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Editorial revision: precision, framing, and internal consistency (4a–4k)

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4a  Moderate principal conclusion: 'no statistically credible evidence'
    replaced with 'no statistically robust evidence within tested frameworks'
    plus clause acknowledging untested mechanisms (threshold effects,
    nonlinear triggering, extreme-event coupling).

4b  Fix independence-assumption framing: 'physically invalid seismic metric'
    → 'physically inappropriate'; separate claim about naive p-values now
    reads 'statistically invalid under the violated serial-independence
    assumption (autocorrelation inflates nominal sample size by 3–5×)'.

4c  3.9σ detrended peak no longer called 'marginal': figure caption and
    nearby text now read 'nominally significant but sensitive to Neff
    estimation, at a lag inconsistent with the claimed mechanism'.

4d  CR terminology standardised: 'global CR index' defined precisely at
    first use in Data section (dimensionless, station mean ≡ 1, ≥3 stations
    per bin); 'CR flux' retained only for the physical quantity.

4e  Geographic conclusion reframed: 'no local mechanism' replaced with
    'inconsistent with simple wave-propagation or diffusion models, but does
    not rule out instantaneous global coupling mechanisms (e.g. atmospheric
    electric field modulation)'.

4f  Bayes factor qualified: parenthetical after BF=0.75 notes the restricted
    two-hypothesis model space and cites Kass & Raftery (1995).

4g  OOS limitations expanded: explicit paragraph noting the 5-yr window
    with no complete solar cycle, limited statistical power, and that
    p_global=0.100 is consistent with—rather than strong evidence against
    —the claim; OOS failure downweighted vs 44-yr in-sample analysis.

4h  Confirmatory vs exploratory scope table added (Table tab:prereg_scope)
    listing pre-specified parameters and which analyses were confirmatory
    vs post-hoc exploratory.

4i  Alternative solar-cycle confounds acknowledged in Discussion: geomagnetic
    activity cycles and long-term seismic clustering added as alternative
    explanations for the shared 10-year periodicity.

4j  Fixed: 'Out-of-sample poos from script 08' removed from Limitations;
    GitHub URL removed from abstract (kept in Data Availability only);
    Discussion run-on sentences broken up.

4k  Abstract rewritten to ≤250 words in five-part structure: prior claim,
    data/methods (two sentences), key quantitative results, scoped
    interpretation, one-sentence limitation. Causal language qualified.

Also adds KassRaftery1995 to refs.bib. PDF: 36 pages.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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\citation{GardnerKnopoff1974} \citation{GardnerKnopoff1974}
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@ -218,16 +221,17 @@
\bibcite{HP1997}{{7}{1997}{{Hodrick and Prescott}}{{}}} \bibcite{HP1997}{{7}{1997}{{Hodrick and Prescott}}{{}}}
\bibcite{Homola2023}{{8}{2022}{{Homola et~al.}}{{}}} \bibcite{Homola2023}{{8}{2022}{{Homola et~al.}}{{}}}
\bibcite{Kanamori1977}{{9}{1977}{{Kanamori}}{{}}} \bibcite{Kanamori1977}{{9}{1977}{{Kanamori}}{{}}}
\bibcite{Kraskov2004}{{10}{2004}{{Kraskov et~al.}}{{Kraskov, St{\"o}gbauer, and Grassberger}}} \bibcite{KassRaftery1995}{{10}{1995}{{Kass and Raftery}}{{}}}
\bibcite{Odintsov2006}{{11}{2006}{{Odintsov et~al.}}{{Odintsov, Boyarchuk, Georgieva, Kirov, and Atanasov}}} \bibcite{Kraskov2004}{{11}{2004}{{Kraskov et~al.}}{{Kraskov, St{\"o}gbauer, and Grassberger}}}
\bibcite{Potgieter2013}{{12}{2013}{{Potgieter}}{{}}} \bibcite{Odintsov2006}{{12}{2006}{{Odintsov et~al.}}{{Odintsov, Boyarchuk, Georgieva, Kirov, and Atanasov}}}
\bibcite{Pulinets2004}{{13}{2004}{{Pulinets and Boyarchuk}}{{}}} \bibcite{Potgieter2013}{{13}{2013}{{Potgieter}}{{}}}
\bibcite{RahnUhlig2002}{{14}{2002}{{Ravn and Uhlig}}{{}}} \bibcite{Pulinets2004}{{14}{2004}{{Pulinets and Boyarchuk}}{{}}}
\bibcite{Schreiber2000}{{15}{2000}{{Schreiber and Schmitz}}{{}}} \bibcite{RahnUhlig2002}{{15}{2002}{{Ravn and Uhlig}}{{}}}
\bibcite{SIDC2024}{{16}{2024}{{SILSO World Data Center}}{{}}} \bibcite{Schreiber2000}{{16}{2000}{{Schreiber and Schmitz}}{{}}}
\bibcite{Stoupel1990}{{17}{1990}{{Stoupel}}{{}}} \bibcite{SIDC2024}{{17}{2024}{{SILSO World Data Center}}{{}}}
\bibcite{Tavares2011}{{18}{2011}{{Tavares and Azevedo}}{{}}} \bibcite{Stoupel1990}{{18}{1990}{{Stoupel}}{{}}}
\bibcite{Theiler1992}{{19}{1992}{{Theiler et~al.}}{{Theiler, Eubank, Longtin, Galdrikian, and Farmer}}} \bibcite{Tavares2011}{{19}{2011}{{Tavares and Azevedo}}{{}}}
\bibcite{Urata2018}{{20}{2018}{{Urata and Tanimoto}}{{}}} \bibcite{Theiler1992}{{20}{1992}{{Theiler et~al.}}{{Theiler, Eubank, Longtin, Galdrikian, and Farmer}}}
\bibcite{USGS2024}{{21}{2024}{{USGS Earthquake Hazards Program}}{{}}} \bibcite{Urata2018}{{21}{2018}{{Urata and Tanimoto}}{{}}}
\gdef \@abspage@last{35} \bibcite{USGS2024}{{22}{2024}{{USGS Earthquake Hazards Program}}{{}}}
\gdef \@abspage@last{36}

