Introduction

The cycle of day and night is one of the most fundamental environmental features shaping life on Earth. Nearly all species, from bacteria to mammals, exhibit daily rhythms in physiology and behavior that align with this 24-hour light-dark cycle1,2,3,4. These rhythms are not merely passive responses to external changes, but are generated by a biological timekeeping system, the circadian “clock,” which allows organisms to anticipate environmental transitions and coordinate internal processes throughout the day5.

This internal temporal organization is essential for health and survival: disruption of circadian timing can affect cognition, metabolism, hormonal function, and mental health6,7,8,9. In humans, the central circadian clock is the suprachiasmatic nuclei (SCN) in the hypothalamus. It is aligned with the 24-hour light-dark cycle mentioned previously through input from the retina. Therefore, changes in environmental light levels shape patterns of sleep and wakefulness and influence the physiological processes that support these behaviours10,11,12.

By this reasoning, it seems logical to expect that sleeping patterns would shift with changes in the amount of light across the year. However, despite this biological grounding, our understanding of seasonal sleep variation in humans at a global scale remains limited. A minority of studies claim that seasonal shifts do not affect sleep duration or quality, while the rest claim that there is some correlation between the two. The magnitude of this correlation is a point of contention throughout the literature, with some studies suggesting that social factors may play a larger role in the duration and quality of sleep13,14,15,16,17,18,19,20,21,22,23,24,25.

A further inspection into existing studies reveals that the discrepancies in final findings largely result from variations in data tracking methods and small sample sizes. Particularly, studies that utilise self-reporting often end up citing no correlation between photoperiod and sleep13,16, while studies that use more objective measures such as EEG signals and wrist-wearables report a more clear link between the two14,15,17,18,19,20,21,23,24,25. Additional sources of bias in many existing studies possibly include unrepresentative samples and highly localised groups of people14,15,17,22,24,25.

We found that recent work by Mattingly et al.19 provides one of the most comprehensive examinations of seasonal sleep variation in real-world settings. Using over 51,000 nights of wearable-derived sleep data from 216 U.S. adults tracked continuously for a full year, the authors show that seasonal effects on sleep are small but robust. Sleep duration reliably decreased as day length increased: each additional hour of daylight shortened sleep by approximately 3.6 minutes, and sleep during spring was ~ 12 minutes shorter than in winter. Seasonal shifts were driven primarily by wake times rather than bedtimes—participants tended to wake earlier in spring and summer, while bedtimes shifted only modestly.

However, this work too suffers from a fundamental limitation: the dataset is geographically restricted. All participants lived within the United States, which spans a relatively narrow range of latitudes. As a result, their study cannot evaluate how seasonal sleep patterns scale across dramatically different photoperiod environments, such as the tropics with nearly constant day length, or high-latitude regions where day length can vary by more than ten hours across the year. In addition, the study could not disentangle environmental influences from cultural or country-level factors, because all participants shared broadly similar social, economic, and climatic contexts. Consequently, the extent to which seasonal effects on sleep differ across societies and latitudes remains unknown. The authors note these limitations explicitly, emphasising the need for larger and more diverse datasets that capture sleep behavior across multiple countries and environmental conditions.

In our work, we address these gaps by analysing wearable-derived sleep data from individuals across a wide range of countries, latitudes, and climatic environments. Because our participants span both hemispheres and occupy equatorial, mid-latitude, and high-latitude regions, the dataset captures the full global range of seasonal light environments. This diversity allows us to quantify how photoperiod effects scale with latitude and how seasonal sleep patterns vary across different cultural and climatic contexts—analyses that were not possible in prior single-country or region-restricted studies.

Specifically, using Bayesian hierarchical models, we test the following hypotheses:

• H1: Within individuals, sleep duration decreases as day length increases, consistent with circadian entrainment to environmental light.

• H2: The magnitude of the photoperiod effect increases with latitude, reflecting the stronger seasonal amplitude of photoperiod at higher latitudes.

• H3: Countries exhibit systematic differences in photoperiod sensitivity even after adjusting for latitude, indicating that sociocultural and environmental contexts modulate seasonal sleep behavior.

