Léo R. Belzile and Rishikesh Yadav’s contribution to the Discussion of ‘the Discussion Meeting on the Analysis of citizen science data’

We congratulate Koh and Opitz for this stimulating piece of work. The complex framework adopted by the authors offers crucial insights into migratory patterns and species behaviours that simpler models may overlook. Much effort has gone into the model specification to account for sampling biases and to ensure interpretability, and it shows. Hierarchical Bayesian models are well suited for this type of modelling exercise, but the inference is complicated and preprocessing tedious. Assuming separability of space and time effects simplifies the problem, and offers the possibility of using leave-one-year-out cross-validation, although this is computationally intensive. The sharing of random effects allows one to borrow strength across data sources, but may lead to model misspecification without great care. Adding covariates, such as land cover, could reduce the residual variability, but we acknowledge that their effect may be nonlinear, and suitable smooths would add multiple fixed effect parameters. One concern is the slow convergence and poor mixing observed in Figure 12, even after thinning. We wonder what the effective sample size is after burn-in. Although standard methods, such as adaptive MCMC (Andrieu & Thoms, 2008; Rosenthal, 2011), could help, hyperparameters may be strongly correlated due to shared components, and joint updates may be necessary to increase the efficiency of the sampler. The performance of Metropolis adjusted Langevin algorithm (MALA) is highly sensitive to the global tuning parameter or prewhitening matrix; locally adaptive schemes could fare better (e.g. Girolami & Calderhead, 2011; Rue & Held, 2005, Section 4.4.1). Although the Markov chains seem to stabilize eventually, running multiple chains could be used to check whether they reach a unique stationary distribution. Model predictions at the data level (e.g. Figure 9) look sensible, but it is unclear whether individual model components are identifiable. For example, consider the function relating the generalized extreme value distribution location parameter μ with the sampling effort, g(xbound,xeffort)=exp(xbound)/{1+exp(−xeffort)}⁠. The functional form of eq. (4) implies that we cannot distinguish between parameters for xbound when xeffort is low. Increases in g (and thus in μ) lead to an earlier minimum arrival rate. We believe data fusion of related databases observed at different locations or resolutions has great potential in the field of spatial extreme value analysis as there is limited information available and pooling can help partly alleviate this.

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