9
paper/main.bbl
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@ -1,4 +1,4 @@
\begin{thebibliography}{21} \begin{thebibliography}{22}
\providecommand{\natexlab}[1]{#1} \providecommand{\natexlab}[1]{#1}
\providecommand{\url}[1]{\texttt{#1}} \providecommand{\url}[1]{\texttt{#1}}
\expandafter\ifx\csname urlstyle\endcsname\relax \expandafter\ifx\csname urlstyle\endcsname\relax
@ -73,6 +73,13 @@ Hiroo Kanamori.
2981--2987, 1977. 2981--2987, 1977.
\newblock \doi{10.1029/JB082i020p02981}. \newblock \doi{10.1029/JB082i020p02981}.
\bibitem[Kass and Raftery(1995)]{KassRaftery1995}
Robert~E. Kass and Adrian~E. Raftery.
\newblock Bayes factors.
\newblock \emph{Journal of the American Statistical Association}, 90\penalty0
(430):\penalty0 773--795, 1995.
\newblock \doi{10.1080/01621459.1995.10476572}.
\bibitem[Kraskov et~al.(2004)Kraskov, St{\"o}gbauer, and \bibitem[Kraskov et~al.(2004)Kraskov, St{\"o}gbauer, and
Grassberger]{Kraskov2004} Grassberger]{Kraskov2004}
Alexander Kraskov, Harald St{\"o}gbauer, and Peter Grassberger. Alexander Kraskov, Harald St{\"o}gbauer, and Peter Grassberger.

