Bayesian time series analysis of terrestrial impact cratering

Giant impacts by comets and asteroids have probably had an important influence on terrestrial biological evolution. We know of around 180 high velocity impact craters on the Earth with ages up to 2400Myr and diameters up to 300km. Some studies have identified a periodicity in their age distribution, with periods ranging from 13 to 50Myr. It has further been claimed that such periods may be causally linked to a periodic motion of the solar system through the Galactic plane. However, many of these studies suffer from methodological problems, for example misinterpretation of p-values, overestimation of significance in the periodogram or a failure to consider plausible alternative models. Here I develop a Bayesian method for this problem in which impacts are treated as a stochastic phenomenon. Models for the time variation of the impact probability are defined and the evidence for them in the geological record is compared using Bayes factors. This probabilistic approach obviates the need for ad hoc statistics, and also makes explicit use of the age uncertainties. I find strong evidence for a monotonic decrease in the recorded impact rate going back in time over the past 250Myr for craters larger than 5km. The same is found for the past 150Myr when craters with upper age limits are included. This is consistent with a crater preservation/discovery bias modulating an otherwise constant impact rate. The set of craters larger than 35km (so less affected by erosion and infilling) and younger than 400Myr are best explained by a constant impact probability model. A periodic variation in the cratering rate is strongly disfavoured in all data sets. There is also no evidence for a periodicity superimposed on a constant rate or trend, although this more complex signal would be harder to distinguish.

💡 Research Summary

The paper presents a rigorous Bayesian analysis of the terrestrial impact‑crater record to test whether the impact rate has varied periodically over the past few hundred million years. The author begins by noting that roughly 180 impact craters are known on Earth, with ages up to 2.4 Gyr, and that many previous studies have claimed periodicities ranging from 13 to 50 Myr, often linking them to the Sun’s vertical oscillation through the Galactic plane. However, those studies frequently suffer from methodological flaws such as misinterpretation of p‑values, over‑emphasis of periodogram peaks, and failure to compare against plausible alternative models.

To address these issues, the author treats impacts as a stochastic process and defines explicit probabilistic models for the time‑dependent impact rate λ(t). The models considered are: (i) a uniform (constant) rate, (ii) a linear trend (λ(t)=a+bt), (iii) a sinusoidal modulation (λ(t)=A sin(2πt/P)+C), and (iv) a combination of a sinusoid and a linear trend. Each model is assigned a uniform prior over a reasonable parameter range, and all models are given equal prior probability. The Bayesian evidence P(D|M) for each model is obtained by integrating the likelihood over the full parameter space, thereby automatically penalising model complexity.

The data set is drawn from the Earth Impact Database (as of September 2010). The primary sample consists of 59 craters with diameters ≥5 km and ages ≤250 Myr. Age uncertainties are treated as 1‑σ Gaussian errors; craters with only upper‑age limits are incorporated via appropriate cumulative‑distribution terms; for a few craters lacking explicit uncertainties a 10 % relative error is assumed, and for those given as ranges a Gaussian with σ=0.30 × range is used. Additional subsets are constructed (e.g., craters ≥35 km and ≤400 Myr) to test the effect of preservation bias.

The Bayesian framework is first validated on simulated data sets that mimic uniform, trending, and periodic impact histories, confirming that the method correctly recovers the generating model. When applied to the real crater data, the results are clear:

1. For the 5‑km‑and‑larger sample (≤250 Myr), the linear‑decrease model is strongly favoured over the uniform model, with a Bayes factor of roughly 30. This indicates a monotonic decline in the observed impact rate toward the past, which the author interprets as a preservation/discovery bias: older, smaller craters are progressively eroded or buried and thus under‑recorded.

2. For the subset of large craters (diameter ≥35 km, ≤400 Myr), the uniform model receives the highest evidence, suggesting that for sufficiently large impacts the preservation bias is negligible and the true impact rate has been roughly constant over this interval.

3. All periodic models, whether pure sinusoid or sinusoid plus trend, are strongly disfavoured (Bayes factors < 0.1) across every data set. The analysis therefore finds no statistical support for any periodic component in the impact record, contradicting many earlier claims.

The discussion compares these findings with previous literature, emphasizing that many earlier detections of periodicity arose from inappropriate frequentist hypothesis testing, where rejecting a null “random” model was mistakenly taken as evidence for a specific periodic model. By contrast, the Bayesian approach evaluates the absolute probability of each model, accounting for parameter uncertainties and model complexity. The author also notes that the method naturally incorporates age uncertainties and upper limits, avoiding the need to discard “poor” data.

In conclusion, the study demonstrates that the terrestrial impact record does not contain a detectable periodic signal and that the apparent decline in impact frequency with age is best explained by geological preservation bias rather than genuine variations in the impact flux. The Bayesian methodology presented provides a robust template for future time‑series analyses of sparse, uncertain geological data.