These hypotheses provide a structured framework for quantifying global, environmental, and sociocultural influences on seasonal sleep variation.

Results

Implementation details

All Bayesian hierarchical models were implemented in PyMC 5 using the No-U-Turn Sampler (NUTS), an adaptive Hamiltonian Monte Carlo algorithm well suited for high-dimensional hierarchical structures26. The model and priors were specified as shown in section 4.4.

Sampling used four parallel chains, each with 2000 tuning iterations and 2000 posterior draws, producing 8000 total posterior samples per parameter. A target acceptance rate of 0.90 was selected to ensure stable NUTS adaptation given the model’s depth.

Core seasonal and daylength effects

To quantify the seasonal structure in sleep duration, we first estimated the effect of day length (photoperiod) and calendar season on nightly sleep while accounting for individual-, country-, and device-level heterogeneity. Table 1 summarises the posterior estimates for the key environmental predictors.

Table 1 Posterior summaries for core environmental and seasonal effects

Full size table

We observed a clear and robust negative association between day length and sleep duration. The global photoperiod coefficient, β__P, indicated –0.073 minutes of sleep per additional minute of daylight, corresponding to –4.4 minutes of sleep every additional hour of daylight. This effect replicates prior studies and demonstrates that, at a global scale, longer days reliably shorten sleep duration.

In contrast, the seasonal indicator variables showed negligible additional explanatory power, and their 95% credible intervals overlapped zero. To assess whether photoperiod accounted for variation that might otherwise be attributed to seasonal indicators, we refit the model without latitude-dependent terms.

Despite this, seasonal coefficients remained small, with 95% credible intervals spanning zero, indicating minimal independent contribution of calendar season even when photoperiod was removed. In the no-photoperiod model, the number of user- and country-level intercepts whose credible intervals excluded zero increased from 436 to 452, reflecting a redistribution of explained variation toward stable baseline effects. This pattern suggests that coarse seasonal labels do not capture consistent global structure in sleep duration.

Evidence for seasonal sleep patterns in prior work may be driven in part by the geographically constrained nature of those studies. Within a single country or city, populations experience broadly synchronized seasonal transitions, allowing seasonal labels to serve as effective proxies for environmental and behavioural change. In globally distributed samples, by contrast, seasonal responses differ markedly across latitudes and cultures, limiting the ability of categorical season definitions to capture consistent structure in sleep behaviour.

Importantly, our analysis focuses exclusively on total sleep duration. Seasonal structure may still manifest in other dimensions of sleep that were not examined here, such as bedtimes, wake times, or night-to-night regularity. Prior work suggests that seasonal effects can operate through shifts in sleep timing rather than changes in total duration. Consequently, the absence of robust seasonal effects in sleep duration does not preclude meaningful seasonal patterning in sleep timing or circadian alignment, which remains an important direction for future work.

As expected, weekends were associated with substantially longer sleep. The posterior estimate for the weekend coefficient was strongly positive at around 13 minutes, with narrow uncertainty, validating the model’s sensitivity to known behavioural regularities.

β P__L: Latitude gradients

The latitude-photoperiod interaction termwas estimated as show in Table 2.

Table 2 Posterior summary for the latitude–photoperiod interaction term (β__P__L)

Full size table

Although directionally consistent with the hypothesis, the effect size is extremely small. Thus, we concluded that photoperiod-sensitivity does not scale with latitude.

Country-level heterogeneity

We examined how individual countries differed in both their baseline sleep duration and their sensitivity to seasonal changes in daylight. This enabled us to capture real-world cultural, social, and environmental differences that cannot be explained by latitude alone.

Table 3 reports the subset of countries whose photoperiod slopes differ significantly from the global effect β__P. Although most countries cluster near the overall mean, eight nations show posterior photoperiod slopes whose credible intervals do not overlap the global effect (Fig. 1b, c). These deviations indicate potential heterogeneity in photoperiod responsiveness, though estimates for sparsely sampled countries should be interpreted cautiously.

