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math.ST2026

Causal Graphs, Markov Properties and Do-calculus for Stochastic Differential Equations

Philip Boeken, Joris M. Mooij

The paper develops a causal graphical framework for stochastic differential equations, defining conditions for well‑posed observational and interventional distributions and extendi…

math.ST2026

Topological Criteria for Hypothesis Testing with Finite-Precision Measurements

Philip Boeken, Eduardo Skapinakis, Konstantin Genin +1

We establish topological necessary and sufficient conditions under which a pair of statistical hypotheses can be consistently distinguished when i.i.d. observations are recorded on…

math.ST2026

Are Bayesian networks typically faithful?

Philip Boeken, Patrick Forré, Joris M. Mooij

Faithfulness is a common assumption in causal inference, often motivated by the fact that the faithful parameters of linear Gaussian and discrete Bayesian networks are typical, and…

math.ST2025

Conditional Forecasts and Proper Scoring Rules for Reliable and Accurate Performative Predictions

Philip Boeken, Onno Zoeter, Joris M. Mooij

Performative predictions are forecasts which influence the outcomes they aim to predict, undermining the existence of correct forecasts and standard methods of elicitation and esti…

math.ST2024

Dynamic Structural Causal Models

Philip Boeken, Joris M. Mooij

We study a specific type of SCM, called a Dynamic Structural Causal Model (DSCM), whose endogenous variables represent functions of time, which is possibly cyclic and allows for la…