Statistical inference in observational science typically relies on a fundamental assumption: as sample size increases and uncertainties decrease, the inferred results should converge to the true physical quantities. This assumption underpins the notion that big data lead to more reliable conclusions. In Galactic archaeology, stellar ages inferred from spectroscopic surveys are widely used to reconstruct the formation history of the Milky Way disk. The age metallicity relation (AMR) and its derived formation timescale are often regarded as key physical diagnostics of early disk evolution. This interpretation carries an implicit premise: that observational quality does not introduce systematic bias into age inference. Here we show that this premise may fail. Using a large sample of subgiant stars, we identify a region in the observational quality parameter space (signal-to-noise ratio and parallax precision) where the inferred formation timescale exhibits a systematic offset of 0.5-1 Gyr relative to an independent asteroseismic reference, while the statistical uncertainties remain small, thus producing a stable-but-wrong inference state.
We present a machine learning framework for testing general relativity (GR) with gravitational wave signals from binary black hole mergers. Using the source parameters of 173 BBH events from the GWTC catalog as a realistic astrophysical population, we generate simulated GR waveforms and construct beyond GR (BGR) waveforms by applying controlled phase deformations. We introduce a response function formalism that provides a systematic framework for quantifying how any observable responds to modifications of GR. We train convolutional neural networks (CNNs) on two input representations: whitened waveforms and a response function type observable derived from the waveform mismatch, which isolates the effect of phase deviations from the bulk signal. Using response functions as the CNN input improves the classification sensitivity by a factor of approximately 33 compared to whitened waveforms, demonstrating that the choice of observable representation is as important as the classifier architecture. We study the fundamental limits of this classification through Bayes optimal error analysis, averaging methods that reveal coherent patterns hidden in noise, and a comparison between CNN accuracy and a single feature classifier as a proxy for human performance. At all deformation scales, the CNN outperforms the best single feature approach. We extend the framework to physically motivated theories using the parameterized post Einsteinian (ppE) formalism and apply it to massive gravity, where the classifier detects deviations for graviton masses of order $m_g \sim 10^{-23}\;\mathrm{eV}/c^2$ with aLIGO design sensitivity.