@@ -53,7 +56,19 @@ data {
   // Mean of initial log cases
   array[2, g * expr_r_seed] real expr_leobs_int_p; 
   array[2, 1] real expr_r_int_p;
- array[2, 1] real expr_beta_sd_p;
+  array[2, 1] real expr_beta_sd_p;
+    // Observation sub-module
+  int expo_lrd_n; // Length of the generation time
+  // Parrtial PMF describing the reporting delay (reversed and logged)
+  vector[expo_lrd_n] expo_lrlrd; 
+  // Observation model to use for the latent process. Currently 0 = none
+  int expo_obs;
+  int expo_fnindex;
+  int expo_fncol;
+  int expo_rncol;
+  matrix[expo_fnindex, expo_fncol + 1] expo_fdesign;
+  matrix[expo_fncol,  expo_rncol + 1] expo_rdesign;
+  array[2, 1] real expo_beta_sd_p;
 
   // Reference day model
   int model_refp;
@@ -119,11 +134,15 @@ transformed data{
 
 parameters {
   // Expectation model
-  // Initial log observations by group
+    // Growth rate submodule
+    // Initial log observations by group
   matrix[expr_r_seed, g] expr_leobs_int; 
   real expr_r_int; 
   vector[expr_fncol] expr_beta;
   vector<lower=0>[expr_rncol] expr_beta_sd;
+    // Observation sub-module
+    vector[expo_fncol] expo_beta;
+    vector<lower=0>[expo_rncol] expo_beta_sd;
 
   // Reference model
   array[model_refp ? 1 : 0] real<lower=-10, upper=logdmax> refp_mean_int;
@@ -149,6 +168,8 @@ parameters {
 transformed parameters{
   // Expectation model
   vector[expr_t] r; // Log growth rate of observations
+  array[g] vector[expr_ft]  exp_latent_lobs; // Expected final observations
+  vector[expo_obs ? expo_fnindex : 0] expo_modifier; // Reporting modifier
   array[g] vector[t]  exp_lobs; // Expected final observations
   // Reference model
   vector[refp_fnrow] refp_mean;
@@ -164,12 +185,27 @@ transformed parameters{
 
   // Expectation model
   profile("transformed_expected_final_observations") {
+  // Get log growth rates and map to expected latent observations
   r = combine_effects(
     expr_r_int, expr_beta, expr_fdesign, expr_beta_sd, expr_rdesign, 1
   );
-  exp_lobs = log_expected_obs_from_r(
-    expr_leobs_int, r, expr_g, expr_t, expr_r_seed, expr_gt_n, expr_lrgt, t, g
+  exp_latent_lobs = log_expected_obs_from_r(
+    expr_leobs_int, r, expr_g, expr_t, expr_r_seed, expr_gt_n, expr_lrgt,
+    expr_ft, g
   );
+  // Get reporting modifiers and map latent expected observations to expected
+  // observations
+  if (expo_obs) {
+    expo_modifier = combine_effects(
+      0, expo_beta, expo_fdesign, expo_beta_sd, expo_rdesign, 1
+    );
+    exp_lobs = log_expected_obs_from_latent_obs(
+      exp_latent_lobs, expo_lrd_n, expo_lrlrd, t, g, expo_modifier
+    );
+  }else{
+    exp_lobs = exp_latent_lobs;
+  }
+
   }
 
   // Reference model
@@ -224,6 +260,7 @@ transformed parameters{
 model {
   profile("model_priors") {
   // Expectation model
+    // Growth rate sub-module
   // Initial intercept of log observations 
   to_vector(expr_leobs_int) ~ normal(expr_leobs_int_p[1], expr_leobs_int_p[2]);
   // Intercept of growth rate
@@ -232,7 +269,16 @@ model {
   effect_priors_lp(
     expr_beta, expr_beta_sd, expr_beta_sd_p, expr_fncol, expr_rncol
   );
-  
+    // Observation model sub-module
+  // Reporting modifiers
+  effect_priors_lp(
+    expo_beta, expo_beta_sd, expo_beta_sd_p, expo_fncol, expo_rncol
+  );
+  // Reporting overdispersion (1/sqrt)
+  if (model_obs) {   
+    sqrt_phi[1] ~ normal(sqrt_phi_p[1], sqrt_phi_p[2]) T[0,]; 
+  }
+
   // Reference model
   if (model_refp) {
     refp_mean_int ~ normal(refp_mean_int_p[1], refp_mean_int_p[2]);
@@ -260,11 +306,6 @@ model {
       miss_beta, miss_beta_sd, miss_beta_sd_p, miss_fncol, miss_rncol
     );
   }
-
-  // Observation model
-  if (model_obs) {   // reporting overdispersion (1/sqrt)
-    sqrt_phi[1] ~ normal(sqrt_phi_p[1], sqrt_phi_p[2]) T[0,]; 
-  }
   }
   // Log-Likelihood either by snapshot or group depending on settings/model
   if (likelihood) {
diff --git a/inst/stan/functions/log_expected_obs_from_latent_obs.stan b/inst/stan/functions/log_expected_obs_from_latent_obs.stan
new file mode 100644
index 000000000..6ea4e8562
--- /dev/null
+++ b/inst/stan/functions/log_expected_obs_from_latent_obs.stan
@@ -0,0 +1,20 @@
+  array[] vector log_expected_obs_from_latent_obs(
+    array[] vector exp_latent_lobs, int rd_n, vector lrrd, int t,
+    int g, vector modifier
+  ) {
+    array[g] vector[t] exp_lobs;
+    for (k in 1:g) {
+      if (rd_n == 1) {
+        exp_lobs[k] = exp_latent_lobs[k] + rep_vector(lrrd[1], t);
+      }else{
+        for (i in 1:t){
+          exp_lobs[k][i] = 
+            log_sum_exp(
+              segment(exp_latent_lobs[k], i, rd_n) + lrrd
+            );
+        }
+      }
+      exp_lobs[k] = exp_lobs[k] + segment(modifier, (k-1) * t + 1, t);
+    }
+    return(exp_lobs);
+  }
diff --git a/man/enw_expectation.Rd b/man/enw_expectation.Rd
index ae7126b98..ee5add8e0 100644
--- a/man/enw_expectation.Rd
+++ b/man/enw_expectation.Rd
@@ -4,22 +4,45 @@
 \alias{enw_expectation}
 \title{Expectation model module}
 \usage{
-enw_expectation(formula = ~rw(day, by = .group), generation_time = 1, data)
+enw_expectation(
+  r = ~rw(day, by = .group),
+  generation_time = 1,
+  observation = ~1,
+  latent_reporting_delay = 1,
+  data,
+  ...
+)
 }
 \arguments{
-\item{formula}{A formula (as implemented in \code{\link[=enw_formula]{enw_formula()}}) describing
+\item{r}{A formula (as implemented in \code{\link[=enw_formula]{enw_formula()}}) describing
 the generative process used for expected incidence. This can use features
 defined by reference date as defined in \code{metareference} as produced by
 \code{\link[=enw_preprocess_data]{enw_preprocess_data()}}. By default this is set to use a daily group
-specific random walk. Note that the daily group specific random walk is
-currently the only option supported by \code{\link[=epinowcast]{epinowcast()}}.}
+specific random walk.}
 
