models are actually slightly better than the $f_{{\rm esc,Ly}\alpha}$ models
(Table 7 and Figure 12). The $L$(LyC) predictions suffered from the large
uncertainty in estimating the intrinsic LyC production from the FUV continuum.
The available Balmer line measurements make estimating the intrinsic
Ly$\alpha$ luminosity less of a concern. Another explanation for the better
performance of the $L$(Ly$\alpha$) predictions may be mundane; since it
depends on predicting the intrinsic Ly$\alpha$, $f_{{\rm esc,Ly}\alpha}$ is a
more model-dependent measurement than $L$(Ly$\alpha$) and consequently has a
greater uncertainty (26% on average for $f_{{\rm esc,Ly}\alpha}$ vs 21% for
the Ly$\alpha$ flux alone). Again the $L$(Ly$\alpha$) JWST model (Table 7 and
Figure 12b) has slightly worse $R^{2}$ and RMS metrics than the fiducial model
because of the lack of information about line-of-sight gas.

Figure 12: Examples of $L$(Ly$\alpha$) model predictions using the variable
sets for the fiducial model (a) and the JWST model (b). Symbols are the same
as in Figure 2. We exclude galaxies with negative $L$(Ly$\alpha$). The models
do a better job at predicting $L$(Ly$\alpha$) compared to $f_{{\rm
esc,Ly}\alpha}$.

Tables 10 and 11 in the Appendix list the top-ranked variables for predicting
$f_{{\rm esc,Ly}\alpha}$ and $L$(Ly$\alpha$). For $f_{{\rm esc,Ly}\alpha}$, we
find that H i absorption strength and nebular dust attenuation are two of the
most important predictive variables. In contrast, the UV dust attenuation is
less important, always ranking after E(B-V)neb in forward and backward
selection. As a nebular emission line, Ly$\alpha$ escape is more closely
linked to the nebular attenuation rather than the attenuation experienced by
the stellar light.

For $L$(Ly$\alpha$), the most important variables include $\Sigma_{\rm SFR}$,
$M_{\rm 1500}$, E(B-V)neb, EW(H$\beta$), and EW(H i,abs). These five variables
are also statistically significant in either the fiducial model ($\Sigma_{\rm
SFR}$), the fiducial+EW(H i,abs) model (EW(H$\beta$), EW(H i,abs)), or both
(E(B-V)neb and $M_{\rm 1500}$). The dependence on UV luminosity reflects the
fact that higher SFRs enhance Ly$\alpha$ production, while the dependence on
E(B-V)neb and EW(H i,abs) arises because lower dust attenuation and lower H i
column densities enhance Ly$\alpha$ escape. As a recombination line, the
H$\beta$ EW is also directly linked to nebular Ly$\alpha$ production. While
the dependence on $\Sigma_{\rm SFR}$ may reflect the role of feedback in
Ly$\alpha$ escape, it may also serve to quantify aperture losses, as more
extended galaxies may have more of their Ly$\alpha$ emission scatter outside
the COS aperture.

Runnholm et al. (2020) also assess the most important variables in predicting
$L$(Ly$\alpha$) using the Lyman-$\alpha$ Reference Sample (LARS). They find
that the top five ranked variables by both forward and backward selection are
SFR, E(B-V)neb, $M_{*}$, $r_{\rm 50}$, and the gas covering fraction. If using
observables, the top variables are the FUV luminosity and the UV size. Despite
the different methodologies between the LARS Ly$\alpha$ measurements and the
LzLCS+ Ly$\alpha$ measurements, our results generally agree with their
findings, as $\Sigma_{\rm SFR}$, E(B-V)neb, and the galaxy FUV luminosity also
appear among our most important predictors.

