arXiv subjects

Ming-Feng Ho

Publications and source records attributed to Ming-Feng Ho.

At least 19 recordsLinked to original sources

arXiv2026

FLARE MCMC: Fidelity-based Layer-Adaptive REcursive proposals for MCMC

Markov chain Monte Carlo (MCMC) requires only the ability to evaluate the likelihood, making it a common technique for inference in complex models. However, it can have a slow mixing rate, requiring the generation of many samples to obtain good estimates and an overall high computational cost. FLARE MCMC is a multi-fidelity layered MCMC method that exploits lower-fidelity approximations of the true likelihood calculation to improve mixing and leads to overall faster performance. Such lower-fidelity likelihoods are commonly available in scientific and engineering applications where the model involves a simulation whose resolution or accuracy can be tuned. Our technique uses recursive, layered chains with simple layer tuning; it does not require the likelihood to take any form or have any particular internal mathematical structure. We demonstrate experimentally that FLARE MCMC achieves larger effective sample sizes for the same computational time across different scientific domains including hydrology and cosmology.

cs.AI↗

arXiv2025

Small-scale Lyman alpha forest cosmology with PRIYA: Constraints from XQ100 and KODIAQ-SQUAD one-dimensional flux power spectra

We present a new cosmological analysis of the small-scale Lyman alpha forest 1D flux power spectrum (P1D) using high-resolution quasar spectra from XQ100 and KODIAQ-SQUAD, interpreted through the PRIYA emulator. PRIYA is a suite of galaxy formation simulations spanning a range of cosmological and inhomogeneous HeII reionization parameters, enabling few-percent-level predictions of the P1D. These datasets, probing down to $k \sim 6\,h\,\mathrm{Mpc}^{-1}$ at $z = 2-5$, offer access to non-linear scales inaccessible to large-volume surveys like eBOSS. We find that the XQ100 P1D yields constraints on the primordial power spectrum parameters $(A_P, n_P)$ at pivot scale $k_0 = 0.78\,\mathrm{Mpc}^{-1}$ that are consistent with PRIYA results from eBOSS DR14 and Planck CMB, albeit with broader uncertainties. Notably, this is achieved without external IGM temperature data, showing that XQ100 alone provides stronger constraints on thermal history than eBOSS DR14. In contrast, the KODIAQ-SQUAD P1D favors a significantly higher $A_P$ value, driven by the selection bias toward high-column density absorbers (HCDs). We also find that the P1D at $k > 0.045\,\mathrm{s/km}$ is more sensitive to Lyman limit system contamination and thermal history. When imposing a prior on $(A_P, n_P)$, the reduced $\chi^2$ remains unchanged and the inferred mean IGM temperature is unaffected, suggesting that cosmological and thermal parameters are largely sensitive to different scales. The XQ100 P1D therefore provides complementary information on thermal nuisance parameters, which can be jointly fit with eBOSS or DESI P1D measurements to improve cosmological constraints.

astro-ph.CO↗

arXiv2025

Ten-dimensional neural network emulator for the nonlinear matter power spectrum

We present GokuNEmu, a ten-dimensional neural network emulator for the nonlinear matter power spectrum, designed to support next-generation cosmological analyses. Built on the Goku $N$-body simulation suite and the T2N-MusE emulation framework, GokuNEmu predicts the matter power spectrum with $\sim 0.5 \%$ average accuracy for redshifts $0 \leq z \leq 3$ and scales $0.006 \leq k/(h\,\mathrm{Mpc}^{-1}) \leq 10$. The emulator models a 10D parameter space that extends beyond $\Lambda$CDM to include dynamical dark energy (characterized by $w_0$ and $w_a$), massive neutrinos ($\sum m_\nu$), the effective number of neutrinos ($N_\text{eff}$), and running of the spectral index ($\alpha_\text{s}$). Its broad parameter coverage, particularly for the extensions, makes it the only matter power spectrum emulator capable of testing recent dynamical dark energy constraints from DESI. In addition, it requires only $\sim $2 milliseconds to predict a single cosmology on a laptop, orders of magnitude faster than existing emulators. These features make GokuNEmu a uniquely powerful tool for interpreting observational data from upcoming surveys such as LSST, Euclid, the Roman Space Telescope, and CSST.

astro-ph.CO↗

arXiv2025

Design and optimization of neural networks for multifidelity cosmological emulation

