Markov Chain Monte Carlo Sampling Research Articles

New method for estimating molecular cloud distances based on Gaia, 2MASS, and the TRILEGAL galaxy model

We propose a new method for estimating the distances of molecular clouds traced by CO line emission. Stars from 2MASS and Gaia EDR3 are selected as on-cloud stars when they are projected on a cloud. The background on-cloud stars have redder colors on average than the foreground stars. Instead of searching for stars projected away from the cloud, we employed the TRILEGA galaxy model to mimic the stellar population without cloud extinction along the sightline toward the cloud. Our method does not require an exact boundary of a cloud. The boundaries are highly variable and depend on the sensitivity of the molecular line data. For each cloud, we compared the distributions of on-cloud stars to the TRILEGAL stellar populations in the diagram of J−Ks color versus distance. The intrinsic J−Ks colors of main-sequence and evolved stars from TRILEGAL were considered separately, and they were used as the baseline for subtracting the observed J−Ks colors. The baseline-corrected J−Ks color was deployed with the Bayesian analysis and Markov chain Monte Carlo sampling to determine the distance at which the J−Ks color jump is largest. This method was successfully applied to measure the distances of 27 molecular clouds, which were selected from previously published cloud samples. By replacing TRILEGAL with the GALAXIA galaxy model, we were able to measure the distances for 21 of the 27 clouds. The distances of the 21 clouds based on the GALAXIA model agree well with those based on the TRILEGAL model. The distances of the 27 clouds estimated by this method are consistent with previous estimates. We will apply this new method to a larger region of the gaseous galactic plane, in particular, for the inner galactic region, where a region free of CO emission is hard to separate from the crowded field of clouds.

The missing quasar image in the gravitationally lensed quasar HE0230−2130: Implications for the cored lens mass distribution and dark satellites

Strongly lensed systems with peculiar configurations allow us to probe the local properties of the deflecting lens mass while simultaneously testing general profile assumptions. The quasar HE0230−2130 is lensed by two galaxies at similar redshifts (Δz ∼ 0.003) into four observed images. Using modeled quasar positions from fitting the brightness of the quasar images in ground-based imaging data from the Magellan telescope, we find that lens-mass models where each of these two galaxies is parametrized with a singular power-law (PL) profile predict five quasar images. One of the predicted images is unobserved despite it being distinctively offset from the lensing galaxies and likely bright enough to be observable. This missing image gives rise to new opportunities to study the mass distribution of these galaxies. To interpret the quad configuration of the system, we tested 12 different profile assumptions with the aim of obtaining lens-mass models that correctly predict only four observed images. We tested the effects of adopting: cored profiles for the lensing galaxies; external shear; and additional profiles to represent a dark matter clump. We find that half of our model classes can produce the correct image multiplicity. By comparing the Bayesian evidence of different model parametrizations, we favor two model classes: (i) one that incorporates two singular PL profiles for the lensing galaxies and a cored isothermal sphere in the region of the previously predicted fifth image (rNIS profile), and (ii) one with a bigger lensing galaxy parametrized by a singular PL profile and the smaller galaxy by a cored PL profile with external shear. We estimated the mass of the rNIS clump for each candidate model of our final Markov chain Monte Carlo sample, and find that only 2% are in the range of 106 M⊙ ≤ MrNIS ≤ 109 M⊙, which is the predicted mass range of dark matter subhalos in cold dark matter simulations, or the mass of dark-matter-dominated and low-surface-brightness galaxies. We therefore favor the models with a cored mass distribution for the lens galaxy close to the predicted fifth image. Our study further demonstrates that lensed quasar images are sensitive to the dark matter structure in the gravitational lens. We are able to describe this exotic lensing configuration with relatively simple models, which demonstrates the power of strong lensing for studying galaxies and lens substructure.

