ICA 2026 · Methodology

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Episode-wise attention dynamics in recurrent Japanese heatwaves.

Kunhao Yangpresenter Shibaura Institute of Technology Homepage Google Scholar ResearchGate ORCID · Mengyuan Fu Waseda University Google Scholar ResearchGate ORCID · Mikihito Tanaka Waseda University Google Scholar ORCID

Hover an author for affiliation & profile links

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The problem

When the same hazard keeps coming back, does the news keep caring?

Heatwaves are recurrent, comparable shocks — the ideal natural experiment for attention.
Surveys show rising news avoidance & alert fatigue — but that's self-report.
We want a behavioral, data-level signature: does the 4th wave get less traction than the 1st?

We measure an observable journalism/engagement pattern, not a psychological state. "Fatigue" here = attenuated response to repeated shocks.

media

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heatwave-related articles / day (share of all Yahoo! News JP)

audience

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heatwave-related comments / day (share of all comments)

trigger

30°C

population-weighted daily Tmax threshold defines a heat spell

window

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Data & the exogenous driver

Attention is an exogenous response to temperature — and the two channels differ

Daily heat article & comment share (%) with temperature. Hover for values.

Cross-correlation vs temperature by lag. Both peak at lag 0; media tracks heat far more tightly (r≈0.77) than the audience (r≈0.47).

Method

Segment events, then measure two facets of attention

Events are detected from the attention signal itself (peak prominence, split at troughs), not from a brittle temperature rule. Each facet is regressed on within-season event order with a hierarchical (partial-pooling) Bayesian model controlling for heat intensity and year, returning credible intervals rather than an underpowered two-stage regression.

facet 1 · speed

Shape-timing

half-rise = days to reach ½ of the peak (mobilization speed); half-decay = days from the peak back to ½ (forgetting speed) — both model-free. Fatigue ⇒ slower rise and/or faster decay in later events.

Characteristic shapes of the candidate models

Rise — speed of mobilization

Decay — speed of forgetting

Full equations & sources on the supplementary slide.

facet 2 · amplitude

Efficiency

Attention volume per degree-day of heat. Fatigue ⇒ efficiency declines with event order.

Hierarchical regression model

log(attention)_s = β₀ + β_dd·log(degree-days)_s + β_order·order_s + β_year + u_spell + ε

β_order < 0 = fatigue. Partial pooling by spell (random intercept u_spell); credible intervals from a 4-chain Gibbs sampler — not a two-stage regression.

Result 1 — speed of mobilization

Attention accelerates into each heatwave

Early growth is a mix of power-law and exponential shapes.
Jin exponent η > 1 (median ≈ 1.4 media, 1.9 audience): accelerating, concave-up early growth — descriptively the substitutive-process signature, not a mechanism claim.
Mobilization is rapid: half-rise ≈ 1–2 days at daily resolution.

Bursts are sharp at daily resolution, so per-event rise shape is weakly identified (see Limitations).

A representative rise, all candidate growth models.

Result 2 — speed of forgetting

Decay is single-exponential; richer models are not supported

Post-peak decay is predominantly single-exponential, half-life ≈ 2–3 days.
Candia bi-exponential and log-normal are never selected (0 / 29 windows) — not identifiable on short, single-realization bursts.
A within-summer decay of days cannot resolve a multi-year cultural-memory channel.

On the shortest windows exponential and power-law are statistically indistinguishable (14 / 24); per-event shape is reported with this caveat.

A representative decay, all four candidate models.

Result 3 — the fatigue signal (amplitude)

Later heatwaves convert the same heat into less attention

media articles per degree-day vs within-season order

audience comments per degree-day vs within-season order

≈ ½

attention-per-degree of the 5th wave vs the 1st

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articles: order correlation (both years)

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comments: order correlation (both years)

Synthesis — amplitude vs speed

Two operationalizations, different evidential strength

Efficiency (amplitude): credibly negative in both channels, P(fatigue) ≈ 0.93–0.95.
Shape-timing (speed): half-rise null; half-decay leans negative but its credible interval includes zero.
The amplitude estimand recovers the order effect where the speed estimand does not.