Accurate and efficient simulation-based emulators are essential for interpreting cosmological survey data down to nonlinear scales. Multifidelity emulation techniques reduce simulation costs by combining high- and low-fidelity data, but traditional regression methods such as Gaussian processes struggle with scalability in sample size and dimensionality. In this work, we present T2N-MusE, a neural network framework characterized by (i) a novel 2-step multifidelity architecture, (ii) a 2-stage Bayesian hyperparameter optimization, (iii) a 2-phase $k$-fold training strategy, and (iv) a per-$z$ principal component analysis strategy. We apply T2N-MusE to selected data from the Goku simulation suite, covering a 10-dimensional cosmological parameter space, and build emulators for the matter power spectrum over a range of redshifts with different configurations. We find the emulators outperform our earlier Gaussian process models significantly and demonstrate that each of these techniques is efficient in training neural networks or/and effective in improving generalization accuracy. We observe a reduction in the mean error by more than a factor of five and in the worst-case error by approximately a factor of eight in leave-one-out cross-validation, relative to previous work. This framework has been used to build the most powerful emulator for the matter power spectrum, GokuNEmu, and will also be used to construct emulators for other statistics in future.

astro-ph.CO↗

arXiv2025

Hints of an Anomalous Lens Population towards the Galactic Bulge

The dark and dynamic parts of the Galaxy, including the bulk shape and movement of the Galactic Bulge and characteristics of dark compact object populations, such as a hypothetical population of primordial black holes (PBHs), are difficult to study directly by their very nature, but are critical to our understanding of the universe. Fortunately, all of these mysteries can be uniquely studied via gravitational microlensing, a method of astronomical detection that traces mass and dynamics as opposed to light. Using the OGLE-IV microlensing survey bulge fields, we apply a Bayesian hierarchical model to jointly infer properties of the Galaxy, the characteristics of compact objects, and and test PBHs with an extended mass distribution as a test PBHs as a viable explanation of dark matter, extending work focused on the Small and Large Magellanic Clouds, both with much lower event-rates. We infer a preference within the data for a lower patternspeed in the galactic model and a wider mass spectrum for compact objects. When adding a PBH component to the favored astrophysical model from our initial investigations, we find a Bayes factor of $\ln\mathcal{B} = 20.23$ preferring the PBH model. Upon further investigation of these results, we find the critical feature in the PBH model to be the velocity distribution, which is fundamentally different than the velocity distribution of astrophysical objects and uniquely able to explain a large number of low parallax, low timescale microlensing events. Noting that this effect is not unique to PBHs, we consider the implications of these results as applied to a hypothetical population of PBHs and discuss alternative explanations, including a variety of other possible astrophysical and survey or analysis systematics.

astro-ph.GA↗

arXiv2025

Ten-parameter simulation suite for cosmological emulation beyond $\Lambda$CDM

We present Goku, a suite of cosmological $N$-body simulations, and the corresponding 10-dimensional emulator, GokuEmu, for the nonlinear matter power spectrum. The simulations span the base parameters of $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmology and its extensions, including dynamical dark energy ($w_0$, $w_a$), the sum of the neutrino masses ($\sum m_\nu$), the effective number of neutrinos ($N_\text{eff}$), and the running of the scalar spectral index ($\alpha_\text{s}$), enabling tests of new physics with data from upcoming surveys like the Roman Space Telescope, Euclid, and LSST. Designed within the MF-Box framework, which integrates multi-scale and multi-fidelity simulations, the suite includes high-fidelity simulations evolving $3000^3$ particles in $1\,(\text{Gpc}/h)^3$ volumes and low-fidelity simulations with $750^3$ particles across varying box sizes. This approach achieves percent-level accuracy in high-likelihood regions and 5% accuracy across broader parameter ranges, while reducing computational costs by 94% compared to single-fidelity methods. The simulations adopt an accurate treatment of massive neutrinos, enhancing predictions of the matter power spectrum on nonlinear scales. Key innovations include an adaptive sampling strategy and the use of beam search to optimize generalization accuracy. The emulator is valid for redshifts $z \leq 3$ and scales $0.01 \lesssim k / (h \, \text{Mpc}^{-1}) \lesssim 10$. Beyond the matter power spectrum, the simulations also support analyses of other statistical measures, such as the halo mass function. The emulator and its training data are publicly available at https://github.com/astro-YYH/GokuEmu, providing a valuable resource for cosmological parameter inference and model testing.