##  5 Discussion

Both theoretical and observational studies have long recognized that LyC
escape is likely anisotropic due to the inherently inhomogeneous structure of
the ISM (e.g., Gnedin et al., 2008; Wise & Cen, 2009; Kim et al., 2013;
Zastrow et al., 2013; Paardekooper et al., 2015; Cen & Kimm, 2015; Trebitsch
et al., 2017; Keenan et al., 2017; Rivera-Thorsen et al., 2017, 2019; Kim et
al., 2023). LyC may escape in a “picket-fence” geometry, emerging only through
holes in the ISM (e.g., Heckman et al., 2001), and simulations find that
supernova feedback may carve these low-density paths in the ISM (e.g., Wise &
Cen, 2009; Cen & Kimm, 2015; Paardekooper et al., 2015; Trebitsch et al.,
2017). Observationally, the detection of residual flux from saturated low-
ionization absorption lines (e.g., Heckman et al., 2001, 2011; Gazagnes et
al., 2018) and the co-existence of narrow Ly$\alpha$ emission with underlying
broad absorption (e.g., McKinney et al., 2019) provide evidence for optical
depth variations within galaxies. Highly ionized channels observed in some
low-redshift galaxies (e.g., Zastrow et al., 2013; Bik et al., 2018) and
spatially resolved LyC observations in the lensed Sunburst Arc at $z=2.37$
(Rivera-Thorsen et al., 2019; Kim et al., 2023) likewise imply that LyC may
escape through narrow opening angles, perhaps driven by outflows (e.g., Amorín
et al., 2024). Even when $f_{\rm esc}$ is large, with escape occurring in most
or all directions, H i column density variations will still lead to variations
in the observed $f_{\rm esc}$ along different lines of sight (e.g., Gazagnes
et al., 2020).

Because of the anisotropy of LyC escape, estimating global $f_{\rm esc}$
values from line-of-sight LyC detections is difficult, particularly since the
observed $f_{\rm esc}$ depends both on galaxy properties and on orientation.
The multivariate Cox models present new evidence for the anisotropy of LyC
escape by showing that the global properties of the strongest LCEs ($f_{\rm
esc}$$\gtrsim 0.4$) do not distinguish them from weaker LCEs ($f_{\rm
esc}$$\sim 0.04$; see §3.6). At $z\sim 3$, Nakajima et al. (2020) reach a
similar conclusion, finding that high O32 galaxies can have wide variations in
$f_{\rm esc}$, despite sharing comparable spectral properties. We find that
the only variable that successfully predicts the high observed $f_{\rm esc}$
of the strongest LCEs is EW(H i,abs), which traces the line-of-sight H i
absorption. This result supports the picture described by Gazagnes et al.
(2020), where galaxies with high O32 may have sufficient ionizing radiation to
ionize most lines of sight, but where the highest $f_{\rm esc}$ occurs in only
the most diffuse channels.

Multivariate survival analysis models such as those presented here may offer a
tool for quantifying the line-of-sight variation in $f_{\rm esc}$ among galaxy
populations. Given a large reference sample of galaxies with measurements of
relevant global properties, the Cox models generate the probability
distribution of $f_{\rm esc}$ for a given set of variables. If the variation
in the observed $f_{\rm esc}$ for similar galaxies results only from
orientation effects, the derived probability distributions should reflect the
distribution of $f_{\rm esc}$ across all sightlines.

Although the outsized importance of EW(H i,abs) in accurately predicting high
observed $f_{\rm esc}$ suggests that favorable orientation accounts for the
strongest LCEs in the LzLCS+, orientation alone may not fully explain the
scatter between predicted and observed $f_{\rm esc}$ across the entire LzLCS+
sample. LyC escape will depend on local properties, which global variables may
not accurately capture (e.g., Rivera-Thorsen et al., 2019). Observational
studies at higher spatial resolution and simulations that track the evolution
of $f_{\rm esc}$ with high spatial resolution will help reveal the origin of
$f_{\rm esc}$ variations in otherwise similar galaxies.

The variable rankings in §3.3 show that the two most essential variables in
predicting the line-of-sight $f_{\rm esc}$ are variables sensitive to the
line-of-sight H i gas (EW(H i,abs)) and the line-of-sight dust (E(B-V)UV or
$\beta_{\rm 1550}$). Although $z>6$ observations will not be able to measure
the former, $\beta_{\rm 1550}$ is easily accessible. JWST observations of the
epoch of reionization are rapidly expanding the available measurements of
$\beta_{\rm 1550}$ at high redshift (e.g., Schaerer et al., 2022a; Mascia et
al., 2023b; Saxena et al., 2023; Morishita et al., 2023), and this variable
alone can provide useful constraints on $f_{\rm esc}$ (Chisholm et al., 2022).
By examining the spread of $\beta_{\rm 1550}$ values for a fixed intrinsic
$M_{\rm 1500}$ or set of galaxy properties, high-redshift studies could gain
insight into the possible variation in the line-of-sight $f_{\rm esc}$ among a
population, at least the variation due to changing levels of dust attenuation.
To understand the H i component of the LyC absorption and its variation, high-
redshift studies will need to rely on simulations and lower-redshift
observations.