60
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[]\T1/lmr/bx/n/14.4 (-20) Raw Pair-wise Cor-re-la-tions Be-tween CR, Seis-mic, []\T1/lmr/bx/n/14.4 (-20) Raw Pair-wise Cor-re-la-tions Be-tween CR, Seis-mic,
and Sunspot and Sunspot
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\T1/lmr/m/n/12 (-20) We have con-ducted a rig-or-ous, pre-registered repli-ca-t \T1/lmr/m/n/12 (-20) We have con-ducted a rig-or-ous, pre-registered repli-ca-t
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\begin{abstract} \begin{abstract}
\noindent \noindent
\citet{Homola2023} reported a statistically significant positive correlation \citet{Homola2023} reported a statistically significant positive correlation
($r \approx 0.31$) between galactic cosmic-ray (CR) flux measured by neutron ($r \approx 0.31$) between galactic cosmic-ray (CR) flux and global seismicity
monitors and global seismicity (M~$\geq$~4.5) at a time lag of $\tau = +15$~days, at a lag of $\tau = +15$~days, suggesting that elevated CR flux precedes
suggesting that elevated CR flux precedes increased earthquake activity. increased earthquake occurrence.
That earlier value used a physically invalid seismic metric (direct sum of moment That value relied on an inappropriate seismic metric (direct summation of
magnitudes $M_W$, which are logarithmic); the correct metric — summed radiated energy moment magnitudes, which are logarithmic); the correct energy-based metric
$E = 10^{1.5 M_W + 4.8}$\,J per bin \citep{Kanamori1977} — yields $r(+15\,\text{d}) = 0.081$. \citep{Kanamori1977} gives $r(+15\,\text{d}) = 0.081$.
We present a systematic replication and extension of this claim using data from
44 Neutron Monitor Database (NMDB) stations, the USGS global earthquake catalogue,
and SILSO daily sunspot numbers spanning 1976--2025.
Our analysis proceeds in four stages. We systematically replicate and extend this analysis using the \emph{global
\textit{Stage~1} replicates the raw cross-correlation (with correct seismic energy metric: CR index} — the normalised neutron-monitor count rate (dimensionless, station
$r(+15\,\text{d}) = 0.081$, peak $r = 0.139$ at $\tau = -525$~days) but demonstrates mean $\equiv 1$) averaged over 44 NMDB stations with $\geq 3$ reporting per
that naive $p$-values are invalid because temporal autocorrelation and a shared 5-day bin — the USGS earthquake catalogue ($M \geq 4.5$; $n \approx 232{,}000$
$\sim$11-year solar cycle inflate the apparent significance. events, 1976--2025), and SILSO sunspot numbers.
\textit{Stage~2} applies iterative amplitude-adjusted Fourier transform (IAAFT) Methods include IAAFT surrogate tests ($10^4$ realisations), Hodrick--Prescott
surrogate tests with $10^4$ realisations: after Hodrick--Prescott (HP) detrending detrending, geographic localisation (7{,}037 station--cell pairs,
to remove the solar-cycle component, the peak correlation drops to Benjamini--Hochberg correction), a pre-registered out-of-sample validation
$r = 0.101$ and achieves formal significance ($p_\text{global} < 10^{-4}$, $>3.9\sigma$), (2020--2025, $10^5$ surrogates), and seven additional robustness checks
but $r(+15\,\text{d}) = 0.027$ --- well within the surrogate null distribution. (block bootstrap, partial correlation, spectral coherence, mutual information,
\textit{Stage~3} scans $34 \times 207 = 7{,}037$ station--grid-cell pairs for missing-data sensitivity, bin-size sensitivity, and earthquake declustering).
geographic localisation; 455 pairs survive Benjamini--Hochberg correction
(expected false discoveries: 352), and the optimal lag $\tau^*$ shows no
dependence on great-circle distance ($\beta = -0.45$~days/1000~km, $p = 0.21$),
consistent with an isotropic CR signal rather than a local mechanism.
\textit{Stage~4} applies a pre-registered out-of-sample test on an independent
2020--2025 window ($T = 390$ five-day bins, $10^5$ phase-randomisation
surrogates on a Tesla M40 GPU):
$r(+15\,\text{d}) = 0.030$ (surrogate 95th percentile~$= 0.101$),
$p_\text{global} = 0.100$ --- consistent with noise.
Fitting a sinusoid to the 1976--2025 annual cross-correlation timeseries yields
a best-fit period of $P = 13.0$~years and a Bayes factor of $\text{BF} = 0.75$,
slightly favouring a constant (no modulation) over a sinusoidal relationship.
We conclude that the CR--seismic correlation reported by \citet{Homola2023} is an After solar-cycle detrending, $r(+15\,\text{d})$ falls to 0.027--0.037 across
artefact of the shared solar-cycle modulation of both galactic CR flux and three methods, all within IAAFT surrogate null distributions.
global seismicity, and not evidence of a physical causal link. The pre-registered out-of-sample test yields $r(+15\,\text{d}) = 0.030$ and
All analysis code, pre-registration document, and results are publicly available at $p_\text{global} = 0.100$.
\url{https://github.com/pingud98/cosmicraysandearthquakes}. Partial correlation on unfiltered data reduces $r(+15\,\text{d})$ by 63\%
after sunspot regression; mutual information at the claimed lag is
indistinguishable from zero ($p = 1.000$).
The geographic scan finds no propagation-delay signature
($\beta = -0.45$~d/1000~km, $p = 0.21$).
We find no statistically robust evidence for a causal CR--seismic relationship
within the linear cross-correlation and surrogate-testing frameworks tested
here, after controlling for solar-cycle modulation.
The primary limitation is that the 2020--2025 validation window
(${\approx}5$~yr, no complete solar cycle) provides limited statistical power,
and nonlinear or threshold-based coupling mechanisms were not assessed.
\end{abstract} \end{abstract}
\textbf{Keywords:} cosmic rays; seismicity; surrogate test; solar cycle; \textbf{Keywords:} cosmic rays; seismicity; surrogate test; solar cycle;
@ -123,9 +119,11 @@ Three statistical pitfalls immediately suggest themselves:
\item \textbf{Temporal autocorrelation.} \item \textbf{Temporal autocorrelation.}
Both CR flux and seismicity exhibit strong low-frequency structure Both CR flux and seismicity exhibit strong low-frequency structure
(solar cycle, regional seismic cycles). (solar cycle, regional seismic cycles).
Treating successive 5-day bins as independent dramatically inflates Treating successive 5-day bins as independent is statistically invalid
the degrees of freedom; a Bretherton effective-$N$ correction \citep{Bretherton1999} under the violated serial-independence assumption: autocorrelation
is required. inflates the nominal sample size from $T \approx 3{,}200$ bins to an
effective $N_\text{eff} \approx 600$--$2{,}900$ (see Table~\ref{tab:neff}),
requiring a Bretherton-style effective-$N$ correction \citep{Bretherton1999}.
\item \textbf{Shared solar-cycle trend.} \item \textbf{Shared solar-cycle trend.}
Galactic CR flux is modulated by the heliospheric magnetic field, which Galactic CR flux is modulated by the heliospheric magnetic field, which
@ -174,9 +172,14 @@ daily coverage over the in-sample window 1976--2019, and \textbf{35 stations}
over the out-of-sample window 2020--2025. over the out-of-sample window 2020--2025.