astro-ph.CO↗

arXiv2024

On Finding Black Holes in Photometric Microlensing Surveys

There are expected to be millions of isolated black holes in the Galaxy resulting from the death of massive stars. Measuring the abundance and properties of this remnant population would shed light on the end stages of stellar evolution and the evolution paths of black hole systems. Detecting isolated black holes is currently only possible via gravitational microlensing which has so far yielded one definitive detection. The difficulty in finding microlensing black holes lies in having to choose a small subset of events based on characteristics of their lightcurves to allocate expensive and scarce follow-up resources to confirm the identity of the lens. Current methods either rely on simple cuts in parameter space without using the full distribution information or are only effective on a small subsets of events. In this paper we present a new lens classification method. The classifier takes in posterior constraints on lightcurve parameters and combines them with a Galactic simulation to estimate the lens class probability. This method is flexible and can be used with any set of microlensing lightcurve parameters making it applicable to large samples of events. We make this classification framework available via the popclass python package. We apply the classifier to $\sim10,000$ microlensing events from the OGLE survey and find $23$ high-probability black hole candidates. Our classifier also suggests that the only known isolated black hole is an observational outlier according to current Galactic models and allocation of astrometric follow-up on this event was a high-risk strategy.

astro-ph.SR↗

arXiv2024

Investigating the mixing between two black hole populations in LIGO-Virgo-KAGRA GWTC-3

We introduce a population model to analyze the mixing between hypothesised power-law and $\sim 35 M_\odot$ Gaussian bump black hole populations in the latest gravitational wave catalog, GWTC-3, estimating their co-location and separation. We find a relatively low level of mixing, $3.1^{+5.0}_{-3.1}\%$, between the power-law and Gaussian populations, compared to the percentage of mergers containing two Gaussian bump black holes, $5.0^{+3.2}_{-1.7}\%$. Our analysis indicates that black holes within the Gaussian bump are generally separate from the power-law population, with only a minor fraction engaging in mixing and contributing to the $\mathcal{M} \sim 14 M_\odot$ peak in the chirp mass. This leads us to identify a distinct population of Binary Gaussian Black Holes (BGBHs) that arise from mergers within the Gaussian bump. We suggest that current theories for the formation of the massive $35 M_\odot$ Gaussian bump population may need to reevaluate the underlying mechanisms that drive the preference for BGBHs.

astro-ph.HE↗

arXiv2023

Astrometric Microlensing by Primordial Black Holes with The Roman Space Telescope

Primordial Black Holes (PBHs) could explain some fraction of dark matter and shed light on many areas of early-universe physics. Despite over half a century of research interest, a PBH population has so far eluded detection. The most competitive constraints on the fraction of dark matter comprised of PBHs ($f_{\rm DM}$) in the $(10^{-9}-10)M_{\odot}$ mass-ranges come from photometric microlensing and bound $f_{\rm DM}\lesssim10^{-2}-10^{-1}$. With the advent of the Roman Space Telescope with its sub-milliarcsecond (mas) astrometric capabilities and its planned Galactic Bulge Time Domain Survey (GBTDS), detecting astrometric microlensing signatures will become routine. Compared with photometric microlensing, astrometric microlensing signals are sensitive to different lens masses-distance configurations and contains different information, making it a complimentary lensing probe. At sub-mas astrometric precision, astrometric microlensing signals are typically detectable at larger lens-source separations than photometric signals, suggesting a microlensing detection channel of pure astrometric events. We use a Galactic simulation to predict the number of detectable microlensing events during the GBTDS via this pure astrometric microlensing channel. Assuming an absolute astrometric precision floor for bright stars of 0.1 mas for the GBTDS, we find that the number of detectable events peaks at $\approx 10^{3} f_{\rm DM}$ for a population of $ 1 M_{\odot}$ PBHs and tapers to $\approx 10f_{\rm DM}$ and $\approx 100f_{\rm DM}$ at $10^{-4}M_{\odot}$ and $10^{3}M_{\odot}$, respectively. Accounting for the distinguishability of PBHs from Stellar lenses, we conclude the GBTDS will be sensitive to a PBH population at $f_{\rm DM}$ down to $\approx10^{-1}-10^{-3}$ for $(10^{-1}-10^{2})M_{\odot}$ likely yielding novel PBH constraints.

astro-ph.GA↗

arXiv2023

Forecast Cosmological Constraints with the 1D Wavelet Scattering Transform and the Lyman-$\alpha$ forest

