Identifying good alignment positions requires evaluating and comparing different potential alignments. In the Bayesian framework, the measure used for this evaluation is the likelihood. We derive the likelihood of an alignment from its fit to a single cubic B-spline (Eilers and Marx, 1996), fitted to the measurements from all sites, including the reference site (see Fig. 1c).

We model each measured value yi as normally distributed: 2yi∼Normal(μi,σ) where μi is the mean, and the standard deviation σ represents the scatter around the spline. μi is given by the spline function 3μi=∑j=1k+2βjBj(hi) Here, μ can be interpreted as an underlying common signal of which the observations from each site, including the reference site, are noisy realisations. k denotes the number of internal knots of the spline, with more knots implying that the spline can potentially capture higher-frequency variations. βj is the spline coefficient associated with the jth basis function, and Bj(hi) is the jth B-spline basis function evaluated at a reference height hi. A roughness penalty controlled by a smoothing parameter λ is incorporated in the prior on β, such that higher values of λ serve to favour smoother splines (Appendix A). The number of knots and the roughness penalty each influence spline flexibility in different ways: increasing k provides a finer resolution for fitting local features, whereas increasing λ penalizes abrupt changes and yields smoother fits. The knots for the spline can be distributed across the reference height range that the converted measurement heights occupy for a specific combination of shift parameters (α) and scale parameters (ν, i.e. relative sedimentation rates). Our current model implementation uses evenly spaced knots, but knot placement could also follow, for example, the density of measurements. Alternatively, the knots can be fixed at specific heights on the reference scale, in which case combinations of α and ν that result in converted measurement heights falling outside the knot range cannot be evaluated.

The likelihood of an alignment, given β, σ and λ, is determined by the residual deviations of the yi values from the corresponding μi values. The overall likelihood for n data points is obtained by taking the product over all individual likelihoods for each pair of yi and μi: 4L(y|β,σ,λ)=∏i=1n12πσ2×e-(yi-μi)22σ2 We thus assume that the deviations of the data from the spline are independently and identically distributed according to a normal distribution with mean 0 and standard deviation σ.

Our model allows for using more than one type of measurement simultaneously. In this case, a separate spline is fitted to all data, from all sites, for each type of measurement. The product of all likelihoods from all measurement types gives the overall likelihood.

In order to generate alignments of stratigraphic signals from different sites, one site is picked as a fixed reference site. The other sites are shifted and stretched (or squeezed) relative to the fixed reference site r. This requires specifying a shift parameter (height) αs, which anchors an arbitrary, specified height of site s to a height in the reference site r. Here, we anchor the top of site s, so we set αs=αtop,s meaning αtop,s will be the height at site r that aligns with the top of site s. To stretch or squeeze site s, a relative sedimentation rate νs can be specified, where νs is defined relative to the reference site. For any height hx,s at site s, the corresponding height in the reference site r can then be calculated as 5hr=αtop,s-1νs×(htop,s-hx,s) where htop,s is the height of the top of site s. Although we here chose the top of site r as the reference horizon α for simplicity, any horizon at site r can be used as α. A νs<1 implies that site s has a lower sedimentation rate than site r, and consequently, s has to be stretched to match r. A νs>1, i.e. a higher sedimentation rate at site s will lead to s being squeezed to match r.

The model described here is simple in that the same ν is applied to all measurements of the same site. In this scenario, any site may be used as the reference site. Below, we introduce more complex models with more than one sedimentation rate per site, and with hiatuses. With these models, it is practical to select the site with the most sedimentation rate changes and hiatuses as the reference site. This reduces the number of unknown parameters in the model, making it easier to obtain a representative sample from the posterior.

The Bayesian framework requires priors to be placed on all unknown model parameters. In our model, these include the alignment parameters (e.g. α, ν), the smoothing parameter λ, the residual standard deviation σ (if it is not fixed), and the spline coefficients β. The priors on the alignment parameters determine the range of possible alignments and need to be chosen with care. For the other parameters, weakly informative priors with minimal influence on the analysis are preferred (Appendix A). In addition to those priors, we penalise a lack of overlap by specifying a prior probability of data points from different sites overlapping each other.