The volume effect is consistent in sign across both channels and both seasons; the curve-shape effect is not separable from noise at this resolution.

Posterior order coefficient ± 95% credible interval. Left of the dashed line = fatigue direction.

Contribution

An episode-wise, intensity-controlled measure of attention fatigue

Heatwave attention is exogenously temperature-forced; the media channel tracks heat far more tightly than the audience.
Post-peak decay is single-exponential on a 2–3 day timescale; richer two-channel and log-normal models are not supported at episode scale.
Fatigue appears as a volume effect: each successive within-season heatwave earns ~17% less attention per degree-day — about half by the fifth wave — consistently across both channels and both seasons.

A reproducible procedure that turns platform-scale logs into episode-wise measures of attention to recurrent hazards.

Limitations & outlook

Scope of the present evidence

Sample

Ten heat spells across two seasons. Under the hierarchical prior the efficiency 95% credible interval marginally includes zero (frequentist OLS: p < 0.05).

Identification

Per-event curve-shape (speed) is weakly identified at daily resolution; rise and decay timing should be read cautiously.

Confounding

Within-season order co-varies with seasonal expectation and competing news; “fatigue” denotes a behavioral pattern, not a psychological state.

Outlook: additional seasons and hazards, finer-than-daily resolution, pre-registered thresholds, and content-level controls would move a credible signal toward a decisive one.

Supplementary · 1

Model specifications & sources

Rise — speed of mobilization · read-out: half-rise

Exponential

I(t) ∝ e^g·t

g = growth rate; contagion-style growth (classic epidemic null).

Power-law (substitutive)

I(t) ∝ t^η → daily ∝ t^η−1

η = fitness / steepness; emergent from finite-pool competition.

Jin et al. (2019), Nat. Hum. Behav.

Logistic

K ∕ (1 + e^{−k(t−t₀)})

K = saturation, k = steepness, t₀ = inflection; Bass-type diffusion.

Decay — speed of forgetting · read-out: half-decay

Single-exponential

S(t) ∝ e^−β·t (t_½ = ln2 ∕ β)

Memoryless forgetting.

Power-law

S(t) ∝ t^−α

Heavy-tailed relaxation.

Crane & Sornette (2008), PNAS

Log-normal

S(t) ∝ t⁻¹·e^{−(ln t−μ)² ∕ 2σ²}

Novelty-decay of online attention.

Wu & Huberman (2007), PNAS

Candia bi-exponential

S(t) = N∕(p+r−q)·[(p−q)e^−(p+r)t + r·e^−q·t]

Communicative (fast, p+r) + cultural (slow, q) memory.

Candia et al. (2019), Nat. Hum. Behav.

Each segment fit in log space; selected per event by AICc where window length permits. Half-rise / half-decay are model-free (interpolation to ½ peak), so the fatigue read-outs do not depend on the winning form.

Supplementary · 2

Episodes analyzed & measurement

Signals

media daily share of Yahoo! News Japan articles whose title contains a heatwave keyword (猛暑 / 熱波 / 酷暑 / …). audience daily share of comments containing the same keywords.

Episode detection

A heat spell opens when population-weighted daily Tmax ≥ 30 °C. Attention events are additionally segmented from the signal itself by peak prominence (split at troughs). Comment counts are not right-censored for 2024–25 (collected months later).

Supplementary · 3

Hierarchical estimation & convergence

Gaussian varying-intercept model (random intercept by spell), fit with an exact conjugate Gibbs sampler.
Weakly-informative priors: Normal on coefficients, Inverse-Gamma on variances.
Efficiency model pools both channels; the order coefficient is the fatigue effect.

Pooled efficiency model — posterior