Fig. 1: Scaled mean asleep time plotted against day length.

a Plot showing the effect with day-length and asleep time across the entire dataset. The lack of any trend here is expected due to deeply hierarchical structure of the dataset. Estimated trends start to appear when countries with significant offsets are looked at individually, such as in b, where countries have positive b__k values. These trends get even clearer in c, where the country-specific offset in the same direction as the global trend, i.e., a negative b__k value. Countries in both plots (b) and c are listed in the legend in order of size of effect.

Table 3 Posterior summaries for country-level photoperiod slope deviations b__k whose 95% credible intervals do not overlap the global photoperiod effect β__P

Full size table

These country-level slopes are estimated under partial pooling, which stabilizes inference in the presence of highly uneven sample sizes but does not eliminate uncertainty arising from sparse within-country data. Consequently, posterior deviations for countries represented by few individuals should be interpreted as indicative rather than definitive, and primarily as signals for potential heterogeneity rather than precise population-level estimates.

Within these constraints, several countries show estimated photoperiod responses that differ in direction or magnitude from the global average. For example, Australia, Denmark, Luxembourg, and Switzerland exhibit steeper reductions in sleep duration with increasing day length, whereas Italy, Saudi Arabia, Spain, and the United Arab Emirates show weaker or attenuated responses. While these patterns persist after adjusting for latitude, they likely reflect a combination of sociocultural, behavioral, and environmental factors, as well as residual heterogeneity not captured by the available covariates.

Table 4 displays two representative examples of country-level random intercepts, v__k, which quantify deviations from the global average sleep duration after adjusting for environmental and individual factors. For example, Australia shows a positive intercept of roughly +35 minutes, while Brazil shows an even larger deviation of +41 minutes. Both credible intervals are fully above zero, indicating higher estimated baseline sleep duration relative to the global average within the modeled sample.

Table 4 Posterior summaries for selected country-level random intercepts v__k

Full size table

All reported values had a \(\widehat{R}\) value of 1.00, with the only exception being v[Australia]. This deviation was small (\(\widehat{R}\) = 1.01) and was accompanied by a large effective sample size. The posterior summary is therefore still considered stable.

Figures 2 and 3 show caterpillar plots for country-specific deviations in photoperiod sensitivity and baseline sleep duration respectively. Figure 4 shows the average sleep duration across all countries in our dataset.

Fig. 2: Caterpillar plot showing b__k values for all 49 countries.

Intervals span HDI 2.5% and HDI 97.5%. While most of credible intervals overlap 0, a couple countries show very clear effects in response to photoperiod.

Fig. 3: Caterpillar plot showing v__k values for all 49 countries.

Intervals span HDI 2.5% and HDI 97.5%. Random intercepts values are much noisier than countries' photoperiod response, with only Brazil and Australia showing clear effects.

Fig. 4: Average sleep duration by country for each country present in our data.

Country-level heterogeneity is particularly visible in this map, even within a narrow range of latitudes such as the European continent. Furthermore, the lack of any consistent pattern provides further evidence that sleep durations are heavily dependent on cultural contexts.

Discussion

Our findings extend prior single-country studies by examining how sleep duration varies with environmental light exposure across a geographically diverse, multi-country wearable dataset. Across nearly 185,000 nights of sleep recorded from individuals spanning 49 countries, we find a consistent association between photoperiod and sleep duration: nightly sleep decreases by approximately 4.4 minutes for each additional hour of daylight. This estimate closely aligns with results from longitudinal studies conducted within individual countries, suggesting that the relationship between day length and sleep duration generalises across a wide range of geographic and cultural contexts. In contrast, once individual- and country-level heterogeneity is explicitly modelled, categorical season indicators contribute little additional explanatory power, indicating that coarse calendar seasons do not capture consistent structure in sleep duration across globally distributed samples.

One implication of these results is that some seasonal patterns reported in earlier work may partly reflect the geographically constrained nature of those studies rather than intrinsic seasonal effects on sleep duration. Within a single country or city, populations experience broadly synchronised seasonal transitions in daylight, climate, and social schedules, allowing seasonal labels to act as effective proxies for environmental and behavioural change. In globally distributed samples, however, seasonal timing, amplitude, and behavioural responses vary substantially across latitudes and sociocultural contexts. Under these conditions, categorical season definitions are less effective at capturing shared structure in sleep duration, with much of the remaining variation instead absorbed by stable individual- and country-level baselines.

