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At least 217 records · Page 12

A framework for inferring and analyzing pharmacotherapy treatment patterns

Background: To discover pharmacotherapy prescription patterns and their statistical associations with outcomes through a clinical pathway inference framework applied to real-world data. Methods: We apply machine learning steps in our framework using a 2006 to 2020 cohort of veterans with major depressive disorder (MDD). Outpatient antidepressant pharmacy fills, dispensed inpatient antidepressant medications, emergency department visits, self-harm, and all-cause mortality data were extracted from the Department of Veterans Affairs Corporate Data Warehouse. Results: Our MDD cohort consisted of 252,179 individuals. During the study period there were 98,417 emergency department visits, 1,016 cases of self-harm, and 1,507 deaths from all causes. The top ten prescription patterns accounted for 69.3% of the data for individuals starting antidepressants at the fluoxetine equivalent of 20-39 mg. Additionally, we found associations between outcomes and dosage change. Conclusions: For 252,179 Veterans who served in Iraq and Afghanistan with subsequent MDD noted in their electronic medical records, we documented and described the major pharmacotherapy prescription patterns implemented by Veterans Health Administration providers. Ten patterns accounted for almost 70% of the data. Associations between antidepressant usage and outcomes in observational data may be confounded. The low numbers of adverse events, especially those associated with all-cause mortality, make our calculations imprecise. Furthermore, our outcomes are also indications for both disease and treatment. Despite these limitations, we demonstrate the usefulness of our framework in providing operational insight into clinical practice, and our results underscore the need for increased monitoring during critical points of treatment.

60 APPLIED LIFE SCIENCES↗

Inferring Quantum Network Topology Using Local Measurements

Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we propose an efficient protocol for distinguishing and inferring the topology of a quantum network. We leverage entropic quantities-namely, the von Neumann entropy and the measured mutual information-as well as measurement covariance to uniquely characterize the topology. We show that the entropic quantities are sufficient to distinguish two networks that prepare GHZ states. Moreover, if qubit measurements are available, both entropic quantities and covariance can be used to infer the network topology without state-preparation assumptions. We show that the protocol can be entirely robust to noise and can be implemented via quantum variational optimization. Numerical experiments on both classical simulators and quantum hardware show that covariance is generally more reliable for accurately and efficiently inferring the topology, whereas entropy-based methods are often better at identifying the absence of entanglement in the low-shot regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the Probabilistic Analysis of Neural Networks

Neural networks are powerful tools for automated decision-making,seeing increased application in safety-critical domains, such as autonomous driving. Due to their black-box nature and large scale,reasoning about their behavior is challenging. Statistical analysis is often used to infer probabilistic properties of a network, such as its robustness to noise and inaccurate inputs. While scalable, statistical methods can only provide probabilistic guarantees on the quality of their results and may underestimate the impact of low probability inputs leading to undesired behavior of the network.We investigate here the use of symbolic analysis and constraint solution space quantification to precisely quantify probabilistic properties in neural networks. We demonstrate the potential of the proposed technique in a case study involving the analysis of ACAS-Xu, a collision avoidance system for unmanned aircraft control.

neural nets↗

Scaling and merging time-resolved pink-beam diffraction with variational inference

Time-resolved x-ray crystallography (TR-X) at synchrotrons and free electron lasers is a promising technique for recording dynamics of molecules at atomic resolution. While experimental methods for TR-X have proliferated and matured, data analysis is often difficult. Extracting small, time-dependent changes in signal is frequently a bottleneck for practitioners. Recent work demonstrated this challenge can be addressed when merging redundant observations by a statistical technique known as variational inference (VI). However, the variational approach to time-resolved data analysis requires identification of successful hyperparameters in order to optimally extract signal. In this case study, we present a successful application of VI to time-resolved changes in an enzyme, DJ-1, upon mixing with a substrate molecule, methylglyoxal. We present a strategy to extract high signal-to-noise changes in electron density from these data. Furthermore, we conduct an ablation study, in which we systematically remove one hyperparameter at a time to demonstrate the impact of each hyperparameter choice on the success of our model. We expect this case study will serve as a practical example for how others may deploy VI in order to analyze their time-resolved diffraction data.