Each station's daily series was normalised by its long-run mean and resampled Each station's daily series was normalised by its long-run mean and resampled
to non-overlapping 5-day bins. to non-overlapping 5-day bins.
A global CR index was formed as the mean across all stations with valid data in A \emph{global CR index} $x_t$ (dimensionless; each station normalised so its
each bin, requiring at least three stations; bins failing this criterion were long-run mean $\equiv 1$) was formed as the arithmetic mean of valid station
set to \texttt{NaN}. values in each 5-day bin, requiring at least three reporting stations; bins
failing this criterion were set to \texttt{NaN}.
Values above unity indicate a CR-flux enhancement relative to the long-run
station mean; values below unity indicate suppression (e.g.\ Forbush decreases
during solar maximum).
This index is used as the primary predictor variable throughout all analyses.
\subsection{Seismic Activity: USGS Earthquake Catalogue} \subsection{Seismic Activity: USGS Earthquake Catalogue}
\label{sec:usgs} \label{sec:usgs}
@ -197,9 +200,11 @@ $E_\text{bin} = \sum_i E_i$, and the metric is $\log_{10}(E_\text{bin})$
(empty bins set to NaN). (empty bins set to NaN).
This formulation correctly weights large earthquakes: an $M_W\,8.0$ event This formulation correctly weights large earthquakes: an $M_W\,8.0$ event
contributes $\sim$1000$\times$ more energy than an $M_W\,6.0$ event. contributes $\sim$1000$\times$ more energy than an $M_W\,6.0$ event.
Directly summing $M_W$ values — as used in several earlier studies — is Directly summing $M_W$ values --- as used in several earlier studies ---
physically invalid because $M_W$ is logarithmic; such sums do not correspond is physically inappropriate: $M_W$ is a logarithmic quantity, so such sums
to any additive physical quantity. have no additive physical interpretation and artificially amplify the
contribution of solar-cycle-driven catalogue completeness fluctuations to
the seismic time series.
\subsection{Solar Activity: SIDC Sunspot Number} \subsection{Solar Activity: SIDC Sunspot Number}
\label{sec:sidc} \label{sec:sidc}
@ -474,6 +479,40 @@ The pre-registered predictions, scored after unblinding, were:
surrogate 95th percentile. surrogate 95th percentile.
\end{itemize} \end{itemize}
\paragraph{Confirmatory versus exploratory analyses.}
Table~\ref{tab:prereg_scope} distinguishes analyses that were pre-specified
(confirmatory) from those added after data examination (exploratory).
\begin{table}[htbp]
\centering
\caption{Analysis scope and pre-registration status.
Pre-specified parameters locked before data access: $\lambda = 4.54 \times 10^{10}$,
lag range $[-200, +200]$~bins, $M \geq 4.5$, min.\ 3 stations per bin,
5-day bin size, IAAFT surrogate count $S = 10^4$.}
\label{tab:prereg_scope}
\begin{tabular}{lll}
\toprule
Analysis & Type & Pre-specified parameters \\
\midrule
OOS cross-correlation at $\tau = +15$~d & Confirmatory & All \\
OOS global $p$-value (P1--F1) & Confirmatory & All \\
In-sample IAAFT surrogate test & Confirmatory & All \\
HP detrending with $\lambda$ & Confirmatory & $\lambda$ locked \\
Geographic BH scan & Confirmatory & $q = 0.05$, $10°$ grid \\
\addlinespace
STL / sunspot-regression detrending & Exploratory & — \\
Block-bootstrap surrogates (3a) & Exploratory & — \\
Partial correlation analysis (3b) & Exploratory & — \\
Spectral coherence + MI (3c) & Exploratory & — \\
Missing-data sensitivity (3d) & Exploratory & — \\
Bin-size sensitivity (3e) & Exploratory & — \\
Earthquake declustering (3f) & Exploratory & — \\
Sub-period / per-cycle analysis (3g) & Exploratory & — \\
Sinusoidal modulation fit & Exploratory & — \\
\bottomrule
\end{tabular}
\end{table}
\subsection{Combined Timeseries: Sinusoidal Envelope Fit} \subsection{Combined Timeseries: Sinusoidal Envelope Fit}
\label{sec:sinusoid} \label{sec:sinusoid}
@ -556,7 +595,7 @@ panel 3).
We compute both Pearson $r$ (linear; Fisher $z$-transform 95\% CI) and We compute both Pearson $r$ (linear; Fisher $z$-transform 95\% CI) and
Spearman $\rho$ (rank-based; appropriate for the heavy-tailed marginal Spearman $\rho$ (rank-based; appropriate for the heavy-tailed marginal
distributions of $E_t$ and CR flux). distributions of $E_t$ and the global CR index).
Bonferroni correction for $3\ \text{pairs} \times 3\ \text{windows} = 9$ Bonferroni correction for $3\ \text{pairs} \times 3\ \text{windows} = 9$
tests is applied; star levels refer to the corrected $p$-values. tests is applied; star levels refer to the corrected $p$-values.
Full results are given in Table~\ref{tab:rawcorr}. Full results are given in Table~\ref{tab:rawcorr}.
@ -712,7 +751,7 @@ Figure~\ref{fig:homola} shows the full cross-correlation function of the raw
(undetrended) CR index and seismic metric (log$_{10}$ summed energy, Eq.~\ref{eq:energy}) (undetrended) CR index and seismic metric (log$_{10}$ summed energy, Eq.~\ref{eq:energy})
over 1976--2019 ($T = 3{,}215$ five-day bins, 44 stations). over 1976--2019 ($T = 3{,}215$ five-day bins, 44 stations).
The dominant peak is at $\tau = -525$~days ($r = 0.139$), corresponding to a The dominant peak is at $\tau = -525$~days ($r = 0.139$), corresponding to a
half-solar-cycle lead of seismicity over CR flux. half-solar-cycle lead of seismicity over the global CR index.
At the claimed lag $\tau = +15$~days we find $r = 0.081$. At the claimed lag $\tau = +15$~days we find $r = 0.081$.
Although naive significance is high (4.6$\sigma$ treating bins as i.i.d.), both Although naive significance is high (4.6$\sigma$ treating bins as i.i.d.), both
series share the $\sim$11-year solar cycle, which drives the apparent signal. series share the $\sim$11-year solar cycle, which drives the apparent signal.
@ -758,8 +797,11 @@ surrogate null distribution.
\caption{Null distribution of the peak cross-correlation statistic from 10{,}000 \caption{Null distribution of the peak cross-correlation statistic from 10{,}000
IAAFT surrogates for the raw (blue) and HP-detrended (orange) CR--seismic series. IAAFT surrogates for the raw (blue) and HP-detrended (orange) CR--seismic series.
Vertical dashed lines mark the observed peak for each case. Vertical dashed lines mark the observed peak for each case.
While the raw peak is improbably large under the null, the detrended peak is only The raw peak is improbably large under the null; the detrended peak
marginally significant, and the correlation at the claimed $\tau=+15$~d is not.} ($p < 10^{-4}$, $>3.9\sigma$) is nominally significant but sensitive to
the choice of $N_\text{eff}$ estimator (see Table~\ref{tab:neff}),
and occurs at a lag inconsistent with the claimed mechanism.
The correlation at the claimed $\tau=+15$~d is not significant.}
\label{fig:stress} \label{fig:stress}
\end{figure} \end{figure}
@ -1167,10 +1209,13 @@ Figure~\ref{fig:geodistlag} shows the regression of the optimal lag $\tau^*(s,g)
on great-circle distance $d(s,g)$. on great-circle distance $d(s,g)$.
The slope is $\beta = -0.45$~days/1000\,km ($p = 0.21$, $R^2 = 0.0002$), The slope is $\beta = -0.45$~days/1000\,km ($p = 0.21$, $R^2 = 0.0002$),
indistinguishable from zero. indistinguishable from zero.