Despite large differences in seasonal light amplitude across latitudes, we find little evidence that photoperiod sensitivity itself scales meaningfully with latitude. The interaction between day length and latitude is statistically detectable but extremely small in magnitude, indicating that populations at higher latitudes do not exhibit substantially stronger sleep responses to changes in daylight than those closer to the equator. Instead, substantial heterogeneity emerges at the country level, with several nations exhibiting photoperiod sensitivities that differ significantly from the global mean even after adjusting for latitude. These differences likely reflect sociocultural and behavioural factors—such as work schedules, social norms, and patterns of artificial light exposure—that shape how populations respond to environmental light cues.

Several limitations should be considered when interpreting these findings. First, the hierarchical partial-pooling framework necessarily induces stronger shrinkage for countries with limited data. While this stabilises estimates and prevents noise-driven extremes, it also implies greater uncertainty for sparsely sampled regions and limits the reliability of fine-grained cross-country comparisons in those settings. Second, the sample consists exclusively of users of commercially available wearable devices, a group that is likely skewed toward higher socioeconomic status, greater health engagement, and higher digital literacy. Geographic variation in wearable adoption further contributes to imbalance across countries, increasing uncertainty in under-represented regions. Third, the dataset lacks key demographic and behavioural covariates, including age, sex, occupation, and chronotype; factors that are known to influence sleep duration and circadian responses to light. As a result, some of the heterogeneity attributed to individual or country-level effects may reflect unmeasured demographic or social differences rather than purely environmental factors.

Taken together, these results indicate that global sleep variation is driven primarily by stable individual and national baselines rather than by calendar season, and that photoperiod exerts a modest but reliable influence across diverse settings. By leveraging large-scale wearable data and hierarchical modelling, this study provides a foundation for future work aimed at disentangling environmental and sociocultural determinants of sleep at a global scale and highlights the potential of wearable technologies for studying human adaptation to the seasonal light-dark cycle.

Methods

Dataset overview

Our final dataset consisted of 697 people and 185,143 nights of sleep. These people were spread out over 6 continents and 49 countries. The participants all wore health wearables, through which their sleep was tracked. Table 5 shows how many participants and nights of sleep were present from each country, with Figs. 5 presenting the number of sessions as a heatmap. Section 4.2 presents a detailed description of the rigorous cleaning and preprocessing steps used to create the dataset. All participants were users of commercially available wearable devices connected through the Terra platform. This allows Terra to collect data on daily health metrics, any activity sessions recorded on the health-wearable as well as sleep data, given that the user wears their wearable while sleeping. For any sleep session, this includes the start and end timestamp of the session, the timezone of the user’s wearable, a nap flag of the session, total time spent awake in bed, total time spent asleep, number of REM events during the sleep, light, deep, and REM durations, number of short and long interruptions during the session, sleep latency, wakeup latency, temperature, oxygen saturation, respiratory rate, snoring events and their durations, heart rate, HRV, and sleep efficiency. Some of this data is missing depending on what the device any user is wearing measures. For any activity session the user records, Terra also collects their GPS coordinates during their activity session. The device providers in this study consisted of Garmin, Apple Health, TrainingPeaks, Zepp, Coros, Suunto, and Polar. This sampling frame likely introduces a demographic bias: individuals who own such devices tend to come from higher socioeconomic backgrounds and generally exhibit greater engagement with personal health monitoring27,28,29,30,31. Supplementary Fig. 1 shows the distributions of these devices across participants in different countries. Supplementary Fig. 3 shows sleep duration distributions per device for countries that have similar latitudes and large sample sizes within our dataset. As Terra does not store information regarding age, sex, or gender, these were demographics we did not control for.

Fig. 5: Worldwide sleep distribution in our data.

The colour-scale shows number of sleep sessions on a logarithmic scale due to the large amount of variation in population distribution among countries in our dataset.