47 OTHER INSTRUMENTATION↗

Bayesian Inference and the Effects of Varying Uncertainty Models in Charring Ablator Calibration and Uncertainty Quantification Problems

The Mars Science Laboratory (MSL) vehicle utilized a heat shield constructed from NASA’s Phenolic-Impregnated Carbon Ablator (PICA) material to protect the main structure from the high enthalpy environment encountered during hypersonic atmospheric entry. During the vehicle’s descent through Martian atmosphere, multiple thermocouples embedded within the heat shield captured in-depth material temperature data that allow for studies to be conducted on current material response reconstruction tools. In the present work, material temperature data obtained from thermocouples within the MISP-4 plug (MEDLI (Mars Science Laboratory Entry, Descent, and Landing Instrument) Integrated Sensor Plug) are utilized in the calibration of Theoretical Ablative Composite for Open Testing (TACOT) model parameters in conjunction with NASA’s Porous material Analysis Toolbox (PATO) through Bayesian inference where uncertainty due to parametric, modeling, and experimental sources is simultaneously quantified. Prior to the study, a sensitivity analysis is performed through computation of the robust Sobol indices in an effort to study the relationship between input space and model response and to reduce the dimensionality of the statistical inverse problem. The Bayesian inference methodology necessitates an a-priori choice to be made for the uncertainty model for which numerous possibilities are available. Across most works, however, only basic additive or multiplicative models are utilized with pre-defined magnitudes of uncertainty based on a-priori knowledge or to-be-calibrated multipliers of static covariance matrix structures. The present effort explores the effects of informed uncertainty models, ones with temporal dependence that are simultaneously calibrated through Bayesian inference, on calibrated results for parameters that make up the uncertain input space.

Sensitivity Analysis↗

Trust Your Gut: Comparing Human and Machine Inference from Noisy Visualizations

People commonly utilize visualizations not only to examine a given dataset, but also to draw generalizable conclusions about the underlying models or phenomena. Prior research has compared human visual inference to that of an optimal Bayesian agent, with deviations from rational analysis viewed as problematic. However, human reliance on non-normative heuristics may prove advantageous in certain circumstances. We investigate scenarios where human intuition might surpass idealized statistical rationality. In two experiments, we examine individuals’ accuracy in characterizing the parameters of known data-generating models from bivariate visualizations. Our findings indicate that, although participants generally exhibited lower accuracy compared to statistical models, they frequently outperformed Bayesian agents, particularly when faced with extreme samples. Participants appeared to rely on their internal models to filter out noisy visualizations, thus improving their resilience against spurious data. However, participants displayed overconfidence and struggled with uncertainty estimation. They also exhibited higher variance than statistical machines. Our findings suggest that analyst gut reactions to visualizations may provide an advantage, even when departing from rationality. These results carry implications for designing visual analytics tools, offering new perspectives on how to integrate statistical models and analyst intuition for improved inference and decision-making. The data and materials for this paper are available at https://osf.io/qmfv6

human-machine collaboration↗

Statistical characterization of twin transmission across grain boundaries in magnesium

Here, a detailed statistical analysis of twin transmission (TT) across grain boundaries is performed in rolled, commercial purity magnesium compressed along the rolling direction. EBSD images are acquired from two different cuts: a section containing the rolling (RD) and normal (ND) directions; and a section at 35° to the ND which contains transverse direction (TD). An automated twinning analysis software, METIS, is used to obtain the statistical correlations between deformation twins and other microstructural features by analyzing EBSD microstructures comprising thousands of grains and twins. This detailed statistical analysis reveals that the TT propensity is sensitive to the grain boundary (GB) misorientation angle but not to the GB misorientation axis. Specifically, TT propensity decreases with increasing GB misorientation angle; however, the decreasing trend is not monotonic. Further, the detailed analysis of TT events combining macroscopic Schmid factor and the geometric measures (m’: accounts for the alignment of both twin plane normal and shear directions; m”: accounts for the alignment of only twin shear directions; and m”’: accounts for the alignment of only twin plane normal) helps in understanding and identifying the process of twin-pair formation, i.e., co-nucleation versus transmission, also to identify the role of local stresses at GBs induced by inter-grain interaction versus twinning shear transformation processes. In addition, Bayesian inference is used to draw statistically meaningful conclusions as to the likelihood of transmission given misorientation angles. Lastly, twin chain frequency as a function of chain length is predicted using the probability distribution obtained from the Bayesian inference and compared with the actual data from the EBSD microstructures.