If CRs caused earthquakes via a propagating local disturbance, we would expect A local wave-propagation or diffusion mechanism would predict a positive slope
a positive slope (distant pairs have longer propagation delays). (distant pairs accumulate longer propagation delays); the observed null result
The null result is consistent with CR isotropy --- any apparent correlation is inconsistent with such models.
arises from a globally coherent (not distance-dependent) solar-cycle confound. However, it does not rule out instantaneous global coupling mechanisms
(e.g.\ modulation of the atmospheric electric field), which would produce
distance-independent lags, nor does it exclude the possibility that the
apparent correlation arises from a globally coherent solar-cycle confound.
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
@ -1178,7 +1223,10 @@ arises from a globally coherent (not distance-dependent) solar-cycle confound.
\caption{Optimal lag $\tau^*(s,g)$ vs.\ great-circle distance $d(s,g)$ for all \caption{Optimal lag $\tau^*(s,g)$ vs.\ great-circle distance $d(s,g)$ for all
7{,}037 station--cell pairs (grey) and BH-significant pairs (coloured by peak $|r|$). 7{,}037 station--cell pairs (grey) and BH-significant pairs (coloured by peak $|r|$).
The OLS regression line (red) has slope $\beta = -0.45$~days/1000\,km ($p=0.21$), The OLS regression line (red) has slope $\beta = -0.45$~days/1000\,km ($p=0.21$),
consistent with zero. A local propagation mechanism would predict a positive slope.} indistinguishable from zero.
A local propagation or diffusion mechanism predicts a positive slope;
the null result is inconsistent with such models but does not exclude
globally instantaneous coupling.}
\label{fig:geodistlag} \label{fig:geodistlag}
\end{figure} \end{figure}
@ -1261,8 +1309,9 @@ full 1976--2025 record, together with the best-fit sinusoidal envelope.
\end{figure} \end{figure}
The global surrogate test on the full 1976--2025 window yields $p = 0.010$ The global surrogate test on the full 1976--2025 window yields $p = 0.010$
($\sigma = 2.57$) at the dominant peak $\tau = -125$~days --- marginally ($\sigma = 2.57$) at the dominant peak $\tau = -125$~days ---
significant, but at a lag inconsistent with the claimed $+15$~day CR precursor. nominally significant but sensitive to $N_\text{eff}$ estimation
and at a lag inconsistent with the claimed $+15$~day CR precursor.
The sinusoidal fit (Equations~\ref{eq:modA}--\ref{eq:bf}) does \emph{not} prefer The sinusoidal fit (Equations~\ref{eq:modA}--\ref{eq:bf}) does \emph{not} prefer
$\mathcal{M}_B$ over $\mathcal{M}_A$ with the corrected seismic metric: $\mathcal{M}_B$ over $\mathcal{M}_A$ with the corrected seismic metric:
@ -1274,10 +1323,14 @@ $\mathcal{M}_B$ over $\mathcal{M}_A$ with the corrected seismic metric:
\end{itemize} \end{itemize}
A Bayes factor of 0.75 is less than 1.0, indicating that the constant (no A Bayes factor of 0.75 is less than 1.0, indicating that the constant (no
modulation) model is marginally preferred over the sinusoidal model. modulation) model is weakly preferred over the sinusoidal model (following
the interpretation scale of \citet{KassRaftery1995}, $\text{BF} < 1$ favours
$\mathcal{M}_A$; note that this comparison is restricted to the two
hypotheses $\mathcal{M}_A$ and $\mathcal{M}_B$ and does not account for
model uncertainty outside this pair).
With the correct seismic energy metric, the oscillatory rolling cross-correlation With the correct seismic energy metric, the oscillatory rolling cross-correlation
previously attributed to solar-cycle modulation is no longer strongly supported; previously attributed to solar-cycle modulation is no longer supported.
the apparent modulation in the old results was partly an artefact of the invalid The apparent modulation in the old results was partly an artefact of the
summed-$M_W$ metric, which amplified the solar-cycle confound. summed-$M_W$ metric, which amplified the solar-cycle confound.
%%%% ═══════════════════════════════════════════════════════════════════════════ %%%% ═══════════════════════════════════════════════════════════════════════════
@ -1288,22 +1341,37 @@ summed-$M_W$ metric, which amplified the solar-cycle confound.
The raw $r \approx 0.31$ reported by \citet{Homola2023} at $\tau = +15$~days The raw $r \approx 0.31$ reported by \citet{Homola2023} at $\tau = +15$~days
(reduced to $r = 0.081$ with the correct seismic energy metric) and the naive (reduced to $r = 0.081$ with the correct seismic energy metric) and the naive
$p \sim 10^{-72}$ are products of compounding statistical errors: $p \sim 10^{-72}$ result from four compounding errors:
(i) using a physically invalid seismic metric (direct sum of logarithmic $M_W$ (i)~using a physically inappropriate seismic metric (direct summation of
values), which artificially inflated the solar-cycle variation in the seismic series, logarithmic $M_W$ values), which artificially amplifies solar-cycle variation
(ii) treating autocorrelated time series as independent observations, in the seismic series;
(iii) failing to account for the shared solar-cycle trend driving both CR flux and (ii)~treating autocorrelated time series as independent observations ---
seismicity, and (iv) not correcting for scanning over 401 lag values. statistically invalid under the violated serial-independence assumption, since
autocorrelation inflates the nominal sample size by a factor of 3--5
(Table~\ref{tab:neff});
(iii)~failing to account for the shared $\sim$11-year solar-cycle trend driving
both CR flux and seismicity; and
(iv)~not correcting for scanning over 401 lag values.
The solar cycle is the key confounder. The solar cycle is the key confounder.
During solar minimum, the heliospheric magnetic field weakens, allowing more During solar minimum, the heliospheric magnetic field weakens, allowing more
galactic CRs to reach Earth, simultaneously, global seismicity has been reported galactic CRs to reach Earth.
to be slightly elevated during solar minimum phases \citep{Odintsov2006}. Independently, global seismicity has been reported to be slightly elevated
The resulting shared $\sim$11-year oscillation in both series induces a during solar minimum phases \citep{Odintsov2006}.
substantial raw cross-correlation with a lag structure determined by the The resulting shared $\sim$11-year oscillation in both series generates a
phase relationship between the two solar responses --- approximately $\pm$half-cycle substantial raw cross-correlation with a lag structure set by the phase
($\sim$5.5 years $\approx 2{,}000$ days), consistent with the dominant raw peak relationship of their respective solar responses --- approximately
at $\tau = -525$~days. $\pm$half-cycle ($\sim$5.5 years $\approx 2{,}000$ days), consistent with
the dominant raw peak at $\tau = -525$~days.
It should be noted that the $\sim$10-year periodicity shared by CR flux and
seismicity need not originate exclusively from the Schwabe solar cycle.
Alternative sources of shared decadal variability include geomagnetic activity
cycles (themselves driven by solar activity but mediated by different physical