We selected three records from the Anti-Atlas mountains in Southern Morocco, corresponding to the Oued Sdas, the Tiout and the Talat n' Yissi sections, which were part of West-Gondwana during the early Cambrian (Magaritz et al., 1991; Maloof et al., 2005, 2010; Tucker, 1986). Oued Sdas and Tiout harbour multiple precise U–Pb radiometric ages (Landing et al., 2021; Maloof et al., 2010). Talat n' Yissi has no radiometric dates, but a radiometric date exists from the stratigraphically equivalent Lemdad syncline (Landing et al., 1998) that has been correlated biostratigraphically to Talat n'Yissi with the Antatlasia gutta-pluviae zone (Maloof et al., 2005); we include this date in the analysis. We will align these sites with each other, and with a δ13C record from the Sukharikha section from the northwestern Siberian platform (Kouchinsky et al., 2007), corresponding to the palaeocontinent Siberia. There are no radiometric dates available for the Siberian section for this stratigraphic interval. Data that was inferred to be below the lower leg of the prominent “5p” excursion (lowest peak in Fig. 3a and d) was excluded to simplify the correlation, reducing the number of modelled sedimentation rates unconstrained by radiometric dates. This cropping of data affects the Oued Sdas and Sukharikha sections; Fig. 3 shows all data that was included in the analysis. δ13C values were used as reported by the authors of the respective publications without any scaling or other adjustments.

To align the four sites on the age scale, we specify an α parameter on the absolute age scale (Ma) for each site, and use absolute, rather than relative sedimentation rates (expressed in mMyr-1). We encapsulate variation in sedimentation rates (ν) by partitioning sites into members, formations or lithological units, leading to multiple sedimentation rates per site. As there are few radiometric dates to constrain sedimentation rates, partitions shared between the Moroccan sites are set to have the same relative sedimentation rate across sites. To account for potentially faster or slower sedimentation rates at different sites, a site-specific sedimentation rate multiplier ζ is added for Oued Sdas and Talat n'Yissi that is multiplied with the ν from those sites. The ν for a partition applies to all sites at which this partition occurs; for Tiout, they are used unaltered, and no ζ is needed for Sukharikha as there are no shared partitions with other sites. We partition the Moroccan data based on the lithostratigraphy from Maloof et al. (2005). We divide the Adoudounian Tifnout Member into a lower part (Tifnout l.), and an upper stromatolitic part (Tifnout stromatolite), as preliminary results suggested pronounced sedimentation variability between those parts. We subdivide the Lie de Vin Formation into three members; the Igoudine Formation is subdivided into two members. The Amouslek and Isaafen formations are not subdivided. The Sukharikha section is divided into two formations, which we assign separate sedimentation rates. At the boundary, a substantial hiatus is evinced by the truncation of the “7p” δ13C peak (Kouchinsky et al., 2007). We include the duration of this hiatus (δ) as an additional unknown parameter in the model.

The model requires priors to be specified for each of its 18 alignment parameters: Four α, eleven ν, two ζ and one δ (Fig. 4). These priors are broadly guided by the radiometric dates and by previous work (Bowyer et al., 2023; Landing et al., 2021; Sinnesael et al., 2024). The α for the Tiout and Sukharikha sites are placed at the height positions of the first trilobite fossil remains found at Tiout (Sinnesael et al., 2024), and the first appearance of Siberian trilobites correlated to Sukharikha (Landing et al., 2021; Varlamov et al., 2008). Here, we place normal distributed priors with mean age 520 Ma and a wide standard deviation of 2 Myr on the α parameters at Tiout and Sukharikha. This prior reflects the notion that first appearance dates of trilobites may be broadly similar at ≈520Ma, but not necessarily identical, and the data is allowed to determine the exact age of each α. The α priors for Oued Sdas and Talat n'Yissi are placed at the position of the lowest or the only available radiometric date, respectively, consisting of normal distributions with mean age equal to the mean age estimate of the radiometric data and a wide standard deviation of 2 Myr.

For the sedimentation rates, priors informed by an astrochronology of the Tiout section (Sinnesael et al., 2024) are used for the following five stratigraphic partitions: The lower, middle and upper members of the Lie de Vin Formation, and for the lower and upper (Tiout Member) members of the Igoudine Formation. Those priors are chosen such that the 95 percentile interval of ν spans the minimum and maximum of the astrochronological sedimentation rate estimates when using an uncertainty of ±1 short eccentricity cycle for each partition, with an estimated duration of short (≈100kyr) eccentricity cycles ranging from 92.5–100.5 kyr (two standard deviations, following Lantink et al., 2022).