36 MATERIALS SCIENCE↗

On the Relationship Between Global Land-Ocean Temperature and Various Descriptors of Solar-Geomagnetic Activity and Climate

Examined are sunspot cycle- (SC-) length averages of the annual January-December values of the Global Land-Ocean Temperature Index ( ) in relation to SC-length averages of annual values of various descriptors of solar-geomagnetic activity and climate, incorporating lags of 0-5 yr. For the overall interval SC12-SC23, the is inferred to correlate best against the parameter incorporating lag = 5 yr, where the parameter refers to the resultant aa value having removed that portion of the annual aa average value due to the yearly variation of sunspot number (SSN). The inferred correlation between the and is statistically important at confidence level cl > 99.9%, having a coefficient of linear correlation r = 0.865 and standard error of estimate se = 0.149 degC. Excluding the most recent cycles SC22 and SC23, the inferred correlation is stronger, having r = 0.969 and se = 0.048 degC. With respect to the overall trend in the , which has been upwards towards warmer temperatures since SC12 (1878-1888), solar-geomagnetic activity parameters are now trending downwards (since SC19). For SC20-SC23, in contrast, comparison of the against SC-length averages of the annual value of the Mauna Loa carbon dioxide ( ) index is found to be highly statistically important (cl >> 99.9%), having r = 0.9994 and se = 0.012 degC for lag = 2 yr. On the basis of the inferred preferential linear correlation between the and , the current ongoing SC24 is inferred to have warmer than was seen in SC23 (i.e., >0.526 degC), probably in excess of 0.68 degC (relative to the 1951-1980 base period).

Wilson, Robert M.↗

On the Correlation Between Maximum Amplitude and Smoothed Monthly Mean Sunspot Number during the Rise of the Cycle (from t = 0-48 months Past Sunspot Minimum)

During the rise from sunspot minimum to maximum, the observed value of smoothed monthly mean sunspot number at maximum RM is found to correlate with increasing strength against the current value of smoothed monthly mean sunspot number R(t), where t is the elapsed time in months from minimum. On the basis of the modern era sunspot cycles (i.e., cycles 10-22), the inferred linear correlation is found to be statistically important (i.e., at the 95-percent level of confidence) from about 11 mo past minimum and statistically very important (i.e.. at the 99-percent level of confidence) from about 15 mo past minimum; ignoring cycle 19, the largest cycle of the modern era, the inferred linear correlation is found to be statistically important from cycle onset. On the basis of R(t), estimates of RM can be gauged usually to within about +/- 30 percent during the first 2 yr and to within about +/- 20 percent (or better) after the first 2 yr of a cycle's onset. For cycle 23, because controversy exists regarding the placement of its minimum (i.e., its onset), being either May 1996 or perhaps August 1996 (or shortly thereafter), estimates of its RM are divergent, being lower (more like a mean size cycle) when using the earlier epoch of minimum and higher (above average in size) when using the later-occurring minimum. For smoothed monthly mean sunspot number through October 1997 (t = 17 or 14 mo, respectively), having a provisional value of 32.0. the earlier minimum date projects an RM of 110.3 +/- 33.1, while the later minimum date projects one of 137.2 +/- 41.2. The projection is slowly decreasing in size using the earlier onset date, while it is slowly increasing in size using the later onset date.

Wilson, Robert M.↗

Inference of bipolar neutrino flavor oscillations near a core-collapse supernova based on multiple measurements at Earth

Neutrinos in compact-object environments, such as core-collapse supernovae, can experience various kinds of collective effects in flavor space, engendered by neutrino-neutrino interactions. These include “bipolar” collective oscillations, which are exhibited by neutrino ensembles where different flavors dominate at different energies. Considering the importance of neutrinos in the dynamics and nucleosynthesis in these environments, it is desirable to ascertain whether an Earth-based detection could contain signatures of bipolar oscillations that occurred within a supernova envelope. To that end, we, in this study, continue examining a cost-function formulation of statistical data assimilation (SDA) to infer solutions to a small-scale model of neutrino flavor transformation. SDA is an inference paradigm designed to optimize a model with sparse data. Our model consists of two monoenergetic neutrino beams with different energies emanating from a source and coherently interacting with each other and with a matter background, with radially varying interaction strengths. We attempt to infer flavor transformation histories of these beams using simulated measurements of the flavor content at locations “in vacuum” (that is, far from the source), which could in principle correspond to Earth-based detectors. Within the scope of this small-scale model, we found that: (i) based on such measurements, the SDA procedure is able to infer whether bipolar oscillations had occurred within the protoneutron star envelope, and (ii) if the measurements sample the full amplitude of the neutrino oscillations in vacuum, then the amplitude of the prior bipolar oscillations is well predicted. This result intimates that the inference paradigm can well complement numerical integration codes, via its ability to infer flavor evolution at physically inaccessible locations.