Induced polarization of clay-rich materials — Part 3: Partially saturated mixtures of clay and pyrite

Source rocks for oil and gas are often associated with shales that are rich in pyrite and kerogen. Induced polarization is a suitable tool to characterize these formations. We develop a new experimental database of 43 laboratory experiments using mixtures of clay and pyrite under fully or partially water-saturated conditions. The liquid water saturation is in the range of 20%–100%, whereas the pyrite content is in the range of 0%–17%. Spectral-induced polarization measurements are performed in the frequency range of 0.1 Hz to 45 kHz at room temperature (approximately 25°C ± 1°C). The complex conductivity spectra are fitted with a Cole-Cole model, and the Cole-Cole parameters are determined using a stochastic procedure based on a Markov chain Monte Carlo sampler. The Cole-Cole parameters associated with low-frequency dispersion are then plotted as a function of the (water) saturation and pyrite content (volume fractions). Four predictions of the model are tested against the experimental data. We find that the model is able to explain the results, including (1) the chargeability depends on the pyrite content in a predictable way, (2) the (instantaneous) conductivity depends on the saturation according to Archie’s law, (3) the Cole-Cole exponent does not depend on the saturation and pyrite content (except at very small pyrite content of <1 vol%), and (4) the relaxation time is inversely proportional to the instantaneous conductivity. We also develop a more advanced petrophysical model using a double Cole-Cole distribution, in which one distribution is associated with the clay minerals and the other is associated with the pyrite.

Non-Gaussian normative modelling with hierarchical Bayesian regression

Abstract Normative modelling is an emerging technique for parsing heterogeneity in clinical cohorts. This can be implemented in practice using hierarchical Bayesian regression, which provides an elegant probabilistic solution to handle site variation in a federated learning framework. However, applications of this method to date have employed a Gaussian assumption, which may be restrictive in some applications. We have extended the hierarchical Bayesian regression framework to flexibly model non-Gaussian data with heteroskdastic skewness and kurtosis. To this end, we employ a flexible distribution from the sinh-arcsinh (SHASH) family, and introduce a novel reparameterisation and a Markov chain Monte Carlo sampling approach to perform inference in this model. Using a large neuroimaging dataset collected at 82 different sites, we show that the results achieved with this extension are equivalent or better than a warped Bayesian linear regression baseline model on most datasets, while providing better control over the parameters governing the shape of distributions that the approach is able to model. We also demonstrate that the attained flexibility is useful for accurately modelling highly nonlinear relationships between aging and imaging derived phenotypes, which shows that the extension is important for pushing the field of normative modelling forward. All methods described here are available in the open-source pcntoolkit.

Convergence Diagnostics for Entity Resolution

Entity resolution is the process of merging and removing duplicate records from multiple data sources, often in the absence of unique identifiers. Bayesian models for entity resolution allow one to include a priori information, quantify uncertainty in important applications, and directly estimate a partition of the records. Markov chain Monte Carlo (MCMC) sampling is the primary computational method for approximate posterior inference in this setting, but due to the high dimensionality of the space of partitions, there are no agreed upon standards for diagnosing nonconvergence of MCMC sampling. In this article, we review Bayesian entity resolution, with a focus on the specific challenges that it poses for the convergence of a Markov chain. We review prior methods for convergence diagnostics, discussing their weaknesses. We provide recommendations for using MCMC sampling for Bayesian entity resolution, focusing on the use of modern diagnostics that are commonplace in applied Bayesian statistics. Using simulated data, we find that a commonly used Gibbs sampler performs poorly compared with two alternatives.

Bayesian inversion and uncertainty analysis

AbstractQuantification of non‐uniqueness and uncertainty is important for transient electromagnetism (TEM). To address this issue, we develop a trans‐dimensional Bayesian inversion schema for TEM data interpretation. The trans‐dimensional posterior probability density (PPD) offers a solution to model selection and quantifies parameter uncertainty resulting from the model selection from all possible models rather than determining a single model. We use the reversible‐jump Markov chain Monte Carlo sampler to draw ensembles of models to approximate PPD. In addition to providing reasonable model selection, we address the reliability of the inversion results for uncertainty analysis. This strategy offers reasonable guidance when interpreting the inversion results. We make the following improvements in this paper. First, in terms of algorithmic acceleration, we use the nonlinear optimization inversion results as the initial model and implement the multi‐chain parallel method. Second, we develop double factors to control the sampling step size of the proposed distribution, so that the sampling models cover the high‐probability region of the parameter space as much as possible. Finally, we provide the potential scale reduction factor‐η convergence criteria to assess the convergence of the samples and ensure the rationality of the output models. The proposed methodology is first tested on synthetic data and subsequently applied to a field dataset. The TEM inversion results show that probability inversion can provide reliable references for data interpretation through uncertainty analysis.