To specify priors for the remaining Moroccan partitions (lower part of Tifnout Fm., Tifnout stromatolite, Amouslek Fm., and Isaafen Fm.), sedimentation rates between the radiometric dates from Oued Sdas and Tiout are calculated using the mean ages of the dates. The prior on ln⁡(ν) is defined as a normal distribution with a mean of 5.39, corresponding to the mean of the empirical sedimentation rates from Oued Sdas and Tiout, calculated on the logarithmic scale. A wide standard deviation of 0.75 is set, resulting in the 95 percentile interval of ν spanning 50.3–951 mMyr-1. This interval significantly exceeds the range of sedimentation rates inferred from the radiometric dates at Oued Sdas and Tiout, 147 to 314 mMyr-1, allowing for the possibility of lower or higher sedimentation rates in some partitions.

Prior sedimentation rate estimates for the Siberian formations are estimated in the absence of radiometric dates, very broadly based on global correlations by Bowyer et al. (2023). These correlations suggest average sedimentation rates on the order of 20–30 mMyr-1; we place a normal prior on ln⁡(ν) with a mean of 3.30 and a standard deviation of 0.75, resulting in a 95 percentile interval of ν spanning 6.23–117.9 mMyr-1, which allows for the possibility of significantly different sedimentation rates from those inferred by Bowyer et al. (2023).

Finally, a prior needs to be placed on the duration of the hiatus δ between the Sukharikha and the Krasnoporog formations. Kouchinsky et al. (2007) do not give an indication of the potential duration of this hiatus, but if the under- and overlying δ13C peaks are correlated as indicated by previous work (Bowyer et al., 2022; Landing et al., 2021), a relatively short hiatus of ≈1Myr is likely. To express considerable uncertainty about the duration of the hiatus, we place an exponential prior on δ with a rate of 1, which places 95% of prior probability on the duration being <3Myr, with 5 % probability accounting for the possibility of a longer gap.

The cubic spline comprises 40 evenly spaced knots, allowing it to closely follow trends in the δ13C records while keeping the MCMC runtime manageable, as a higher knot count increases computational cost. For the smoothing parameter λ, we applied a gamma prior with StratoBayes' default values of aλ=1 and bλ=1000. We fixed σ, which is the residual standard deviation of the overall spline, at 0.66, which is the average residual standard deviation of individual cubic splines fitted to each δ13C record from the four respective sites. These individual splines were constructed with 40 knots evenly spaced across the height range of each respective site and fitted with Gibbs sampling using 2000 iterations, discarding 25 % of samples as burn-in. The same default λ priors as described above were applied, while the prior for these splines' standard deviations was specified as a gamma prior on the precision τ, with aτ=bτ=0.01 (see Appendix A for details).

This model is more complex than our earlier examples, and hence requires longer runs with more chains. We conducted four independent model runs, each with 750 000 iterations and 24 chains. The runs were executed in parallel using four workers on a desktop computer (Intel i7-10700 CPU, 8 cores/16 threads, 40 GB RAM) and completed within 5 days. The first 150 000 iterations were discarded as burn-in. From the remaining 600 000, every 50th iteration was retained, resulting in 12 000 samples per run and 48 000 samples in total.

Inspection of trace plots of the model runs indicates stationarity and good mixing of the chains with the exception of infrequent visits of secondary posterior modes (Appendix B, Fig. B1). The potential scale reduction factor (using Eq. 4 in Vats and Knudson, 2021) is between 1.00 and 1.05 for all alignment parameters, suggesting approximate convergence of the MCMC. The multivariate effective sample size (Vats et al., 2019) of the 48 000 samples is 4161.

To identify distinctly different alignments in the posterior, a hierarchical density-based cluster analysis (Campello et al., 2015) was conducted using the inferred ages of all partition boundaries of the four sites (Fig. 4a and b). We specified 1 % of samples (480) as the minimum number of points per cluster, resulting in three distinct clusters with 93 %, 2.8 % and 2.6 % of posterior samples, respectively, and 1.5 % of samples not being assigned to any cluster. These alignment clusters also differ in the prior probabilities and likelihoods associated with individual posterior samples. On average, samples from alignment 1 tend to exhibit a lower degree of overlap, but a higher likelihood (Fig. 4c), indicating a better fit to the data.

Using samples from the posterior of the model parameters, alignments can be generated. Figure 6 visualises three alignments drawn from the three alignment clusters identified in the posterior. For each alignment cluster, the iteration with partition boundary ages that are, on average, closest to the median ages of the partition boundaries within that cluster is selected for displaying. All three alignments exhibit a good match between the long-term trends of the δ13C curves from the four sites and the common spline curve, although many shorter-term deviations are visible (Fig. 6a–c). The spline curve notably follows the more densely sampled sites (Oued Sdas, Talat n'Yissi) more so than the thinly sampled sites (Tiout, Sukharikha), resulting in greater deviations of the latter two sites.