Our models provide some clues as to which physical properties most affect a
galaxy’s H i distribution and resulting $f_{\rm esc}$. In the absence of EW(H
i,abs) and Ly$\alpha$ measurements, which more directly trace H i, the models
find that $\Sigma_{\rm SFR}$ and O32 are the most important variables in
predicting $f_{\rm esc}$, given constraints on the dust attenuation from
$\beta_{\rm 1550}$ (§3.4). These variables suggest that feedback is key in
determining a galaxy’s average H i column density. Interestingly, we find in
§3.5 that O32 may be more important in lower mass galaxies ($\log_{\rm
10}$($M_{*}$/ M☉) $<8.8$), whereas $\Sigma_{\rm SFR}$ takes on greater
importance in the higher mass LzLCS+ galaxies. Previous studies have suggested
that the mechanism responsible for LyC escape may be different in different
galaxy populations (e.g., Flury et al., 2022b; Katz et al., 2023). Here, we
find that differences in the multivariate $f_{\rm esc}$ models are
specifically associated with galaxy mass, rather than luminosity. We
hypothesize that the typical star formation histories of the low- and high-
mass LzLCS+ galaxies may differ, with the lower-mass starbursts exhibiting
burstier star formation (e.g., Lee et al., 2007). Radiative feedback in
extremely young, strong starbursts may drive LyC escape over wide opening
angles in these low-mass galaxies, whereas the cumulative effect of supernovae
in longer-lived concentrated starbursts could regulate LyC escape at higher
masses (e.g., Bremer & Dayal, 2023).

While the same physical processes, such as bursty star formation with
radiative feedback or an extended star formation episode with supernova
feedback, may occur at high redshift, they may not occur in exactly the same
type of galaxies as the LzLCS+. In particular, at a given stellar mass, a
high-redshift galaxy could have a different gas mass, total mass, or star
formation history compared to the same stellar mass galaxy at low redshift.
Nevertheless, the distinct models for the low- vs. high-mass subsets in the
LzLCS+ demonstrate that different parameters and physical mechanisms may
regulate LyC escape in different types of galaxies. These differences could
explain why some studies disagree regarding the properties of LCEs (e.g.,
Alexandroff et al., 2015; Rutkowski et al., 2017; Izotov et al., 2018b; Naidu
et al., 2018). Depending on the sample probed, high O32 or high $\Sigma_{\rm
SFR}$ may or may not be a relevant predictor of $f_{\rm esc}$. Understanding
the origin of the relationships between O32, $\Sigma_{\rm SFR}$, and $f_{\rm
esc}$ in low- vs. high-mass LzLCS+ galaxies will require more observational
and theoretical studies examining the interplay between star formation
history, geometry, and feedback in these types of galaxies.

##  6 Summary

LyC escape depends on a range of galaxy properties, from gas and dust
distributions in the ISM to galaxy star formation histories and the resulting
stellar feedback. Because of this complexity, $f_{\rm esc}$ correlates
observationally with a variety of parameters, and correlations with individual
variables show high scatter. Using the results of the LzLCS and other $z\sim
0.3$ LyC observations from the literature, we have generated new multivariate
models to predict $f_{\rm esc}$. We use the statistical technique of survival
analysis, specifically the Cox proportional hazards model (Cox, 1972), which
accounts for data from both LyC detections and $f_{\rm esc}$ upper limits from
non-detections. With these models, we explore which combinations of variables
best predict $f_{\rm esc}$ and discuss the possible physical basis for these
trends.

We summarize our main findings below.

  1. 1.