Table 5 Number of unique participants by country and percentage share of the sample

Full size table

All participants were provided notice and consented to Terra’s processing of their data to operate, maintain and improve the Terra platform and to generate aggregated analytics and insights. The analysis was conducted on a de-identified dataset. Direct identifiers were removed or not made available to the researchers and results are reported only in aggregate. Where location signals were used, they were used only to derive country-level attributes for analysis and were not reported at an individual level. As the study involved secondary analysis of de-identified data with no participant contact or intervention, NHS Research Ethics Committee review was not required, as confirmed using the HRA decision tool.

Cleaning and preprocessing

The primary objectives of data cleaning were to remove sleep episodes not representative of consolidated nocturnal sleep, ensure that each participant contributed a sufficient and well-distributed set of observations across the year, and verify that assigned geographic locations accurately reflected true residence. Figure 6 provides a flowchart showing amount of entries kept and excluded at preprocessing step.

Fig. 6: Flowchart showing the number of sleep records retained and excluded at each preprocessing step, from all Terra data to the final dataset.

Exclusions include records removed for insufficient yearly recordings, missing location, mismatched timezones, naps, and abnormal deviations from data and physiology.

Most wearable-device providers explicitly label sleep episodes as naps. All entries identified as naps were removed to ensure that only consolidated nocturnal sleep periods were analyzed. To further eliminate artefactual or incomplete recordings, we applied a two-stage duration filtering procedure. First, for each participant, we used a median absolute deviation (MAD) rule to identify extreme outliers, excluding any sleep duration deviating by more than 3 MAD from the individual-level median. This approach adapts to each person’s typical sleep range and removes device-level segmentation errors without imposing arbitrary global thresholds. Second, we excluded episodes shorter than 3 hours, as such durations are physiologically implausible as consolidated nocturnal sleep in free-living adults and typically reflect fragmented or partially recorded sleep. After filtering, the empirical distribution of sleep durations fell within biologically plausible limits (3.00–14.88 hours).

To ensure that each participant contributed a sufficiently long and seasonally informative trajectory, we imposed three data-coverage requirements.

First, participants were required to have at least 305 days between their first and last recorded sleep entry. Exploratory analysis showed a marked decline in recording activity after this point, and because start dates were uniformly distributed across the calendar, a 305-day span provides potential coverage across all four seasons while avoiding unnecessary loss of participants with slightly incomplete annual records.

Second, to prevent highly sparse or uneven temporal sampling, we required each participant to contribute at least 100 distinct sleep episodes over their observation window. This ensures stable estimation of individual sleep averages and within-person photoperiod sensitivity.

Third, we required a minimum of 10 complete nights of sleep within every three-month interval, providing sufficient within-season stability while preserving geographic diversity that would be lost under stricter thresholds used in single-country studies. As a robustness check, we re-estimated the photoperiod-sleep models using an alternative requirement of 20 nights per interval and obtained nearly identical estimates of the global photoperiod and seasonal effects, photoperiod-latitude scaling, and cross-country variation in photoperiod sensitivity (Supplementary Tables 1, 2, and 3), indicating that our findings are not sensitive to the specific choice of the 10-night criterion.

The wearable devices used in this study record geolocation only during activity events and not during sleep, which required developing a procedure to infer each individual’s most likely country of residence and ensure spatial consistency between their activity and sleep records. To do this, we first sampled a set of random activity coordinates for each participant across the full year in which they contributed sleep data and assigned each sampled point to a country using standard geospatial lookup tools. Sleep records, in contrast, report only timezone information, so we cross-validated the inferred activity country with the timezone associated with each of the individual’s sleep episodes. This validation explicitly accounted for daylight saving time transitions, mid-year timezone shifts, and the fact that several countries span multiple timezones. Short-term travel does not influence country assignment, as sleep episodes with timezones that did not match the inferred activity country were removed.

