  Citizen science mobilises many observers and gathers huge datasets but often
without strict sampling protocols, which results in observation biases due to
heterogeneity in sampling effort that can lead to biased statistical
inferences. We develop a spatiotemporal Bayesian hierarchical model for
bias-corrected estimation of arrival dates of the first migratory bird
individuals at a breeding site. Higher sampling effort could be correlated with
earlier observed dates. We implement data fusion of two citizen-science
datasets with fundamentally different protocols (BBS, eBird) and map posterior
distributions of the latent process, which contains four spatial components
with Gaussian process priors: species niche; sampling effort; position and
scale parameters of annual first date of arrival. The data layer includes four
response variables: counts of observed eBird locations (Poisson);
presence-absence at observed eBird locations (Binomial); BBS occurrence counts
(Poisson); first arrival dates (Generalized Extreme-Value). We devise a Markov
Chain Monte Carlo scheme and check by simulation that the latent process
components are identifiable. We apply our model to several migratory bird
species in the northeastern US for 2001--2021, and find that the sampling
effort significantly modulates the observed first arrival date. We exploit this
relationship to effectively bias-correct predictions of the true first arrival
dates.