The $f_{\rm esc}$ predictions from our fiducial model match the observed
$f_{\rm esc}$ of $z\sim 0.3$ LCEs with an RMS of 0.36 dex, and our best-
performing model, which includes H i absorption lines, reaches an RMS of 0.31
dex. These multivariate models offer a substantial improvement over
correlations with single variables, which can span $\gtrsim$ 2 dex in $f_{\rm
esc}$ for a given galaxy property (e.g., Wang et al., 2021; Flury et al.,
2022b; Saldana-Lopez et al., 2022; Chisholm et al., 2022). (§§3.1-3.2).

  2. 2.

Our best-performing model accurately predicts $f_{\rm esc}$ even for galaxies
that are outliers in a single-variable selection. This model, which includes H
i absorption line measurements, is the only model that reproduces the high
observed $f_{\rm esc}$ values of the strongest LCEs in the LzLCS+. Among the
variables we consider, weak H i absorption is the only distinctive property of
these strong LCEs, which suggests that these high $f_{\rm esc}$ values may
occur only along fortuitous sightlines. (§3.6).

  3. 3.

The most important variables in the models, as determined by forward and
backward selection, are the EW of the H i Lyman series absorption lines and
either E(B-V)UV or the UV slope $\beta_{\rm 1550}$. These properties trace the
line-of-sight H i absorption and UV dust attenuation, which determine the
line-of-sight $f_{\rm esc}$ that we measure (e.g., Saldana-Lopez et al.,
2022). In our fiducial model, E(B-V)UV is a statistically significant
variable, along with $f_{{\rm esc,Ly}\alpha}$, $\Sigma_{\rm SFR}$, E(B-V)neb,
and O32. Excluding E(B-V)UV or $f_{{\rm esc,Ly}\alpha}$ has the greatest
adverse effects on model performance, and including $f_{{\rm esc,Ly}\alpha}$
appears to be particularly important for identifying non-LyC emitters. These
analyses show which variables are the most important to include for accurate
predictions; models using only the statistically significant variables or the
3-5 top-ranked variables achieve comparable accuracy to models with a longer
list of inputs (§§3.2-3.3).

  4. 4.

We generate a “JWST model” for predicting $f_{\rm esc}$, which can apply to
$z>6$ observations. The model excludes Ly$\alpha$ and absorption line
measurements, which will be inaccessible for most $z>6$ galaxies. When
compared with the $z\sim 0.3$ LCEs, this model has a higher scatter
(RMS$=0.47$ dex) than the fiducial model, but it can distinguish LCEs from
non-emitters. Three variables in this model are statistically significant:
$\beta_{\rm 1550}$, $\Sigma_{\rm SFR}$, and O32. These three variables alone
can predict $f_{\rm esc}$ with an RMS of 0.46 dex in the $z\sim 0.3$ sample.
(§3.4).

  5. 5.

We find that $f_{\rm esc}$ may depend on different variables for high- vs.
low-mass galaxies. $\Sigma_{\rm SFR}$ is statistically significant for the
high-mass subsample but not the low-mass subsample and is the top-ranked
variable for the high-mass subsample by forward and backward selection. In
contrast, $M_{\rm 1500}$ and O32 are statistically significant for the low-
mass subsample but not for the high-mass subsample. These differences suggest
that the physical causes of LyC escape and the feedback mechanisms involved
could differ across the galaxy population, with ionization and radiative
feedback potentially playing a greater role in low-mass galaxies. (§3.5).

  6. 6.

The multivariate Cox models are less successful at accurately predicting
alternative measures of LyC escape, such as $F_{\lambda{\rm
LyC}}/F_{\lambda{\rm 1100}}$ and the LyC luminosity. We hypothesize that
accurately predicting these properties requires information about the
unattenuated SED shape, which is not included in our set of variables. (§4.1).

  7. 7.

We also create Cox models to predict Ly$\alpha$, specifically the $f_{{\rm
esc,Ly}\alpha}$ and Ly$\alpha$ luminosity. Unlike the LyC $f_{\rm esc}$
predictions, H i absorption EW and E(B-V)neb, rather than E(B-V)UV, are two of
the most important variables for predicting $f_{{\rm esc,Ly}\alpha}$. For
$L$(Ly$\alpha$), top-ranked and statistically significant variables are the H
i absorption EW, E(B-V)neb, $M_{\rm 1500}$, EW(H$\beta$), and $\Sigma_{\rm
SFR}$, which are similar to results found for the LARS sample (Runnholm et
al., 2020). (§4.2).

