How Does Bayesian Causal Discovery Fail? Characterising Structural Consequences in Linear Gaussian Networks under Latent Confounding

Bayesian causal discovery is widely used for its ability to quantify epistemic uncertainty over directed acyclic graphs (DAGs) through posterior inference. However, its behaviour under latent confounding remains poorly understood, as existing work typically notes that confounding breaks identifiability without characterising how the posterior distribution over DAGs responds. In this work, we analyse posterior behaviour under latent confounding in linear Gaussian causal models, focusing on additive latent confounding between exactly two observed variables. We derive a critical correlation threshold above which the score function favours graphs with a spurious edge between the confounded variables, and show that this threshold decreases with sample size -- more data lowers the correlation required for the spurious edge to be favoured. Beyond this threshold, we characterize two distinct posterior failure regimes determined by the local structure around the confounded variables. Our findings are supported by exact posterior computations on multiple graph structures, demonstrating both the predicted failure regimes.

How does downsampling affect needle electromyography signals? A generalisable workflow for understanding downsampling effects on high-frequency time series

Automated analysis of needle electromyography (nEMG) signals is emerging as a tool to support the detection of neuromuscular diseases (NMDs), yet the signals' high and heterogeneous sampling rates pose substantial computational challenges for feature-based machine-learning models, particularly for near real-time analysis. Downsampling offers a potential solution, but its impact on diagnostic signal content and classification performance remains insufficiently understood. This study presents a workflow for systematically evaluating information loss caused by downsampling in high-frequency time series. The workflow combines shape-based distortion metrics with classification outcomes from available feature-based machine learning models and feature space analysis to quantify how different downsampling algorithms and factors affect both waveform integrity and predictive performance. We use a three-class NMD classification task to experimentally evaluate the workflow. We demonstrate how the workflow identifies downsampling configurations that preserve diagnostic information while substantially reducing computational load. Analysis of shape-based distortion metrics showed that shape-aware downsampling algorithms outperform standard decimation, as they better preserve peak structure and overall signal morphology. The results provide practical guidance for selecting downsampling configurations that enable near real-time nEMG analysis and highlight a generalisable workflow that can be used to balance data reduction with model performance in other high-frequency time-series applications as well.