PRODIGE - envelope to disk with NOEMA III. The origin of complex organic molecule emission in SVS13A

Complex organic molecules (COMs) have been found toward low-mass protostars, but the origins of the COM emission are still unclear. It can be associated with, for example, hot corinos, outflows, and/or accretion shock and disk atmospheres. We aim to disentangle the origin of the COM emission toward the chemically rich protobinary system SVS13A using six O-bearing COMs. We conducted NOrthern Extended Millimeter Array (NOEMA) observations toward SVS13A as part of the PROtostars DIsks: Global Evolution (PRODIGE) program. Our previous DCN observations reveal a possible infalling streamer, which may affect the chemistry of the central protobinary by inducing accretion outbursts and/or shocked gas. We further analyzed six O-bearing COMs: CH3OH aGg'- (CH2OH)2 C2H5OH CH2(OH)CHO CH3CHO and CH3OCHO . Although the COM emission is not spatially resolved, we constrained the source sizes to $ arcsec (90$-$120 au) by conducting uv-domain Gaussian fitting. Interestingly, the high-spectral-resolution data reveal complex line profiles with multiple peaks; although the line emission is likely dominated by the secondary, VLA4A, at LSR =7.36$ km s$^ $, the numbers of peaks (sim $2-5$), the velocities, and the linewidths of these six O-bearing COMs are different. The local thermodynamic equilibrium (LTE) fitting unveils differences in excitation temperatures and emitting areas among these COMs. We further conducted multiple-velocity-component LTE fitting to decompose the line emission into different kinematic components. As a result, the emission of these COMs is decomposed into up to six velocity components from the LTE modeling. The physical conditions (temperature, column density, and source size) of these components from each COM are obtained, and Markov chain Monte Carlo sampling was performed to test the fitting results. We find a variety in excitation temperatures ($100-500$ K) and source sizes (D$ au) from these kinematic components from different COMs. The emission of each COM can trace several components, and different COMs most likely trace different regions. Given this complex structure, we suggest that the central region is inhomogeneous and unlikely to be heated by only protostellar radiation. We conclude that accretion shocks induced by the large-scale infalling streamer likely exist and contribute to the complexity of the COM emission. This underlines the importance of high-spectral-resolution data when analyzing COM emission in protostars and deriving relative COM abundances.

Exploring the deceleration parameter in f(T) gravity: A comprehensive analysis using parametrization techniques and observational data

In this paper, we employ parametrization techniques within the framework of [Formula: see text] gravity to investigate the deceleration parameter (DP), a key quantity characterizing the universe’s expansion dynamics. By analyzing the DP, we gain valuable insights into the nature of cosmic constituents and their impact on the universe’s evolution. We utilize a combination of observational data, including 31 Cosmic Chronometers (CC) measurements, 1048 Type Ia Supernovae (SNIa), 17 Baryon Acoustic Oscillation (BAO) measurements, Cosmic Microwave Background (CMB), 162 Gamma Ray Bursts (GRB), and 24 observations of compact radio quasars (Q). We employ the Markov chain Monte Carlo (MCMC) sampling technique to estimate the best-fit range of model parameters. Cosmological and cosmographic parameters are investigated, and their implications in the context of cosmology have been discussed. We also analyze the statefinder and [Formula: see text] diagnostic to gain deeper insights into the universe’s behavior. Furthermore, we conduct statistical analyses to compare our model with the standard [Formula: see text]CDM model. Our investigation also includes the study of physical parameters, providing comprehensive insights into the cosmological behavior within the [Formula: see text] gravity framework. The results and comparisons presented in this work contribute to a deeper understanding of the universe’s dynamics and provide valuable implications for the cosmological model under consideration.