Our models highlight the complexity of LyC escape and the dependence of
$f_{\rm esc}$ on multiple variables. Multivariate Cox models represent a new
tool to investigate the relationships between $f_{\rm esc}$ and galaxy
properties and to predict $f_{\rm esc}$ in the epoch of reionization. These
models offer a substantial improvement over $f_{\rm esc}$ predictions based on
a single variable, and the models presented here can be refined and expanded
to incorporate future observations. Our results show which variables have the
greatest effect on $f_{\rm esc}$ predictions for the LzLCS+ sample and for
galaxies in different mass ranges. By exploring these same variables, future
simulations could try to reproducing these scalings and determine their
physical origin. These flexible multivariate models also offer an empirical
approach to predicting $f_{\rm esc}$ at high redshift. In a follow-up paper
(Paper II, Jaskot et al., in prep.), we apply Cox models derived from the
LzLCS+ to $z\sim 3$ and $z>6$ samples and provide the best-fit models to the
community for application to future observations.333We have also created a
python script, available at https://github.com/sflury/LyCsurv, that generates
Cox model $f_{\rm esc}$ predictions using any desired combination of variables
from the LzLCS+. The LzLCS+ dataset used in this paper is available at the
same page, and version 0.1.0 of the code is archived in Zenodo (Flury et al.,
2024).

We thank Kate Follette for interesting discussions that led to this project,
and we thank the anonymous referee for comments that improved the clarity of
this work. AEJ and SRF acknowledge support from NASA through grant HST-
GO-15626. STScI is operated by AURA under NASA contract NAS-5-26555. ASL
acknowledges support from Knut and Alice Wallenberg Foundation. MT
acknowledges support from the NWO grant 0.16.VIDI.189.162 (“ODIN”). Tables
8-11 list the four top-ranked variables by forward selection, backward
selection, and an MC rank ordering for the $F_{\lambda{\rm
LyC}}/F_{\lambda{\rm 1100}}$, $L$(LyC), $f_{{\rm esc,Ly}\alpha}$, and
$L$(Ly$\alpha$) predictions. We describe these ranking methods in §2.4 and
discuss the results in §§4.1 and 4.2. The “Full Model” uses $\beta_{\rm 1550}$
as a measure of UV dust attenuation and includes multiple variables that trace
Ly$\alpha$ or UV absorption line strength. The “Fiducial+HI Model” uses
E(B-V)UV to quantify dust attenuation, $f_{{\rm esc,Ly}\alpha}$ as a measure
of Ly$\alpha$, and EW(H i,abs) as the only absorption line variable. The “JWST
Model” excludes absorption line and Ly$\alpha$ variables. =2.25in

Table 8: Most Important Variables for $F_{\lambda{\rm LyC}}/F_{\lambda{\rm
1100}}$ Predictions

Rank | Full Model | Fiducial+HI Model | JWST Model
---|---|---|---
| Forward | Backward | Forward | Backward | Forward | Backward
Top-Ranked Variables
1 | EW(H i,abs) | EW(H i,abs) | EW(H i,abs) | EW(H i,abs) |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$)
2 |  $R_{l}$(H i,abs) | $M_{\rm 1500}$ | $M_{\rm 1500}$ | $M_{\rm 1500}$ | $\beta_{\rm 1550}$ |  $\log_{\rm 10}$(O32)
3 | $M_{\rm 1500}$ | EW(Ly$\alpha$) | $f_{{\rm esc,Ly}\alpha}$ | $f_{{\rm esc,Ly}\alpha}$ | 12+$\log_{\rm 10}$(O/H) |  $\log_{\rm 10}$(EW(H$\beta$))
4 | $\beta_{\rm 1550}$ | $\beta_{\rm 1550}$ |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) | E(B-V)neb |  $\log_{\rm 10}$(EW(H$\beta$)) | $\beta_{\rm 1550}$
Top Variables by MC Rank Order
| EW(H i,abs) [1.01] | EW(H i,abs) [2.87] | EW(H i,abs) [1.00] | EW(H i,abs) [1.94] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [1.13] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [1.09]
|  $R_{l}$(H i,abs) [2.86] |  $R_{l}$(H i,abs) [5.83] |  $f_{{\rm esc,Ly}\alpha}$ [3.57] |  $f_{{\rm esc,Ly}\alpha}$ [3.64] |  $\log_{\rm 10}$(O32) [3.22] |  $\log_{\rm 10}$(O32) [2.14]
|  $f_{{\rm esc,Ly}\alpha}$ [7.20] |  $\log_{\rm 10}$(EW(H$\beta$)) [5.95] |  $M_{\rm 1500}$ [3.79] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [4.58] |  $\log_{\rm 10}$(EW(H$\beta$)) [5.45] |  $\log_{\rm 10}$(EW(H$\beta$)) [3.11]
| EW(Ly$\alpha$) or $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [7.50] | EW(Ly$\alpha$) [6.68] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [4.21] |  $\log_{\rm 10}$(O32) [4.85] |  $\beta_{\rm 1550}$ [3.97] |  $\beta_{\rm 1550}$ [4.73]