The posterior age estimates for the stratigraphic positions of the radiometric dates broadly match the age estimates that were used as inputs in the analysis (Fig. 6d). The deviations are greatest for the Talat n'Yissi date (Ta1), which has large uncertainty and therefore less influence on the analysis, and the second date from Oued Sdas (Ou2). The first appearances of trilobites are visualised alongside the dates in Fig. 6d, and are dated to 519.46 Ma (519.25–519.68 Ma) at Tiout. The age estimate for the first Siberian trilobites differs considerably between the different alignment solutions: For the most likely alignment 1, the age estimate is 520.79 Ma (520.98–520.61 Ma), and for alignment 2 the estimate is somewhat higher at 521.05 Ma (521.19–520.91 Ma). Alignment 3 suggests a significantly later appearance of Siberian trilobites at 519.98 Ma (520.15–519.84 Ma). All three alignments place the appearance of the first Siberian trilobites before their appearance at Tiout, with the temporal gap (computed directly from the posterior distribution) being estimated at 1.33 Myr (1.09–1.54 Myr) for alignment 1, 1.71 Myr (1.54–1.87 Myr) for alignment 2, and 0.63 Myr (0.53–0.74 Myr) for alignment 3.

The posterior of the model runs allows the construction of age models that span the entire height of each site (Fig. 7). As sedimentation rates are constrained to be constant within the pre-defined partitions, sedimentation rate changes are visible as inflections at the boundaries of these partitions. Age uncertainties are relatively low at Tiout and most of Oued Sdas, which are relatively well constrained by radiometric dates in the top (Tiout) and middle (Oued Sdas) parts of the sections, as well as by astronomical priors on sedimentation rates. Uncertainty noticably increases towards the top and bottom of Oued Sdas. The lowest partition of Oued Sdas is constrained only by its match to the lower part of the Sukharikha Fm., their age estimates are thus varying considerably between different alignments (Fig. 6). Differences in the positioning of the δ13C curves between alignments are greatest at Talat n'Yissi and the Siberian Krasnoporog Fm. (Fig. 6), which results in large uncertainties in the age models (Fig. 7c and d).

We used StratoBayes to correlate and date four lower Cambrian carbonate sections using δ13C records, radiometric dates and astrochronological sedimentation rate estimates. From a large space of possible alignment configurations (Fig. 4), the software identified alignment solutions that visibly match the large-scale features in the δ13C records from multiple sites, while simultaneously achieving an approximate fit to the radiometric dates (Fig. 6).

The most likely alignment solution from the posterior, alignment 1 (probability=93%), results in a correlation of the three Moroccan sites that has much in common with that proposed by Maloof et al. (2005). In our model, we used common sedimentation rates for the stratigraphic partitions (members, formations) shared between the sites, whilst allowing sedimentation rates to systematically differ from the reference sedimentation rates at Tiout by adding a site-specific multiplier. This multiplier, ζ, is 1.02 (95 % credible interval: 0.97–1.08) for Oued Sdas, meaning the model estimates very similar sedimentation rates for Tiout and Oued Sdas (Fig. 6a), consistent with their close geographical proximity. Sedimentation rates for the shared partitions at Talat n'Yissi are lower by a factor of 0.86 (0.76–0.96), which would be consistent with a moderately lower accommodation space at Talat n'Yissi relative to Tiout and Oued Sdas (as suggested by Fig. 3b in Maloof et al., 2005). We deliberately chose broad priors that did not explicitly enforce a relationship between sedimentation rates and palaeogeography; nonetheless, the model identified a geologically plausible solution. In contrast, the higher ζTalat n'Yssi of alignment 2 (probability=2.8%, 1.07–1.37) and alignment 3 (probability=2.6%, 2.07–2.45) are harder to reconcile with the palaeogeographic context.

Alignments 2 and 3 also suggest different sedimentation rates between Tiout and Oued Sdas, with a higher value of ζOued Sdas (1.13–1.26) being estimated by alignment 2, and a lower value of ζOued Sdas (0.83–0.88) by alignment 3. The most consistent lithostratigraphic alignment between Tiout and Oued Sdas is achieved by alignment 1, meaning that the age estimates for partition boundaries (based on members or formations) are most similar (Fig. 6). For the more distant Talat n'Yissi, age estimates of partition boundaries differ to varying degrees across all three alignments.