We make forecasts for the constraining power of the 1D Wavelet Scattering Transform (WST) when used with a Lyman-$\alpha$ forest cosmology survey. Using mock simulations and a Fisher matrix, we show that there is considerable cosmological information in the scattering transform coefficients not captured by the flux power spectrum. We estimate mock covariance matrices assuming uncorrelated Gaussian pixel noise for each quasar, at a level drawn from a simple lognormal model. The extra information comes from a smaller estimated covariance in the first-order wavelet power, and from second-order wavelet coefficients which probe non-Gaussian information in the forest. Forecast constraints on cosmological parameters from the WST are more than an order of magnitude tighter than for the power spectrum, shrinking a $4D$ parameter space by a factor of $10^6$. Should these improvements be realised with DESI, inflationary running would be constrained to test common inflationary models predicting $\alpha_s = - 6\times 10^{-4}$ and neutrino mass constraints would be improved enough for a $5-\sigma$ detection of the minimal neutrino mass.

astro-ph.CO↗

arXiv2023

Disentangling the Black Hole Mass Spectrum with Photometric Microlensing Surveys

From the formation mechanisms of stars and compact objects to nuclear physics, modern astronomy frequently leverages surveys to understand populations of objects to answer fundamental questions. The population of dark and isolated compact objects in the Galaxy contains critical information related to many of these topics, but is only practically accessible via gravitational microlensing. However, photometric microlensing observables are degenerate for different types of lenses, and one can seldom classify an event as involving either a compact object or stellar lens on its own. To address this difficulty, we apply a Bayesian framework that treats lens type probabilistically and jointly with a lens population model. This method allows lens population characteristics to be inferred despite intrinsic uncertainty in the lens-class of any single event. We investigate this method's effectiveness on a simulated ground-based photometric survey in the context of characterizing a hypothetical population of primordial black holes (PBHs) with an average mass of $30 M_{\odot}$. On simulated data, our method outperforms current black hole (BH) lens identification pipelines and characterizes different subpopulations of lenses while jointly constraining the PBH contribution to dark matter to ${\approx}25$\%. Key to robust inference, our method can marginalize over population model uncertainty. We find the lower mass cutoff for stellar origin BHs, a key observable in understanding the BH mass gap, particularly difficult to infer in our simulations. This work lays the foundation for cutting-edge PBH abundance constraints to be extracted from current photometric microlensing surveys.

astro-ph.IM↗

arXiv2023

MF-Box: Multi-fidelity and multi-scale emulation for the matter power spectrum

We introduce MF-Box, an extended version of MFEmulator, designed as a fast surrogate for power spectra, trained using N-body simulation suites from various box sizes and particle loads. To demonstrate MF-Box's effectiveness, we design simulation suites that include low-fidelity suites (L1 and L2) at $256 \,\mathrm{Mpc}/h$ and $100 \,\mathrm{Mpc}/h$, each with $128^3$ particles, and a high-fidelity suite (HF) with $512^3$ particles at $256 \,\mathrm{Mpc}/h$, representing a higher particle load compared to the low-fidelity suites. MF-Box acts as a probabilistic resolution correction function, learning most of the cosmological dependencies from L1 and L2 simulations and rectifying resolution differences with just 3 HF simulations using a Gaussian process. MF-Box successfully emulates power spectra from our HF testing set with a relative error of $< 3\%$ up to $k \simeq 7 \,h/\mathrm{Mpc}$ at $z \in [0, 3]$, while maintaining a cost similar to our previous multi-fidelity approach, which was accurate only up to $z = 1$. The addition of an extra low-fidelity node in a smaller box significantly improves emulation accuracy for MF-Box at $k > 2 \,h/\mathrm{Mpc}$, increasing it by a factor of $10$. We conduct an error analysis of MF-Box based on computational budget, providing guidance for optimizing budget allocation per fidelity node. Our proposed MF-Box enables future surveys to efficiently combine simulation suites of varying quality, effectively expanding the range of emulation capabilities while ensuring cost efficiency.

astro-ph.CO↗

arXiv2023

Machine Learning Uncovers the Universe's Hidden Gems: A Comprehensive Catalogue of CIV Absorption Lines in SDSS DR12