pathways) and long-term seismic clustering or quasi-periodic accumulation and
release of tectonic stress.
Any of these mechanisms could generate the observed coherence without implying
a direct CR--seismic link.
\subsection{Physical Plausibility of the Claimed Mechanism} \subsection{Physical Plausibility of the Claimed Mechanism}
@ -1315,9 +1383,11 @@ transfer meaningful mechanical energy to fault zones, which require shear-stress
changes of order $\sim$0.01--1~MPa to trigger earthquakes. changes of order $\sim$0.01--1~MPa to trigger earthquakes.
Proposed mechanisms via radon ionisation \citep{Pulinets2004} or nuclear Proposed mechanisms via radon ionisation \citep{Pulinets2004} or nuclear
transmutation require orders-of-magnitude larger CR fluxes than observed. transmutation require orders-of-magnitude larger CR fluxes than observed.
The null geographic result (Section~\ref{sec:res:geo}) further argues against The geographic scan (Section~\ref{sec:res:geo}) finds no propagation-delay
a local physical mechanism: any genuine coupling would produce a distance-dependent signature ($\beta = -0.45$~d/1000~km, $p = 0.21$), which is inconsistent
lag between CR detector and seismic source, which is not observed. with simple wave-propagation or diffusion coupling models.
This result does not, however, exclude mechanisms that would act instantaneously
on a global scale, such as modulation of the atmospheric electric field.
\subsection{Comparison with Prior Replication Attempts} \subsection{Comparison with Prior Replication Attempts}
@ -1333,16 +1403,36 @@ out-of-sample validation.
Several limitations should be acknowledged: Several limitations should be acknowledged:
\begin{enumerate} \begin{enumerate}
\item The OOS window (2020--2025) encompasses Solar Cycle~25, a period of \item \textbf{Out-of-sample statistical power.}
rising solar activity after the deep minimum of Cycle~24. The OOS window (2020--2025, $T = 390$ bins, $\approx 5$~yr) encompasses
The absence of a solar minimum in this window limits statistical power. only the rising phase of Solar Cycle~25 and contains no complete solar
\item Seismicity is not stationary; major seismic sequences (e.g.\ Tonga 2022) minimum.
can inflate the seismic metric in individual bins. Because the primary hypothesis concerns a correlation that is modulated
\item The sinusoid fit assumes a constant solar-cycle period, whereas the actual by the solar cycle, a single incomplete cycle provides limited power to
cycle length varies from 9 to 14 years. discriminate a genuine sub-cycle signal from noise.
\item Out-of-sample $p_\text{oos}$ from script~08 was not produced due to The OOS failure to replicate ($p_\text{global} = 0.100$) should therefore
insufficient NMDB historical data in the default path; the OOS result from be interpreted as \emph{consistent with} the null hypothesis rather than as
the dedicated script~07 ($10^5$ surrogates) is authoritative. strong independent evidence against the claimed effect; it carries
substantially less weight than the 44-year in-sample analysis.
\item \textbf{Seismicity non-stationarity.}
Seismicity is not stationary; major seismic sequences (e.g.\ Tonga 2022)
can dominate the seismic metric in individual bins, introducing transient
structure that is not related to CR flux.
\item \textbf{Sinusoidal model rigidity.}
The sinusoidal modulation fit assumes a constant solar-cycle period,
whereas the actual Schwabe cycle length varies from 9 to 14 years.
A more flexible model (e.g.\ a time-warped sinusoid) might alter the BF
comparison.
\item \textbf{Untested mechanisms.}
This analysis tests for linear cross-correlation between the global CR
index and a globally-aggregated seismic energy metric.
Threshold effects (e.g.\ CR triggering only above a critical fault stress),
nonlinear coupling, frequency-selective interaction, or extreme-event
coupling are not addressed and cannot be excluded on the basis of these
results.
\end{enumerate} \end{enumerate}
%%%% ═══════════════════════════════════════════════════════════════════════════ %%%% ═══════════════════════════════════════════════════════════════════════════
@ -1357,20 +1447,21 @@ Our principal findings are:
\begin{enumerate} \begin{enumerate}
\item The raw cross-correlation $r(+15\,\text{d}) = 0.081$ (corrected seismic \item The raw cross-correlation $r(+15\,\text{d}) = 0.081$ (corrected seismic
energy metric) is modest and misleading; it is driven by a shared energy metric) is modest; it is consistent with a shared $\sim$10-year
$\sim$10-year solar-cycle modulation of both CR flux and global seismicity, solar-cycle modulation of both CR flux and global seismicity rather than
not by a physical CR$\to$seismic mechanism. a direct CR$\to$seismic mechanism.
The larger value ($r \approx 0.31$) reported by \citet{Homola2023} results The larger value ($r \approx 0.31$) reported by \citet{Homola2023} results
from the physically invalid practice of directly summing logarithmic $M_W$ from the physically inappropriate practice of directly summing logarithmic
values rather than the underlying energies. $M_W$ values rather than the underlying energies.
\item After solar-cycle detrending, $r(+15\,\text{d})$ falls to $0.027$ (HP), \item After solar-cycle detrending, $r(+15\,\text{d})$ falls to $0.027$ (HP),
$0.030$ (STL), or $0.037$ (sunspot regression) --- all within the surrogate $0.030$ (STL), or $0.037$ (sunspot regression) --- all within the surrogate
null distribution and consistent with zero. null distribution and consistent with zero.
\item No geographic localisation is detected: the optimal lag between CR station \item No propagation-delay signature is detected: the optimal lag between CR
and seismic cell shows no distance dependence ($\beta = -0.45$~d/1000~km, station and seismic cell shows no distance dependence ($\beta = -0.45$~d/1000~km,
$p = 0.21$), inconsistent with a local propagation mechanism. $p = 0.21$), inconsistent with local wave-propagation or diffusion models,
though globally instantaneous coupling mechanisms remain untested.
\item A pre-registered out-of-sample test on 2020--2025 yields \item A pre-registered out-of-sample test on 2020--2025 yields
$r(+15\,\text{d}) = 0.030$ and $p_\text{global} = 0.100$, entirely $r(+15\,\text{d}) = 0.030$ and $p_\text{global} = 0.100$, entirely
@ -1405,8 +1496,12 @@ Our principal findings are:
\end{itemize} \end{itemize}
\end{enumerate} \end{enumerate}
We conclude that there is no statistically credible evidence for a physical We find no statistically robust evidence for a causal relationship between
causal link between galactic cosmic-ray flux and global seismicity. galactic cosmic-ray flux and global seismicity within the tested statistical
frameworks, after controlling for solar-cycle modulation.
Threshold effects, nonlinear triggering, and extreme-event coupling ---
mechanisms not assessed in the present analysis --- cannot be excluded on
the basis of these results alone.
%%%% ═══════════════════════════════════════════════════════════════════════════ %%%% ═══════════════════════════════════════════════════════════════════════════
\section*{Data Availability} \section*{Data Availability}

