DynCount

Bayesian dynamic models for Poisson and binomial time series.

DynCount fits state-space models to non-Gaussian time series. A latent trajectory z[t] follows flexible dynamics — a first-order random walk or a stationary AR(1) process — and the observations are linked to it through either a Poisson (log link) or a binomial (logit link) observation model. Estimation is by Metropolis-within-Gibbs MCMC using the Gaussian Markov random field full conditionals.

The package implements and extends the methodology of Zens and Bijak (2026), Dynamic Count Models with Flexible Innovation Processes for Irregular Maritime Migration, The Annals of Applied Statistics, doi:10.1214/26-AOAS2171; see citation("DynCount").

Installation

install.packages("DynCount")

Features

• Latent dynamics: first-order random walk ("rw", default) or stationary AR(1) ("ar1", with an intercept; rho sampled on (-1, 1)).
• Four innovation structures for the latent increments: "gaussian", "t" (degrees of freedom sampled), "mixture" (finite scale mixture of normals), "sv" (stochastic volatility, via stochvol).
• Forecasting during MCMC. Set horizon = H when fitting and forecasts are produced inside the sampler, propagating parameter, state and innovation uncertainty. forecast() then extracts the stored draws.
• User-modifiable priors via dynamic_prior(); simulation, summaries, and plotting tools.
• Optional drift / intercept mu (include_mu = TRUE): a drift under the random walk and an intercept under AR(1). Disabled by default (mu = 0) under the random walk.
• Poisson offset (offset =): a known log-exposure term, so the mean is exp(offset_t + z_t).
• Poisson (log link) and binomial (logit link, known trials) observation models, sharing one interface.
• Time-constant zero inflation for both families, separating structural from sampling zeros. Fitted values, replicates and forecasts are stored both unconditionally and conditionally on the gate being open; see ?predict.dynamic_fit.

Quick start

library(DynCount)

## simulate a Poisson random walk and recover the latent rate
sim <- simulate_dynamic_poisson(n = 80, sigma = 0.18, log_rate0 = 2.5, seed = 1)
fit <- fit_dynamic_model(sim$y, family = "poisson", seed = 1)  # latent_dynamics = "rw"

summary(fit)
plot_fitted(fit)

## forecast 20 steps ahead: request the horizon when fitting
fit_fc <- fit_dynamic_model(sim$y, family = "poisson", horizon = 20, seed = 1)
fc <- forecast(fit_fc)
fc$summary      # full path, one row per horizon
fc$final        # the single 20-step-ahead forecast
plot_forecast(fit_fc)

AR(1) dynamics

AR(1) always carries an intercept: include_mu is enabled automatically, giving the process a non-zero stationary mean mu / (1 - rho).

# stationary AR(1) log-rate with mean 4  (mu = 4 * (1 - rho))
sim_ar <- simulate_dynamic_poisson(200, sigma = 0.2, log_rate0 = 4,
                                   rho = 0.9, mu = 0.4, seed = 3)
# include_mu is switched on automatically for AR(1)
fit_ar <- fit_dynamic_model(sim_ar$y, latent_dynamics = "ar1", seed = 3)
summary(fit_ar)            # posteriors of ar1_rho (in (-1, 1)) and intercept_mu

Drift / intercept and offset

## random-walk drift
sim_d <- simulate_dynamic_poisson(200, sigma = 0.12, log_rate0 = 1, mu = 0.03, seed = 4)
fit_d <- fit_dynamic_model(sim_d$y, include_mu = TRUE, seed = 4)   # rho = 1, mu sampled

## Poisson offset (log-exposure); supply forecast_offset for the future
expo <- log(runif(200, 50, 200))
fit_o <- fit_dynamic_model(sim_ar$y, offset = expo, horizon = 8,
                           forecast_offset = log(120), seed = 3)
forecast(fit_o)$final

Zero inflation

data(uk_weekly)
fit_zip <- fit_dynamic_model(uk_weekly$count, zero_inflation = TRUE, seed = 1)
structural_zero_prob(fit_zip)
plot_zero_inflation(fit_zip)

Binomial model

sim_b <- simulate_dynamic_binomial(n = 80, sigma = 0.12, trials = 50, seed = 1)
fit_b <- fit_dynamic_model(sim_b$y, family = "binomial", trials = sim_b$trials,
                           horizon = 8, forecast_trials = 50)
forecast(fit_b)$final

Example data

• uk_weekly — weekly English Channel crossings.
• med_weekly — a longer weekly Mediterranean-crossings series with larger counts and few zeros.

Both are weekly aggregates of detected irregular maritime crossings as used in Zens and Bijak (2026).

Documentation

vignette("DynCount-intro", package = "DynCount")