 \item{generation_time}{A numeric vector that sums to 1 and defaults to 1.
 Describes the weighting to apply to previous generations (i.e as part of a
 renewal equation). When set to 1 (the default) this corresponds to modelling
 the daily growth rate.}
 
+\item{observation}{A formula (as implemented in \code{\link[=enw_formula]{enw_formula()}}) describing
+the modifiers used to adjust expected observations. This can use features
+defined by reference date as defined in \code{metareference} as produced by
+\code{\link[=enw_preprocess_data]{enw_preprocess_data()}}. By default no modifiers are used but a common choice
+might be to adjust for the day of the week. Note as the baseline is no
+modification an intercept is always used and it is set to 0.}
+
+\item{latent_reporting_delay}{A numeric vector that defaults to 1.
+Describes the weighting to apply to past and current latent expected
+observations (from most recent to least). This can be used both to convolve
+based on some assumed reporting delay and to rescale obserations (by
+multiplying a probability mass function by some fraction) to account
+ascertainment etc.}
+
 \item{data}{Output from \code{\link[=enw_preprocess_data]{enw_preprocess_data()}}.}
+
+\item{...}{Additional parameters passed to \code{\link[=enw_add_metaobs_features]{enw_add_metaobs_features()}}. The
+same arguments as passed to \code{enw_preprocess_data()} should be used here.}
 }
 \value{
 A list containing the supplied formulas, data passed into a list
diff --git a/man/enw_extend_date.Rd b/man/enw_extend_date.Rd
index a9b158267..170604991 100644
--- a/man/enw_extend_date.Rd
+++ b/man/enw_extend_date.Rd
@@ -4,12 +4,13 @@
 \alias{enw_extend_date}
 \title{FUNCTION_TITLE}
 \usage{
-enw_extend_date(metaobs, max_delay = 20)
+enw_extend_date(metaobs, days = 20, direction = "end")
 }
 \arguments{
 \item{metaobs}{PARAM_DESCRIPTION}
 
-\item{max_delay}{PARAM_DESCRIPTION, Default: 20}
+\item{direction}{Should new dates be added at the begining or end of
+the data. Default is "end" with "start" also available}
 }
 \value{
 OUTPUT_DESCRIPTION
diff --git a/man/epinowcast.Rd b/man/epinowcast.Rd
index e00a7b99e..e1625555f 100644
--- a/man/epinowcast.Rd
+++ b/man/epinowcast.Rd
@@ -9,8 +9,8 @@ epinowcast(
   reference = epinowcast::enw_reference(parametric = ~1, distribution = "lognormal",
     non_parametric = ~0, data = data),
   report = epinowcast::enw_report(non_parametric = ~0, structural = ~0, data = data),
-  expectation = epinowcast::enw_expectation(formula = ~rw(day, .group), order = 1, data
-    = data),
+  expectation = epinowcast::enw_expectation(formula = ~rw(day, .group), generation_time
+    = 1, observation = ~1, latent_reporting_delay = 1, data = data),
   missing = epinowcast::enw_missing(formula = ~0, data = data),
   obs = epinowcast::enw_obs(family = "negbin", data = data),
   fit = epinowcast::enw_fit_opts(fit = epinowcast::enw_sample, nowcast = TRUE, pp =
@@ -31,7 +31,7 @@ specification as defined using \code{\link[=enw_report]{enw_report()}}.}
 
 \item{expectation}{The expectation model specification as defined using
 \code{\link[=enw_expectation]{enw_expectation()}}. By default this is set to be highly flexible and thus
-weakly informed. Other options are not yet supported.}
+weakly informed.}
 
 \item{missing}{The missing reference date model specification as defined
 using \code{\link[=enw_missing]{enw_missing()}}. By default this is set to not be used.}