We assemble the largest CIV absorption line catalogue to date, leveraging machine learning, specifically Gaussian processes, to remove the need for visual inspection for detecting CIV absorbers. The catalogue contains probabilities classifying the reliability of the absorption system within a quasar spectrum. Our training set was a sub-sample of DR7 spectra that had no detectable CIV absorption in a large visually inspected catalogue. We used Bayesian model selection to decide between our continuum model and our absorption-line models. Using a random hold-out sample of 1301 spectra from all of the 26,030 investigated spectra in DR7 CIV catalogue, we validated our pipeline and obtained an 87% classification performance score. We found good purity and completeness values, both ~80%, when a probability of ~95% is used as the threshold. Our pipeline obtained similar CIV redshifts and rest equivalent widths to our training set. Applying our algorithm to 185,425 selected quasar spectra from SDSS DR12, we produce a catalogue of 113,775 CIV doublets with at least 95% confidence. Our catalogue provides maximum a posteriori values and credible intervals for CIV redshift, column density, and Doppler velocity dispersion. We detect CIV absorption systems with a redshift range of 1.37 $\!-\!$ 5.1, including 33 systems with a redshift larger than 5 and 549 absorbers systems with a rest equivalent width greater than 2 A at more than 95% confidence. Our catalogue can be used to investigate the physical properties of the circumgalactic and intergalactic media.

astro-ph.GA↗

arXiv2023

Cosmological Constraints from the eBOSS Lyman-$\alpha$ Forest using the PRIYA Simulations

We present new cosmological parameter constraints from the eBOSS Lyman-$\alpha$ forest survey. We use a new theoretical model and likelihood based on the PRIYA simulation suite. PRIYA is the first suite to resolve the Lyman-$\alpha$ forest in a ($120$~Mpc/h~)$^3$ volume, using a multi-fidelity emulation technique. We use PRIYA to predict Lyman-$\alpha$ forest observables with $\lesssim 1\%$ interpolation error over an $11$ dimensional ($9$ simulated, $2$ in post-processing) parameter space. We identify an internal tension within the flux power spectrum data. Once the discrepant data is removed, we find the primeval scalar spectral index measured at a pivot scale of $k_0 = 0.78$ Mpc$^{-1}$ to be $n_P = 1.009^{+0.027}_{-0.018}$ at 68\% confidence. This measurement from the Lyman-$\alpha$ forest flux power spectrum alone is in reasonable agreement with Planck, and in tension with earlier eBOSS analyses. The amplitude of matter fluctuations is $\sigma_8 = 0.733^{+0.026}_{-0.029}$ at 68\% confidence, in agreement with Dark Energy Survey weak lensing measurements and other small-scale structure probes and in tension with CMB measurements from Planck and ACT. The effective optical depth to Lyman-$\alpha$ photons from our pipeline is in good agreement with earlier high resolution measurements. We find a linear power at $z=3$ and $k = 0.009$ s/km of $\Delta_L^2 = 0.302^{+0.024}_{-0.027}$ with a slope $n_\mathrm{eff} = -2.264^{+0.026}_{-0.018}$. Our flux power spectrum only chains prefer a low level of heating during helium reionization. When we add IGM temperature data we find $n_P = 0.983\pm 0.020$ and $\sigma_8 = 0.703^{+0.023}_{-0.027}$. Our chains prefer an early and long helium reionization event, as suggested by measurements from the helium Lyman-$\alpha$ forest. In the near future we will use our pipeline to infer cosmological parameters from the DESI Lyman-$\alpha$ data.

astro-ph.CO↗

arXiv2023

PRIYA: A New Suite of Lyman-alpha Forest Simulations for Cosmology

We present the PRIYA suite of cosmological simulations, based on the code and hydrodynamic model of the ASTRID simulation, and designed for cosmological analyses of the Lyman-$\alpha$ forest. Our simulation suite spans a $9$-dimensional parameter space, including $4$ cosmological parameters and $5$ astrophysical/thermal parameters. We have run $48$ low fidelity simulations with $1536^3$ particles in a $120$ Mpc/h box and $3$ high fidelity simulations with $3072^3$ particles in a $120$ Mpc/h box. All our simulations include a full physics model for galaxy formation, including supernova and AGN feedback, and thus also contain a realistic population of DLAs. We advance on earlier simulations suites by larger particle loads, by incorporating new physical models for patchy hydrogen and helium reionization, and by self-consistently incorporating a model for AGN feedback. We show that patchy helium reionization imprints an excess in the 1D flux power spectrum on large scales, which may allow future measurements of helium reionization bubble sizes. Simulation parameters are chosen based on a Latin hypercube design and a Gaussian process is used to interpolate to arbitrary parameter combinations. We build a multi-fidelity emulator for the 1D flux power spectrum and the mean IGM temperature. We show that our final interpolation error is $< 1\%$ and that our simulations produce a flux power spectrum converged at the percent level for $z=5.4$ - $2.2$. Our simulation suite will be used to interpret Lyman-$\alpha$ forest 1D flux power spectra from SDSS and future DESI data releases.

