Moreover, they are the cornerstone of more sophisticated procedures involving non-Gaussian distributions, multivariate random fields, or space-time processes. Parallel computing becomes necessary for avoiding computational and memory restrictions associated with large-scale environmental data science applications.

In this talk, I will explain how high-performance computing can provide solutions to the aforementioned problems using tile-based linear algebra, tile low-rank approximations, as well as multi- and mixed-precision computational statistics. I will introduce ExaGeoStat, and its R version ExaGeoStatR, a powerful software that can perform exascale (10^18 flops/s) geostatistics by exploiting the power of existing parallel computing hardware systems, such as shared-memory, possibly equipped with GPUs, and distributed-memory systems, i.e., supercomputers. I will then describe how ExaGeoStat can be used to design competitions on spatial statistics for large datasets and to benchmark new methods developed by statisticians and data scientists for large-scale environmental data science.

Fitting traditional capture–recapture models to such data requires one to identify all possible sets of capture–recapture histories that may lead to the observed data, which is computationally infeasible even for a small number of capture occasions. In this talk, I will introduce a latent multinomial model to deal with such data, where the observed vector of counts is a non-invertible linear transformation of a latent vector that follows a multinomial distribution depending on model parameters. The latent multinomial model can be fitted efficiently through a saddlepoint approximation based maximum likelihood approach. The model framework is very flexible and can be applied to data collected with different study designs. Simulation studies indicate that reliable estimation results are obtained for all parameters of the proposed model. We apply the model to analysis of golden mantella data collected using batch marks in Central Madagascar.

Modelling spatial dependence through spatially structured random effects can enhance predictive performance in occurrence probabilities across the region of interest. However, incorporating such random effects is known to be computationally expensive and can lead to intolerably long software run times when dealing with a moderately large number of locations (e.g., 100s to 1,000s of locations).In this presentation, we demonstrate how occupancy models can be integrated into the framework of latent Gaussian models, thereby leveraging the computational capabilities of Integrated Nested Laplace Approximation (INLA). INLA enables the efficient fitting of models with random effects. These random effects are not limited to spatial considerations but can also represent time, non-linear effects of covariates, space-time interactions, and more. This approach not only allows us to efficiently fit occupancy models but also makes them more flexible. We illustrate our findings using simulations and a case study

An increasing variety of data sources, particularly from citizen science, presents opportunities but often requires new statistical methods. One example is the UK Big Butterfly Count (BBC), which commenced in 2010 and attracts participation from people who may have little/no experience of biodiversity monitoring. During a 3-week sampling period this summer 1.6 million butterflies were counted by over 100,000 citizen scientists.

BBC data offer the potential to produce trends for habitats which are under-sampled by traditional transect monitoring, such as gardens and urban areas. However, the short BBC sampling season renders counts susceptible to bias caused by interannual variation in the timing of species’ flight periods. I will describe a new method that corrects for this bias using flight period estimates from standardised monitoring data. Suitable methods are needed for a range of data sources to ultimately provide a strong evidence-base for policy development, management, and conservation.

We will consider the application of functional data analysis to in-situ reflectance data, defining optical water types that enhance the processing of earth observation data. Subsequently, we explore how this processed earth observation data aids in identifying local and global spatial patterns in lake water quality. Lastly, we introduce our new project MOT4, which will explore the monitoring and modelling of river water quality across UK catchments, employing cutting-edge data analysis techniques and combining a range of both environmental and ecological measurements.

In this talk I'll explore Jenny Bryan's quote "if all models are wrong, then why not start with one that you understand?" and chat through how to construct some more complicated models using the generalized additive modelling workhorse mgcv.

This method addresses recent biases in model outputs and measurements. A machine learning-based alternative is presented that can leverage a wide array of co-variates, enabling it to capture complex non-linear relationships present in the data. This capability translates to improved predictive accuracy, including at locations where the model has not been explicitly trained.

However, real-world datasets often contain missing variables of varying degrees both spatially and temporally. Alternatively, modelled datasets can provide a complete dataset, but these are often biased. By conceptualising this bias as a skew, we consider a skew Kalman approach to bias-correct the modelled surface-level ozone data and use the bias-corrected data to infill missing data in the observed dataset. The second problem this talk will consider is how well existing methods for big data hold up for spatial data. Spatial models such as Gaussian processes scale cubically with the number of data points and thus quickly become computationally infeasible for moderate to large datasets. Divide and conquer methods allow data to be split into subsets and inference is carried out on each subset before recombining. While well documented in the independent setting, these methods are less popular in the spatial setting. This talk evaluates the performance of divide-and-conquer methods in the spatial setting, using USA temperature data, to achieve approximate results compared to carrying out inference on the full dataset.

In this talk, we discuss the challenges of working with environmental data and how we can adapt models and methods to produce more representative and useful results. In particular, we focus on identifying melt from data that has a soft upper limit in temperatures around 0◦C caused by the melt process of ice, and the difficulties in applying extreme value analysis models to data with poorly defined upper tails. We examine the approach of building up our methods in light of these challenges: progressing from single-site modelling using Gaussian mixture models, to spatial modelling of temperatures using Gaussian processes, to modelling spatial melt events using the Spatial Conditional Extremes model.