79 ASTRONOMY AND ASTROPHYSICS↗

Interpretable Machine Learning Models for Autonomous Characterization of Analogue Ocean World Seawater Chemistry and Biosignature Potential Using Isotope Ratio Data

Background: Future missions to ocean worlds, such as Enceladus and Europa, will attempt to characterize the subsurface seawater chemistry and assess the potential for life. Such missions will be equipped with capabilities to precisely measure volatile isotopes in plumes, atmospheres, and exospheres. Motivation: While large isotopic fractionations can indicate a biological source, there are signatures resulting from abiotic geochemical processes that mimic isotopic biosignatures. While machine learning (ML) has the potential to disentangle competing effects and biotic mimicry, high-dimensional isotope ratio mass spectrometry (IRMS) data is likely to contain noise/irrelevant features and involve complex statistical interactions that make human inference and interpretation difficult. Further, ML predictions with as far-reaching implications as an extraterrestrial biosignature on an ocean world requires the use of interpretable models (i.e., not “black box” models) with physically and mathematically meaningful feature spaces along with false positive diagnostics. Methods: We use volatile CO2 IRMS data of analogue ocean world seawaters to validate an ML approach to provide biogeochemical context for biosignature detection. We employ a feature selection method called nearest-neighbor projected distance regression (NPDR) that detects statistical interactions and helps elucidate the mechanisms of the Random Forest classification models. Results: We train and validate predictive ML models on volatile CO2 IRMS data of analogue ocean world seawaters to predict major salt components (e.g., MgSO4, NaHCO3), pH, ionic strength, and the presence of biosignatures. Features derived from IRMS measurements are augmented with extracted time-series features. Our results show high test accuracy and interpretability, which is increased by interaction network visualization, sample-wise variable importance scores, and single-sample class probability estimates. We demonstrate an ML mission software solution that triggers autonomous data transmission and biogeochemical sample prediction.

geochemistry↗

Advanced data analysis in inertial confinement fusion and high energy density physics

Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas.

47 OTHER INSTRUMENTATION↗

An Investigation Into Possible Systematic Effects on Neutron Star Radius Estimates using NICER-like Synthetic Data

Neutron star cores contain the densest matter in the observable universe. The state of this matter is of interest in numerous fields, but laboratory experiments cannot explore this matter. Although the composition of the matter would be of great interest, macroscopic observables such as the neutron star mass-radius relation depend primarily on the equation of state (EOS). As a result, precise and reliable radius measurements would be valuable in constraining the EOS. However, most attempts at radius measurements are susceptible to systematic errors, meaning the inferred radius can be significantly biased even though the fit to the data appears to be statistically good. Previous studies suggested that radii inferred using X-ray data provided by NASA’s NICER mission may be more immune from such systematic errors. This is in part because, compared with previous measurements that obtained averaged spectra and fluxes, NICER observes millisecond pulsars by timing the photons so precisely, it is possible to obtain the spectrum as a function of rotational phase and see variations such as heated regions on the star rotate into and out of view hundreds of times per second. This extra information seems promising to break degeneracies and mitigate systematic errors, but a more in-depth study is necessary. We report the first steps of that study, in which we generate NICER-like synthetic data and determine the quality of fit and bias in radius obtained when we fit the data using a model different from the model used to generate the data.

Isiah Holt↗

Use of Design of Experiments and Rule-Based Inference in Determining Neural Network Architectures for Loss of Control Detection

In this work, we describe methods for selecting the neural network architectures and input spaces to implement belief state inference on generic commercial transport aircraft. First, we highlight a case study on the planning, execution, and analysis of a set of experiments to determine the configurations of a conditional variational autoencoder (CVAE). We present a structured method that can be used in a number of aerospace applications, to optimize the structure and training parameters of the CVAE for belief state inference, using Design of Experiments (DOE) statistical methodologies. The motivation for this specific DOE was to identify the appropriate hyperparameters for measuring the CVAE reconstruction probability and latent space, such that the measurements can be used to infer qualitative state changes for the aircraft. We demonstrate that this process yields information about a trained neural network’s utility for this specific application, along with a quantifiable range of certainty. We execute 84 experiments using loss-of-control flight maneuver data from a NASA T-2 aircraft, demonstrating that this empirical process allows us to construct cheap and simple models with specific attributes amenable to belief state inference in aerospace applications. While theoretically, we could create a single CVAE with an input space the size of all measurable flight variables and environmental dynamics, it becomes intractable to use such a neural network in an in-situ intelligent multi-agent system. Using the recommendations from our case study, we introduce a technical approach for feasibly describing the belief space by (1) identifying significant statistical relationships among flight variables using rule induction, (2) using a set of rules that cover all features to define the input space of multiple CVAEs, and (3) forming a belief space based on the joint probability density of their collective latent spaces. This results in a series of relatively small matrix multiplications that can be performed in real time, as opposed to large matrix computations in a single CVAE. We demonstrate the application of this approach on the T-2 flight loss-of control experiments, using the architecture and hyperparameter recommendations from the case study. We compare the utilities of an individual CVAE trained on all flight variables and multiple CVAEs defined on subsets of flight variables for detecting qualitative changes in flight. We demonstrate that the use of multiple CVAEs with smaller input spaces permits the CVAE to capture more granular relationships in the latent space, permitting better state space characterization and loss-of-control detection.