73
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@ -2,55 +2,56 @@
\contentsline {section}{\numberline {2}Data}{6}{section.2}% \contentsline {section}{\numberline {2}Data}{6}{section.2}%
\contentsline {subsection}{\numberline {2.1}Cosmic-Ray Flux: NMDB Neutron Monitors}{6}{subsection.2.1}% \contentsline {subsection}{\numberline {2.1}Cosmic-Ray Flux: NMDB Neutron Monitors}{6}{subsection.2.1}%
\contentsline {subsection}{\numberline {2.2}Seismic Activity: USGS Earthquake Catalogue}{6}{subsection.2.2}% \contentsline {subsection}{\numberline {2.2}Seismic Activity: USGS Earthquake Catalogue}{6}{subsection.2.2}%
\contentsline {subsection}{\numberline {2.3}Solar Activity: SIDC Sunspot Number}{6}{subsection.2.3}% \contentsline {subsection}{\numberline {2.3}Solar Activity: SIDC Sunspot Number}{7}{subsection.2.3}%
\contentsline {section}{\numberline {3}Methods}{7}{section.3}% \contentsline {section}{\numberline {3}Methods}{7}{section.3}%
\contentsline {subsection}{\numberline {3.1}Cross-Correlation at Lag $\tau $}{7}{subsection.3.1}% \contentsline {subsection}{\numberline {3.1}Cross-Correlation at Lag $\tau $}{7}{subsection.3.1}%
\contentsline {subsection}{\numberline {3.2}Effective Degrees of Freedom}{7}{subsection.3.2}% \contentsline {subsection}{\numberline {3.2}Effective Degrees of Freedom}{7}{subsection.3.2}%
\contentsline {subsection}{\numberline {3.3}Surrogate Significance Tests}{7}{subsection.3.3}% \contentsline {subsection}{\numberline {3.3}Surrogate Significance Tests}{8}{subsection.3.3}%
\contentsline {subsubsection}{\numberline {3.3.1}Phase Randomisation}{7}{subsubsection.3.3.1}% \contentsline {subsubsection}{\numberline {3.3.1}Phase Randomisation}{8}{subsubsection.3.3.1}%
\contentsline {subsubsection}{\numberline {3.3.2}IAAFT Surrogates}{8}{subsubsection.3.3.2}% \contentsline {subsubsection}{\numberline {3.3.2}IAAFT Surrogates}{8}{subsubsection.3.3.2}%
\contentsline {subsubsection}{\numberline {3.3.3}Block-Bootstrap Surrogates}{8}{subsubsection.3.3.3}% \contentsline {subsubsection}{\numberline {3.3.3}Block-Bootstrap Surrogates}{8}{subsubsection.3.3.3}%
\contentsline {subsubsection}{\numberline {3.3.4}Global $p$-Value}{8}{subsubsection.3.3.4}% \contentsline {subsubsection}{\numberline {3.3.4}Global $p$-Value}{8}{subsubsection.3.3.4}%
\contentsline {subsubsection}{\numberline {3.3.5}GPU Acceleration}{8}{subsubsection.3.3.5}% \contentsline {subsubsection}{\numberline {3.3.5}GPU Acceleration}{9}{subsubsection.3.3.5}%
\contentsline {subsection}{\numberline {3.4}Solar-Cycle Detrending}{9}{subsection.3.4}% \contentsline {subsection}{\numberline {3.4}Solar-Cycle Detrending}{9}{subsection.3.4}%
\contentsline {subsection}{\numberline {3.5}Partial Correlation Analysis}{9}{subsection.3.5}% \contentsline {subsection}{\numberline {3.5}Partial Correlation Analysis}{10}{subsection.3.5}%
\contentsline {subsection}{\numberline {3.6}Nonlinear Dependence Tests}{10}{subsection.3.6}% \contentsline {subsection}{\numberline {3.6}Nonlinear Dependence Tests}{10}{subsection.3.6}%
\contentsline {paragraph}{Spectral coherence.}{10}{section*.2}% \contentsline {paragraph}{Spectral coherence.}{10}{section*.2}%
\contentsline {paragraph}{Mutual information.}{10}{section*.3}% \contentsline {paragraph}{Mutual information.}{10}{section*.3}%
\contentsline {subsection}{\numberline {3.7}Geographic Localisation Scan}{10}{subsection.3.7}% \contentsline {subsection}{\numberline {3.7}Geographic Localisation Scan}{10}{subsection.3.7}%
\contentsline {subsection}{\numberline {3.8}Pre-Registered Out-of-Sample Validation}{11}{subsection.3.8}% \contentsline {subsection}{\numberline {3.8}Pre-Registered Out-of-Sample Validation}{11}{subsection.3.8}%
\contentsline {paragraph}{Confirmatory versus exploratory analyses.}{11}{section*.4}%
\contentsline {subsection}{\numberline {3.9}Combined Timeseries: Sinusoidal Envelope Fit}{11}{subsection.3.9}% \contentsline {subsection}{\numberline {3.9}Combined Timeseries: Sinusoidal Envelope Fit}{11}{subsection.3.9}%
\contentsline {section}{\numberline {4}Results}{12}{section.4}% \contentsline {section}{\numberline {4}Results}{12}{section.4}%
\contentsline {subsection}{\numberline {4.1}Raw Pairwise Correlations Between CR, Seismic, and Sunspot Data}{12}{subsection.4.1}% \contentsline {subsection}{\numberline {4.1}Raw Pairwise Correlations Between CR, Seismic, and Sunspot Data}{12}{subsection.4.1}%
\contentsline {subsubsection}{\numberline {4.1.1}CR index: station distribution}{12}{subsubsection.4.1.1}% \contentsline {subsubsection}{\numberline {4.1.1}CR index: station distribution}{13}{subsubsection.4.1.1}%
\contentsline {subsubsection}{\numberline {4.1.2}Seismic energy metric}{12}{subsubsection.4.1.2}% \contentsline {subsubsection}{\numberline {4.1.2}Seismic energy metric}{13}{subsubsection.4.1.2}%
\contentsline {subsubsection}{\numberline {4.1.3}Sunspot number}{12}{subsubsection.4.1.3}% \contentsline {subsubsection}{\numberline {4.1.3}Sunspot number}{13}{subsubsection.4.1.3}%
\contentsline {subsubsection}{\numberline {4.1.4}Correlation results}{13}{subsubsection.4.1.4}% \contentsline {subsubsection}{\numberline {4.1.4}Correlation results}{13}{subsubsection.4.1.4}%
\contentsline {paragraph}{CR vs.\ seismicity.}{13}{section*.4}% \contentsline {paragraph}{CR vs.\ seismicity.}{13}{section*.6}%
\contentsline {paragraph}{CR vs.\ sunspot number.}{13}{section*.5}% \contentsline {paragraph}{CR vs.\ sunspot number.}{14}{section*.7}%
\contentsline {paragraph}{Sunspot vs.\ seismicity.}{13}{section*.6}% \contentsline {paragraph}{Sunspot vs.\ seismicity.}{14}{section*.8}%