Breaking down the posterior probability into individual components – likelihood (fit of δ13C measurements to the spline, fit of age estimates to the radiometric dates) and prior probability from the overlap penalty – reveals that samples from alignment 1 have a higher likelihood, on average (Fig. 5c). In contrast, alignments 2 and 3 have a greater number of overlapping δ13C points, which results in higher overlap prior probabilities (Fig. 5c). The overlap prior reflects the prior belief that substantial parts of the sections involved in the correlation should be overlapping. However, the weight of that prior is somewhat arbitrary and reflects the technical requirement to facilitate overlap despite non-overlap allowing for closer fit to the spline, similar to the role of the “edge value” in some DTW implementations (Hay et al., 2019). A lower prior weight on overlap would thus have caused alignments 2 and 3 to receive lower posterior probabilities relative to alignment 1. Taken together, the evidence from above leads us to strongly favour alignment 1, and we will focus further discussion on that most likely alignment solution.

A radiometric date of 517.0 Ma (±2 SD: 515.5–518.5 Ma) has been recovered from the Lemdad Syncline in the Atlas mountains (Landing et al., 1998), and has been correlated biostratigraphically to a horizon in the lower Isaafen Fm. at Talat n'Yissi (Maloof et al., 2005). In our alignment 1, this horizon has a posterior age estimate of 519 Ma (519.2–518.8 Ma) – ≈2Myr older than the mean of the radiometric date. This date has informed the age estimates for Talat n'Yssi in Maloof et al. (2005) and Maloof et al. (2010), whereas alignment 1 produces age estimates close to those of Bowyer et al. (2022) and Bowyer et al. (2023). Age estimates deviating from radiometric dates are not necessarily incorrect: Although radiometric dates are sometimes treated as “absolute truth” within the stratigraphic community, they are the result of various sources of technical uncertainties (Condon et al., 2024) and geological interpretations like the actual zircon crystallisation versus eruption age (Keller et al., 2018). This is illustrated by the recalculation of the radiometric date from Landing et al. (1998) to 515.56 Ma (±2 SD: 514.40–516.72 Ma) in the Geological Time Scale 2012 (Schmitz et al., 2012).

The two radiometric dates measured at Tiout at the bottom of and within the Amouslek Formation suggest a sedimentation rate of 146 mMyr-1 (±2 SD: 78.7–613 mMyr-1) for the Amouslek formation. However, the posterior estimates for the sedimentation rate in the Amouslek formation are poorly constrained and high compared to the sedimentation rates of all other partitions, at 3030 mMyr-1 (800–17 300 mMyr-1). It appears that the model has overestimated the Amouslek sedimentation rate in aligning the δ13C record of the overlying Isaafen formation with a part of the Siberian Krasnoporog formation which has similar δ13C values (Fig. 6a). The alignments of Bowyer et al. (2022) imply significant sedimentation rate changes within the Krasnoporog formation, allowing the δ13C records to be better reconciled with the radiometric dates. We didn't allow for sedimentation rate changes within the Krasnoporog formation because the stratigraphic log of Kouchinsky et al. (2007) indicates a uniform facies. Additional sedimentation rate changes might lead to a closer alignment with the radiometric dates, at the cost of greater model complexity.

The alignment of the Siberian Sukharikha section with the Moroccan sites is relatively precise in the lower half of the records: The prominent positive δ13C excursions interpreted as the “5p” and “6p” excursions have a similar magnitude both at Oued Sdas and Sukharikha, and are readily aligned visually (Bowyer et al., 2022) and by our model (Fig. 6). Our model aligns the main 6p peak of Sukharikha with the first subpeak of the second large excursion at Oued Sdas, as in model C in Bowyer et al. (2022). The lesser, positive excursion below the hiatus at the top of the Sukharikha formation lines up with the positive excursion in the lower Lie-de-Vin formation, representing the “II” peak as in model C in Bowyer et al. (2022). The upper parts of the Moroccan records and the Siberian Krasnoporog formation appear to be aligned primarily by matching the prominent positive excursion interpreted as excursion “IV” (Bowyer et al., 2022; Kouchinsky et al., 2007). The “III” peak below is only weakly expressed at Oued Sdas, leading to uncertainty in the alignment with the corresponding part of the Krasnoporog formation, and in the inferred duration of the hiatus even within alignment solution 1 (Fig. B3a–c). Similarly, considerable uncertainty exists in how the top of Talat n'Yissi corresponds to the Krasnoporog formation. This is evident from variations between samples in alignment solution 1 (Fig. B3a–c) and in the wide credible intervals of those parts of the age models (Fig. 7). The relatively small magnitude of δ13C changes limits the model's ability to identify a definitive alignment solution for that part of the record.