Design of experiments↗

An exponential build-up in seismic energy suggests a months-long nucleation of slow slip in Cascadia

Slow slip events result from the spontaneous weakening of the subduction megathrust and bear strong resemblance to earthquakes, only slower. This resemblance allows us to study fundamental aspects of nucleation that remain elusive for classic, fast earthquakes. We rely on machine learning algorithms to infer slow slip timing from statistics of seismic waveforms. We find that patterns in seismic power follow the 14-month slow slip cycle in Cascadia, arguing in favor of the predictability of slow slip rupture. Here, we show that seismic power exponentially increases as the slowly slipping portion of the subduction zone approaches failure, a behavior that shares a striking similarity with the increase in acoustic power observed prior to laboratory slow slip events. Our results suggest that the nucleation phase of Cascadia slow slip events may last from several weeks up to several months.

58 GEOSCIENCES↗

Consistent and reproducible computation of the glass transition temperature from molecular dynamics simulations

In many fields, from semiconductors for opto-electronic applications to ionic liquids (ILs) for separations, the glass transition temperature (Tg) of a material is a useful gauge for its potential use in practical settings. As a result, there is a great deal of interest in predicting Tg using molecular simulations. However, the uncertainty and variation in the trend shift method, a common approach in simulations to predict Tg, can be high. This is due to the need for human intervention in defining a fitting range for linear fits of density with temperature assumed for the liquid and glass phases across the simulated cooling. The definition of such fitting ranges then defines the estimate for the Tg as the intersection of linear fits. We eliminate this need for human intervention by leveraging the Shapiro–Wilk normality test and proposing an algorithm to define the fitting ranges and, consequently, Tg. Through this integration, we incorporate into our automated methodology that residuals must be normally distributed around zero for any fit, a requirement that must be met for any regression problem. Consequently, fitting ranges for realizing linear fits for each phase are statistically defined rather than visually inferred, obtaining an estimate for Tg without any human intervention. The method is also capable of finding multiple linear regimes across density vs temperature curves. We compare the predictions of our proposed method across multiple IL and semiconductor molecular dynamics simulation results from the literature and compare other proposed methods for automatically detecting Tg from density–temperature data. We believe that our proposed method would allow for more consistent predictions of Tg. We make this methodology available and open source through GitHub.

Chemistry↗

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. Here, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

97 MATHEMATICS AND COMPUTING↗

Forecasting constraints on the mean free path of ionizing photons at z ≥ 5.4 from the Lyman-α forest flux autocorrelation function

ABSTRACT Fluctuations in Lyman-α (Ly α) forest transmission towards high-z quasars are partially sourced from spatial fluctuations in the ultraviolet background, the level of which are set by the mean free path of ionizing photons (λmfp). The autocorrelation function of Ly α forest flux characterizes the strength and scale of transmission fluctuations and, as we show, is thus sensitive to λmfp. Recent measurements at z ∼ 6 suggest a rapid evolution of λmfp at z > 5.0 which would leave a signature in the evolution of the autocorrelation function. For this forecast, we model mock Ly α forest data with properties similar to the XQR-30 extended data set at 5.4 ≤ z ≤ 6.0. At each z, we investigate 100 mock data sets and an ideal case where mock data matches model values of the autocorrelation function. For ideal data with λmfp = 9.0 cMpc at z = 6.0, we recover $\lambda _{\text{mfp}}=12^{+6}_{-3}$ cMpc. This precision is comparable to direct measurements of λmfp from the stacking of quasar spectra beyond the Lyman limit. Hypothetical high-resolution data leads to a $\sim 40~{{\ \rm per\ cent}}$ reduction in the error bars over all z. The distribution of mock values of the autocorrelation function in this work is highly non-Gaussian for high-z, which should caution work with other statistics of the high-z Ly α forest against making this assumption. We use a rigorous statistical method to pass an inference test, however future work on non-Gaussian methods will enable higher precision measurements.

Astronomy & Astrophysics↗