Note. — Numbers in brackets indicate the mean of the variable’s ranks in the
100 MC runs.

=2.25in

Table 9: Most Important Variables for $L$(LyC) Predictions

Rank | Full Model | Fiducial+HI Model | JWST Model
---|---|---|---
| Forward | Backward | Forward | Backward | Forward | Backward
Top-Ranked Variables
1 |  $L$(Ly$\alpha$) | EW(Ly$\alpha$) |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) | EW(H i,abs) |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) |  $\log_{\rm 10}$(O32)
2 | E(B-V)neb | $M_{\rm 1500}$ | $f_{{\rm esc,Ly}\alpha}$ | $M_{\rm 1500}$ | $\beta_{\rm 1550}$ | $M_{\rm 1500}$
3 | $M_{\rm 1500}$ | $\beta_{\rm 1550}$ | $M_{\rm 1500}$ |  $\log_{\rm 10}$(O32) | $M_{\rm 1500}$ |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$)
4 | EW(Ly$\alpha$) | EW(H i,abs) |  $\log_{\rm 10}$(O32) | $f_{{\rm esc,Ly}\alpha}$ |  $\log_{\rm 10}$(O32) |  $\log_{\rm 10}$(EW(H$\beta$))
Top Variables by MC Rank Order
|  $L$(Ly$\alpha$) [1.00] |  $M_{\rm 1500}$ [3.05] |  $M_{\rm 1500}$ [2.61] |  $M_{\rm 1500}$ [2.95] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [1.17] |  $\log_{\rm 10}$(O32) [1.71]
|  $M_{\rm 1500}$ [4.43] | EW(Ly$\alpha$) [4.78] | EW(H i,abs) [3.28] | EW(H i,abs) [3.39] |  $\beta_{\rm 1550}$ [3.40] |  $M_{\rm 1500}$ [2.55]
| E(B-V)neb [6.21] | EW(H i,abs) [6.08] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [3.30] |  $f_{{\rm esc,Ly}\alpha}$ [4.27] |  $M_{\rm 1500}$ [3.53] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [2.87]
| EW(Ly$\alpha$) [6.96] |  $\log_{\rm 10}$(O32) [6.52] |  $f_{{\rm esc,Ly}\alpha}$ [3.32] |  $\log_{\rm 10}$(O32) [4.54] |  $\log_{\rm 10}$(O32) [4.38] |  $\log_{\rm 10}$(EW(H$\beta$)) [4.58]

Note. — Numbers in brackets indicate the mean of the variable’s ranks in the
100 MC runs.

=2.25in

Table 10: Most Important Variables for $f_{{\rm esc,Ly}\alpha}$
PredictionsaaVariable lists exclude any measures of Ly$\alpha$.

