A Reproducible Review of Selected Analytical Methods in the Geosciences with R Implementations Using Simulated Data

The geosciences have witnessed a rapid expansion of analytical methods, from classical linear models to geostatistics and modern machine learning. However, no single resource compares a curated selection of these methods systematically while also providing reproducible code. This reproducibility-driven review evaluates seven analytical techniques applied to three simulated geoscience datasets: spatial points, time series, and a spatio-temporal grid. Methods were selected based on their availability in R to ensure transparency and accessibility. This paper serves as a historical review, a comparative benchmarking study, and a practical teaching resource with fully reproducible R code. The methods include linear regression, ARIMAX, ordinary kriging, regression-kriging, random forest, feed-forward neural networks, and BART. For spatial prediction, when evaluated against the true field, linear regression achieved the lowest mean RMSE (1.94 ± 0.23), followed by random forest (2.13 ± 0.23) and ordinary kriging (2.20 ± 0.26)—highlighting the importance of consistent out-of-sample validation. Regression-kriging performed similarly to ordinary kriging (2.22 ± 0.26). For time series, a feed-forward neural network (0.37 ± 0.09) substantially outperformed seasonal ARIMAX (1.90 ± 1.30). For spatio-temporal prediction, random forest and BART performed indistinguishably (0.534 ± 0.004 vs. 0.543 ± 0.004). A practical decision guide, grounded in these empirical results, summarises method selection based on sample size, data type, and research goal—whether inference, prediction, or uncertainty quantification. All code is open and reproducible, providing a template for future method comparisons.