astro-ph.CO↗

arXiv2022

A Multi-Fidelity Emulator for the Lyman-$α$ Forest Flux Power Spectrum

In this work we extend our recently developed multi-fidelity emulation technique to the simulated Lyman-$α$ forest flux power spectrum. Multi-fidelity emulation allows interpolation of simulation outputs between cosmological parameters using many cheap low-fidelity simulations and a few expensive high-fidelity simulations. Using a test suite of small box (30 Mpc/h) simulations, we show that multi-fidelity emulation is able to reproduce the Lyman-$α$ forest flux power spectrum well, achieving an average accuracy when compared to a test suite of $0.8\%$. We further show that it has a substantially increased accuracy over single-fidelity emulators, constructed using either the high or low-fidelity simulations only. In particular, it allows the extension of an existing simulation suite to smaller scales and higher redshifts.

astro-ph.CO↗

arXiv2021

Multi-Fidelity Emulation for the Matter Power Spectrum using Gaussian Processes

We present methods for emulating the matter power spectrum by combining information from cosmological $N$-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter space of a limited number of simulations. We present the first implementation in cosmology of multi-fidelity emulation, where many low-resolution simulations are combined with a few high-resolution simulations to achieve an increased emulation accuracy. The power spectrum's dependence on cosmology is learned from the low-resolution simulations, which are in turn calibrated using high-resolution simulations. We show that our multi-fidelity emulator predicts high-fidelity counterparts to percent-level relative accuracy when using only $3$ high-fidelity simulations and outperforms a single-fidelity emulator that uses $11$ simulations, although we do not attempt to produce a converged emulator with high absolute accuracy. With a fixed number of high-fidelity training simulations, we show that our multi-fidelity emulator is $\simeq 100$ times better than a single-fidelity emulator at $k \leq 2 h \mathrm{Mpc}^{-1}$, and $\simeq 20$ times better at $3 \leq k < 6.4 h \mathrm{Mpc}^{-1}$. Multi-fidelity emulation is fast to train, using only a simple modification to standard Gaussian processes. Our proposed emulator shows a new way to predict non-linear scales by fusing simulations from different fidelities.

astro-ph.CO↗

arXiv2021

Damped Lyman-alpha Absorbers from Sloan Digital Sky Survey DR16Q with Gaussian processes

We present a new catalogue of Damped Lyman-$α$ absorbers from SDSS DR16Q, as well as new estimates of their statistical properties. Our estimates are computed with the Gaussian process models presented in Garnett et al. (2017); Ho et al. (2020) with an improved model for marginalising uncertainty in the mean optical depth of each quasar. We compute the column density distribution function (CDDF) at $2 < z < 5$, the line density ($\textrm{d} N/ \textrm{d} X$), and the neutral hydrogen density ($Ω_{\textrm{DLA}}$). Our Gaussian process model provides a posterior probability distribution of the number of DLAs per spectrum, thus allowing unbiased probabilistic predictions of the statistics of DLA populations even with the noisiest data. We measure a non-zero column density distribution function for $N_{\textrm{HI}} < 3 \times 10^{22} \,\textrm{cm}^{-2}$ with $95\%$ confidence limits, and $N_{\textrm{HI}} \lesssim 10^{22} \,\textrm{cm}^{-2}$ for spectra with signal-to-noise ratios $> 4$. Our results for DLA line density and total hydrogen density are consistent with previous measurements. Despite a small bias due to the poorly measured blue edges of the spectra, we demonstrate that our new model can measure the DLA population statistics when the DLA is in the Lyman-$β$ forest region. We verify our results are not sensitive to the signal-to-noise ratios and redshifts of the background quasars although a residual correlation remains for detections from $z_{\textrm{QSO}} < 2.5$, indicating some residual systematics when applying our models on very short spectra, where the SDSS spectral observing window only covers part of the Lyman-$α$ forest.

astro-ph.GA↗