Rank | Full Model | Fiducial+HI Model | JWST Model
---|---|---|---
| Forward | Backward | Forward | Backward | Forward | Backward
Top-Ranked Variables
1 |  $\log_{\rm 10}$($M_{*}$) | E(B-V)neb |  $\log_{\rm 10}$($M_{*}$) | EW(H i,abs) |  $\log_{\rm 10}$($M_{*}$) | $\beta_{\rm 1550}$
2 | E(B-V)neb | EW(LIS) | EW(H i,abs) | E(B-V)neb | E(B-V)neb | E(B-V)neb
3 | EW(H i,abs) | EW(H i,abs) | E(B-V)neb | E(B-V)UV | 12+$\log_{\rm 10}$(O/H) | 12+$\log_{\rm 10}$(O/H)
4 | EW(LIS) |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) | E(B-V)UV | 12+$\log_{\rm 10}$(O/H) | $\beta_{\rm 1550}$ |  $\log_{\rm 10}$($M_{*}$)
Top Variables by MC Rank Order
| E(B-V)neb [1.61] | E(B-V)neb [2.01] | E(B-V)neb [2.36] | E(B-V)neb [2.43] | E(B-V)neb [2.18] | E(B-V)neb [1.93]
| EW(H i,abs) [3.19] | EW(H i,abs) [2.85] | EW(H i,abs) [2.89] | EW(H i,abs) [2.51] | 12+$\log_{\rm 10}$(O/H) [3.34] | 12+$\log_{\rm 10}$(O/H) [2.91]
| EW(LIS) [5.65] | 12+$\log_{\rm 10}$(O/H) [5.87] | E(B-V)UV [3.92] | 12+$\log_{\rm 10}$(O/H) [4.21 |  $\log_{\rm 10}$(O32) [3.40] |  $\beta_{\rm 1550}$ [3.51]
| 12+$\log_{\rm 10}$(O/H) [6.24] | EW(LIS) [6.39] |  $\log_{\rm 10}$(O32) [3.97] | E(B-V)UV [4.29] |  $\beta_{\rm 1550}$ [3.45] |  $\log_{\rm 10}$($M_{*}$) [4.61]

Note. — Numbers in brackets indicate the mean of the variable’s ranks in the
100 MC runs.

=2.25in

Table 11: Most Important Variables for $L$(Ly$\alpha$) PredictionsaaVariable
lists exclude any measures of Ly$\alpha$.

Rank | Full Model | Fiducial+HI Model | JWST Model
---|---|---|---
| Forward | Backward | Forward | Backward | Forward | Backward
Top-Ranked Variables
1 |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) | $M_{\rm 1500}$ |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) |  $\log_{\rm 10}$(EW(H$\beta$)) |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) |  $\log_{\rm 10}$(EW(H$\beta$))
2 | E(B-V)neb |  $\log_{\rm 10}$(EW(H$\beta$)) | E(B-V)neb | $M_{\rm 1500}$ | E(B-V)neb | $M_{\rm 1500}$
3 | $M_{\rm 1500}$ | EW(H i,abs) | $M_{\rm 1500}$ | EW(H i,abs) | $M_{\rm 1500}$ | 12+$\log_{\rm 10}$(O/H)
4 | 12+$\log_{\rm 10}$(O/H) | E(B-V)neb | 12+$\log_{\rm 10}$(O/H) | E(B-V)UV | 12+$\log_{\rm 10}$(O/H) |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$)
Top Variables by MC Rank Order
|  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [1.73] |  $M_{\rm 1500}$ [1.93] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [2.10] |  $M_{\rm 1500}$ [1.98] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [1.00] |  $M_{\rm 1500}$ [1.94]
| E(B-V)neb [3.24] |  $\log_{\rm 10}$(EW(H$\beta$)) [4.25] | E(B-V)neb [2.71] | EW(H i,abs) [4.15] | E(B-V)neb [2.07] |  $\log_{\rm 10}$(EW(H$\beta$)) [3.71]
|  $M_{\rm 1500}$ [3.50] | EW(H i,abs) [4.88] |  $M_{\rm 1500}$ [3.24] |  $\log_{\rm 10}$(EW(H$\beta$)) [4.21] |  $M_{\rm 1500}$ [3.61] |  $\log_{\rm 10}$($\Sigma_{\rm SFR}$) [4.36]
| 12+$\log_{\rm 10}$(O/H) [5.08] | 12+$\log_{\rm 10}$(O/H) [5.63] | EW(H i,abs) [4.78] | 12+$\log_{\rm 10}$(O/H) [5.18] | 12+$\log_{\rm 10}$(O/H) [3.97] | 12+$\log_{\rm 10}$(O/H) [4.58]

Note. — Numbers in brackets indicate the mean of the variable’s ranks in the
100 MC runs.

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