Raphaël Huser and Andrew Zammit-Mangion’s contribution to the Discussion of the ‘Discussion Meeting on the Analysis of citizen science data’
评论了Koh和Opitz关于迁徙鸟类到达日期极值建模的论文，指出其贝叶斯推断计算成本高，并提出用神经网络进行摊销推断来大幅降低计算时间，适用于大规模公民科学数据分析。
We are grateful for the opportunity to discuss the paper entitled ‘Extreme-value modelling of migratory bird arrival dates: Insights from citizen science data’ (Koh & Opitz, 2025). We congratulate the authors for conducting such an elaborate data analysis of bird arrivals showing how multiple citizen-science data products of varying quality, completeness, and space-time resolutions, can be fused together and modelled jointly using a complex Bayesian hierarchical model. The model implements different likelihood functions over a shared latent structure, and accounts for the sampling effort to remove systematic biases. Our comment focuses on the methods for making inference, and how alternative approaches can be used to substantially reduce the computational cost. The authors perform Bayesian inference using a customized Metropolis–Hastings algorithm, where hyperparameters are updated using Gibbs sampling, and where the latent Gaussian components are updated using block proposals based on the Metropolis-adjusted Langevin algorithm. They report that each iteration takes approximately 6 sec., so a single model fit obtained by drawing 80000 posterior samples takes about 5.5 days. While such an inference time may be acceptable if the model needs to be fitted only a few times, it is clearly too expensive if repeated fitting is necessary, e.g., to conduct an extensive cross-validation study, to analyse different bird species in different study regions, or to incorporate new data, as is often required in citizen science. Recent years have seen the emergence of neural networks being used for amortized inference (see Zammit-Mangion et al., 2025, for a recent review), both in the context of point estimation (e.g. Sainsbury-Dale et al., 2023, 2024) and full posterior inference (e.g., Radev et al., 2022; Radev, Schmitt, Pratz, et al., 2023; Radev, Schmitt, Schumacher, et al., 2023) for models with intractable or unavailable likelihood functions. With such neural ‘amortized’ approaches, inference with new data can be performed repeatedly at a fraction of the time needed using standard Markov chain Monte Carlo methods, after an initial computational cost is incurred to train a neural network using training data simulated from the model of interest. Amortized methods for complex spatio-temporal Bayesian hierarchical models are still in their infancy, but see Zammit-Mangion and Wikle (2020) for an early example. Although neural inference methods can be used to estimate model parameters, they will likely struggle to make inference on latent variables, which are often numerous and highly correlated a posteriori. One solution is to adopt an empirical Bayes approach, where hyperparameters are estimated in a first step (e.g., using neural Bayes estimators; see Sainsbury-Dale et al., 2024), and latent variables are then inferred in a second step conditional on the estimated hyperparameters, perhaps by using a learning network such as that proposed by Liu and Liu (2020). This strategy remains to be tested, especially in cases where the model has a relatively large number of hyperparameters (i.e., more than 20, say) and when the trained neural networks need to be adaptable to small model changes (e.g., to different covariates values). In principle, however, this strategy would allow for fast inference for a wide range of Bayesian hierarchical models, including models for data fusion, thus enabling the analysis of citizen-science data at unprecedented scale.