As an additional empirical check on residence stability, we quantified how often activity events occurred within the inferred home country. Across all participants, 89.87% of activity events occurred in the assigned country, indicating strong internal consistency between inferred residence, habitual activity locations, and sleep-record timezones. After confirming this match, we designated the resulting country as the individual’s residence for analytical purposes and assigned each participant a representative latitude equal to the average latitude of that country. Although this introduces some noise for geographically large countries with substantial latitudinal variation (e.g., the United States or Canada), the resulting bias is expected to be minor for smaller or more compact nations. We are able to confirm this by looking at the mean absolute difference in sampled latitude and assigned latitude by country (Supplementary Table 4) as well as a boxplot of the same quantity across our data (Supplementary Fig. 2). Given the scale of the dataset and our focus on broad geographic and seasonal patterns rather than fine-grained spatial variation, this country-level approximation provides a robust balance between data constraints and analytical accuracy.

Day length calculation

Day length was computed from latitude ϕ and day of year using a standard astronomical approximation based on solar declination32. For agiven latitude ϕ (in radians) and day of year d, solar declination δ was approximated as,

$$\delta (d)=23.4{4}^{\circ }\cdot \sin \left(\frac{2\pi (284+d)}{365}\right)$$

(1)

Using solar declination, the hour angle of the sun _ω_0 could be calculated as shown in equation 233.

$${\omega }_{0}=-\tan (\phi )\tan (\delta )$$

(2)

Day length in hours was then simply obtained by,

$${\rm{daylength}}(d,\phi )=\frac{24}{\pi }{\omega }_{0}$$

(3)

Rationale for Bayesian models

A key motivation for using Bayesian hierarchical modeling in this study arises from both the structure of the dataset and the nature of the scientific questions. Prior studies examining seasonal variation or light-sleep relationships typically rely on frequentist mixed-effects models applied to single-country cohorts with relatively balanced samples, where classical methods perform adequately. In contrast, the present dataset is globally sourced, highly unbalanced, and deeply hierarchical: nightly sleep episodes are nested within individuals, who are nested within 49 countries and multiple device providers, with participant counts varying by more than two orders of magnitude. Estimating country-level photoperiod effects under such imbalance requires a framework that remains stable even for sparsely represented countries, and Bayesian partial pooling provides this capability34,35. By treating country-specific effects as draws from a shared population distribution, the model borrows strength across countries, allowing well-sampled countries to retain data-driven estimates while shrinking sparsely sampled ones toward the global mean to avoid implausible values. This mechanism is essential for testing heterogeneity in photoperiod sensitivity and its scaling with latitude without having the global effect distorted by extreme values from small samples. Frequentist mixed-effects models are known to struggle in such settings—often yielding singular fits, unreliable variance estimates, or convergence issues—whereas the Bayesian framework provides robust partial pooling and full posterior distributions for all levels of the hierarchy, enabling principled uncertainty quantification across small, moderate, and large countries alike36,37.

Model

To quantify global, latitudinal, and country-level variation in photoperiod sensitivity, we fit a Bayesian hierarchical regression model to nightly sleep duration. Let y__i__j__k denote the sleep duration (in hours) for night i of individual j living in country k. For each night, we compute the corresponding photoperiod value P__i__j__k (hours of daylight) based on the individual’s inferred latitude and date. We model sleep duration as:

$${y}_{ijk} \sim {\mathcal{N}}({\mu }_{ijk},{\sigma }_{y})$$

(4)

$${\mu }_{ijk}={\alpha }_{0}+{u}_{j}+{v}_{k}+{w}_{d(j)}+({\beta }_{P}+{b}_{k}){P}_{ijk}+{\beta }_{PL}({P}_{ijk}\cdot {L}_{k})+{\gamma }^{\top }{X}_{ijk}$$

(5)

Where, _α_0 is the global intercept, u__j, v__k, and w__d(j) are random intercepts for participant, country, and wearable device respectively. β__P is the global photoperiod effect, whereas b__k is the country-level photoperiod effect. β__P__L is the fixed effect encoding how photoperiod sensitivity changes with latitude, L__k. X__i__j__k is a vector of covariates including weekend indicators and seasonal controls and γ is the associated coefficient vector.

Bayesian estimation has previously been shown to be sensitive to bad prior design38,39. We used weakly informative priors chosen to regularize the hierarchical model while allowing the data to dominate inference. Normal priors were placed on the intercept and fixed effects,

$${\alpha }_{0},{\beta }_{P},{\beta }_{PL},\gamma \sim {\mathcal{N}}(\mu ,{\sigma }^{2})$$

(6)

providing symmetric shrinkage toward μ and preventing implausibly large effect sizes.