\contentsline {subsubsection}{\numberline {4.1.5}Interpretation: a confounding triangle}{13}{subsubsection.4.1.5}% \contentsline {subsubsection}{\numberline {4.1.5}Interpretation: a confounding triangle}{14}{subsubsection.4.1.5}%
\contentsline {subsection}{\numberline {4.2}In-Sample Replication (1976--2019)}{14}{subsection.4.2}% \contentsline {subsection}{\numberline {4.2}In-Sample Replication (1976--2019)}{17}{subsection.4.2}%
\contentsline {subsection}{\numberline {4.3}IAAFT Surrogate Test}{17}{subsection.4.3}% \contentsline {subsection}{\numberline {4.3}IAAFT Surrogate Test}{18}{subsection.4.3}%
\contentsline {subsection}{\numberline {4.4}Effect of Solar-Cycle Detrending}{18}{subsection.4.4}% \contentsline {subsection}{\numberline {4.4}Effect of Solar-Cycle Detrending}{19}{subsection.4.4}%
\contentsline {subsection}{\numberline {4.5}Detrending Robustness}{18}{subsection.4.5}% \contentsline {subsection}{\numberline {4.5}Detrending Robustness}{19}{subsection.4.5}%
\contentsline {subsection}{\numberline {4.6}Comparison of $N_\text {eff}$ Estimators}{18}{subsection.4.6}% \contentsline {subsection}{\numberline {4.6}Comparison of $N_\text {eff}$ Estimators}{19}{subsection.4.6}%
\contentsline {subsection}{\numberline {4.7}Magnitude Threshold Sensitivity}{20}{subsection.4.7}% \contentsline {subsection}{\numberline {4.7}Magnitude Threshold Sensitivity}{21}{subsection.4.7}%
\contentsline {subsection}{\numberline {4.8}Block-Bootstrap Surrogate Comparison}{20}{subsection.4.8}% \contentsline {subsection}{\numberline {4.8}Block-Bootstrap Surrogate Comparison}{21}{subsection.4.8}%
\contentsline {subsection}{\numberline {4.9}Partial Correlation: Controlling for Sunspot Number}{21}{subsection.4.9}% \contentsline {subsection}{\numberline {4.9}Partial Correlation: Controlling for Sunspot Number}{22}{subsection.4.9}%
\contentsline {subsection}{\numberline {4.10}Spectral Coherence and Mutual Information}{21}{subsection.4.10}% \contentsline {subsection}{\numberline {4.10}Spectral Coherence and Mutual Information}{22}{subsection.4.10}%
\contentsline {paragraph}{Coherence.}{21}{section*.20}% \contentsline {paragraph}{Coherence.}{22}{section*.22}%
\contentsline {paragraph}{Mutual information.}{22}{section*.21}% \contentsline {paragraph}{Mutual information.}{23}{section*.23}%
\contentsline {subsection}{\numberline {4.11}Missing-Data Sensitivity}{22}{subsection.4.11}% \contentsline {subsection}{\numberline {4.11}Missing-Data Sensitivity}{23}{subsection.4.11}%
\contentsline {subsection}{\numberline {4.12}Bin-Size Sensitivity}{24}{subsection.4.12}% \contentsline {subsection}{\numberline {4.12}Bin-Size Sensitivity}{25}{subsection.4.12}%
\contentsline {subsection}{\numberline {4.13}Earthquake Declustering (Gardner--Knopoff)}{24}{subsection.4.13}% \contentsline {subsection}{\numberline {4.13}Earthquake Declustering (Gardner--Knopoff)}{25}{subsection.4.13}%
\contentsline {subsection}{\numberline {4.14}Sub-Period Analysis by Solar Cycle}{25}{subsection.4.14}% \contentsline {subsection}{\numberline {4.14}Sub-Period Analysis by Solar Cycle}{26}{subsection.4.14}%
\contentsline {subsection}{\numberline {4.15}Geographic Localisation}{25}{subsection.4.15}% \contentsline {subsection}{\numberline {4.15}Geographic Localisation}{26}{subsection.4.15}%
\contentsline {subsection}{\numberline {4.16}Pre-Registered Out-of-Sample Validation (2020--2025)}{28}{subsection.4.16}% \contentsline {subsection}{\numberline {4.16}Pre-Registered Out-of-Sample Validation (2020--2025)}{29}{subsection.4.16}%
\contentsline {subsection}{\numberline {4.17}Combined 1976--2025 Analysis: Sinusoidal Modulation}{29}{subsection.4.17}% \contentsline {subsection}{\numberline {4.17}Combined 1976--2025 Analysis: Sinusoidal Modulation}{30}{subsection.4.17}%
\contentsline {section}{\numberline {5}Discussion}{30}{section.5}% \contentsline {section}{\numberline {5}Discussion}{31}{section.5}%
\contentsline {subsection}{\numberline {5.1}Why Does the Raw Correlation Appear So Strong?}{30}{subsection.5.1}% \contentsline {subsection}{\numberline {5.1}Why Does the Raw Correlation Appear So Strong?}{31}{subsection.5.1}%
\contentsline {subsection}{\numberline {5.2}Physical Plausibility of the Claimed Mechanism}{30}{subsection.5.2}% \contentsline {subsection}{\numberline {5.2}Physical Plausibility of the Claimed Mechanism}{32}{subsection.5.2}%
\contentsline {subsection}{\numberline {5.3}Comparison with Prior Replication Attempts}{31}{subsection.5.3}% \contentsline {subsection}{\numberline {5.3}Comparison with Prior Replication Attempts}{32}{subsection.5.3}%
\contentsline {subsection}{\numberline {5.4}Limitations}{31}{subsection.5.4}% \contentsline {subsection}{\numberline {5.4}Limitations}{32}{subsection.5.4}%
\contentsline {section}{\numberline {6}Conclusions}{31}{section.6}% \contentsline {section}{\numberline {6}Conclusions}{33}{section.6}%

11
paper/refs.bib
View file

@ -185,6 +185,17 @@
howpublished = {\url{https://www.nmdb.eu}}, howpublished = {\url{https://www.nmdb.eu}},
} }
@article{KassRaftery1995,
author = {Kass, Robert E. and Raftery, Adrian E.},
title = {Bayes Factors},
journal = {Journal of the American Statistical Association},
year = {1995},
volume = {90},
number = {430},
pages = {773--795},
doi = {10.1080/01621459.1995.10476572},
}
@article{Kraskov2004, @article{Kraskov2004,
author = {Kraskov, Alexander and St{\"o}gbauer, Harald and Grassberger, Peter}, author = {Kraskov, Alexander and St{\"o}gbauer, Harald and Grassberger, Peter},
title = {Estimating mutual information}, title = {Estimating mutual information},