Our estimate for the Moroccan first appearance of trilobites at Tiout from alignment 1, 519.47 Ma (519.68–519.26 Ma), is slightly younger and somewhat less precise than the recent, astrochronological estimate of 519.62 Ma (95 % highest posterior distribution: 519.70–519.54 Ma) by Sinnesael et al. (2024). We attribute this difference to our model simultaneously combining different data types from multiple sites. Additionally, Sinnesael et al. (2024) allowed sedimentation rates to vary between cycles, whereas our model assumed a single sedimentation rate per member. In our alignment 1 solution, the highest δ13C values of Tiout correlate to shortly after the peak of the IV δ13C excursion. This correlation suggests that the actual peak of the excursion at Tiout has not been sampled by Magaritz et al. (1991) and Tucker (1986), which may result in misalignments when correlating the record to other sections. Further δ13C samples from the lower Igoudine and upper Lie-de-Vin formation at Tiout are required to improve correlation with other sections, including the correlation presented herein.

Our model successfully reconstructs the first appearance of trilobites at Tiout, within error, despite using a simpler astrochronology and enforcing a less variable sedimentation rate history than Sinnesael et al. (2024). It also provides the first fully quantitative estimate for the first appearance of trilobites in Siberia based on chemostratigraphic correlation and the Moroccan radiometric dates and astrochronology, at 520.79 Ma (520.98–520.61 Ma). This refines earlier estimates of ≈521Ma (Landing et al., 2021), and quantifies the temporal gap between the appearance of trilobites in Siberia and Morocco as 1.33 Myr (1.09–1.54 Myr). We do not suggest that these estimates are definitive; indeed, we anticipate that the incorporation of additional δ13C data from Tiout, the inclusion of astrochronological estimates of individual short eccentricity cycles, and the relaxation of the assumption of constant sedimentation rates within partitions may update the estimate. A high-resolution temporal sequence of trilobite first occurrence dates could be used to delineate trilobite evolutionary rates and dispersal; to evaluate evolutionary hypotheses on the origins and biomineralisation of trilobites (Holmes and Budd, 2022; Paterson et al., 2019); and to inform the definition of the base of the Cambrian Series 2 (Zhang et al., 2017).

Quantitative stratigraphic correlation and age modelling of diverse geological data represent a long-standing challenge in stratigraphic research. Although many algorithms exist for correlating geochemical and geophysical stratigraphic data (e.g. Baville et al., 2022; Bloem and Curtis, 2024; Hay et al., 2019; Sylvester, 2023); few can readily provide uncertainty estimates or incorporate different types of data simultaneously (e.g. Al Ibrahim, 2022; Edmonsond and Dyer, 2025; Lee et al., 2022). Consequently, integrated statistical approaches have only rarely been applied to complex real-world stratigraphic problems (Hagen et al., 2024; Lee et al., 2022).

Our new method has the potential to be applied to diverse datasets; examples range from shallow borehole data from the Holocene (Finlay et al., 2022) to Proterozoic carbonates (Halverson et al., 2010). The ability of our model to incorporate multiple proxy records simultaneously opens new possibilities for refining stratigraphic correlations. For instance, correlations involving both δ13C and δ87Sr records could benefit from a probabilistic framework that accounts for their respective uncertainties (Bowyer et al., 2022). The integration of multiple proxies, e.g. multiple element ratios, in the StratoBayes framework could allow correlations based on the entire record of all proxies, rather than a few visually distinct transitions (Craigie, 2015).

Beyond geochemical records, our approach could also be applied e.g. to geophysical well-logs such as gamma ray or density logs, and magnetostratigraphic records could be correlated directly rather than relying on visually interpreted polarity reversals (Langereis et al., 2010). While index fossils can currently be integrated as tie points, the modelling framework could be expanded to explicitly model first and last occurrences to better incorporate biostratigraphic uncertainty. Similarly, astrochronological constraints can be expressed as priors on sedimentation rates, but an additional model component would be needed to incorporate all astrochronological information from a given site (Sinnesael et al., 2024).