We calculated the mean duration and standard deviation within our own sleep dataset and found that the mean sleep was 444 minutes, while the standard deviation was 78 minutes. Hence, the prior for _α_0 was set to roughly match these numbers.

$${\alpha }_{0} \sim {\mathcal{N}}(450,9{0}^{2})$$

(7)

Although prior work suggests daylength may decrease sleep duration modestly, effect sizes vary across populations. To avoid introducing directional bias, we centered the β__P prior at 0 and allowed for a wide deviation.

$${\beta }_{P} \sim {\mathcal{N}}(0,1{0}^{2})$$

(8)

As the modulation of photoperiod sensitivity by latitude is poorly characterized in the literature, we used a broad prior.

$${\beta }_{PL} \sim {\mathcal{N}}(0,{5}^{2})$$

(9)

Finally, although seasonal effects are expected to be small, weekend effects are usually much larger. Hence, the prior for γ allowed for a deviation of 30 minutes.

$$\gamma \sim {\mathcal{N}}(0,3{0}^{2})$$

(10)

The standard deviations of the user-level, country-level, and device-level random intercepts were assigned Half-Normal priors,

$${\sigma }_{user},{\sigma }_{country},{\sigma }_{device} \sim {\rm{Half}}-{\rm{Normal}}(\mu ,\tau )$$

(11)

which constrain variance components to be positive and discourage extreme over-dispersion that can arise in weakly constrained hierarchical models.

Values for user intercepts were inferred through results in Mattingly et al.19, while country and device variation were chosen by looking at deviations within Terra’s data.

$${\sigma }_{user} \sim {\rm{Half}}-{\rm{Normal}}(0,60)$$

(12)

$${\sigma }_{country} \sim {\rm{Half}}-{\rm{Normal}}(0,30)$$

(13)

$${\sigma }_{device} \sim {\rm{Half}}-{\rm{Normal}}(0,20)$$

(14)

Night-to-night residual variability in sleep duration was modeled using a Half-Student-t prior, with ν = 3,

$${\sigma }_{y} \sim {\rm{Half-}}{t}_{v}(0,90)$$

(15)

to allow for occasional heavy-tailed deviations in sleep duration while maintaining overall model robustness.

These prior choices follow established recommendations for hierarchical models, which emphasize weakly informative distributions to stabilize variance estimation while avoiding undue influence on posterior inference40.

Data availability

The datasets generated and analysed during the current study are not publicly available due to due to privacy and data protection restrictions. Aggregated summary statistics, including country-, device-, and month-level sleep duration estimates, are available from the corresponding author upon reasonable request.

Code availability

Code for this paper is available upon reasonable request.

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Author notes

1. These authors contributed equally: Alistair Brownlee, Cameron Crawford.

Authors and Affiliations

1. Terra API, Beaconsfield Street, London, UK

   Faraaz Akhtar, Alistair Brownlee & Cameron Crawford

Authors

1. Faraaz Akhtar
2. Alistair Brownlee
3. Cameron Crawford

Contributions

F.A. conceptualised the study, developed the methodology, collected and curated the data, performed the formal analysis, and wrote the original manuscript. A.B. proposed the initial study idea and contributed to data preprocessing and manuscript review. C.C. contributed to data preprocessing and manuscript review. A.B. and C.C. contributed equally to this work. All authors approved the final manuscript.

Corresponding author

Correspondence to Faraaz Akhtar.

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Competing interests

The authors are employees of Terra API, which provides the wearable data infrastructure used in this study.

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Akhtar, F., Brownlee, A. & Crawford, C. Variation in sleep duration across latitudes and countries: a Bayesian hierarchical analysis of wearable data. npj Biol Timing Sleep 3, 27 (2026). https://doi.org/10.1038/s44323-026-00092-2

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• Received: 11 January 2026

• Accepted: 08 June 2026

• Published: 22 June 2026

• Version of record: 22 June 2026

• DOI: https://doi.org/10.1038/s44323-026-00092-2