2-D probabilistic inversion of MT data and uncertainty quantification using the Hamiltonian Monte Carlo method

SUMMARY Bayesian methods provide a valuable framework for rigorously quantifying the model uncertainty arising from the inherent non-uniqueness in the magnetotelluric (MT) inversion. However, widely used Markov chain Monte Carlo (MCMC) sampling approaches usually require a significant number of model samples for accurate uncertainty estimates, making their applications computationally challenging for 2-D or 3-D MT problems. In this study, we explore the applicability of the Hamiltonian Monte Carlo (HMC) method for 2-D probabilistic MT inversion. The HMC provides a mechanism for efficient exploration in high-dimensional model space by making use of gradient information of the posterior probability distribution, resulting in a substantial reduction in the number of samples needed for reliable uncertainty quantification compared to the conventional MCMC methods. Numerical examples with synthetic data demonstrate that the HMC method achieves rapid convergence to the posterior probability distribution of model parameters with a limited number of model samples, indicating the computational advantages of the HMC in high-dimensional model space. Finally, we applied the developed approach to the COPROD2 field data set. The statistical models derived from the HMC approach agree well with previous results obtained by 2-D deterministic inversions. Most importantly, the probabilistic inversion provides valuable quantitative model uncertainty information associated with the resistivity structures derived from the observed data, which facilitates model interpretation.

Capturing Valuation Study Sampling Uncertainty in the Estimation of Health State Utility Values Using the EQ-5D-3L.

Utility scores associated with preference-based health-related quality-of-life instruments such as the EQ-5D-3L are reported as point estimates. In this study, we develop methods for capturing the uncertainty associated with the valuation study of the UK EQ-5D-3L that arises from the variability inherent in the underlying data, which is tacitly ignored by point estimates. We derive a new tariff that properly accounts for this and assigns a specific closed-form distribution to the utility of each of the 243 health states of the EQ-5D-3L. Using the UK EQ-5D-3L valuation study, we used a Bayesian approach to obtain the posterior distributions of the derived utility scores. We constructed a hierarchical model that accounts for model misspecification and the responses of the survey participants to obtain Markov chain Monte Carlo (MCMC) samples from the posteriors. The posterior distributions were approximated by mixtures of normal distributions under the Kullback-Leibler (KL) divergence as the criterion for the assessment of the approximation. We considered the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to estimate the parameters of the mixture distributions. We derived an MCMC sample of total size 4,000 × 243. No evidence of nonconvergence was found. Our model was robust to changes in priors and starting values. The posterior utility distributions of the EQ-5D-3L states were summarized as 3-component mixtures of normal distributions, and the corresponding KL divergence values were low. Our method accounts for layers of uncertainty in valuation studies, which are otherwise ignored. Our techniques can be applied to other instruments and countries' populations. Guidelines for health technology assessments typically require that uncertainty be accounted for in economic evaluations, but the parameter uncertainty of the regression model used in the valuation study of the health instrument is often tacitly ignored.We consider the UK valuation study of the EQ-5D-3L and construct a Bayesian model that accounts for layers of uncertainty that would otherwise be disregarded, and we derive closed-form utility distributions.The derived tariff can be used by researchers in economic evaluations, as it allows analysts to directly sample a utility value from its corresponding distribution, which reflects the associated uncertainty of the utility score.

Quantifying uncertainty in carbon emission estimation: Metrics and methodologies

Carbon emissions are a significant driver of global climate change in today's world. A central concern in discussing carbon emissions is the level of uncertainty associated with them. This study aims to assess the feasibility of using the Mean Squared Error (MSE) as a point estimation measure and confidence interval (CI) as an interval estimation measure to quantify the uncertainty surrounding carbon emissions. To achieve this goal, the bootstrap and Markov Chain Monte Carlo (MCMC) sampling methods were used, utilizing both classical and Bayesian inference methods to uncover the true parameter value.In the context of Bayesian inference, a 2-chain MCMC method proved to be the optimal choice for generating posterior distributions and accurately estimating the true parameter of the distribution θ. The analysis also shows that, while a CI is valuable as an evaluative measure, it does not inherently provide a quantified form of uncertainty and should not be used for quantitative uncertainty assessment. Instead, the Relative Standard Error (RSE) emerges as a promising quantitative measure for capturing the uncertainty of θ, while the percentage uncertainty offers a qualitative perspective. These combined measures provide a comprehensive toolkit for computing and communicating the uncertainty in carbon emission and emission factor values. This reinforces a move towards incorporating transparent uncertainty metrics, ensuring that stakeholders have access to reliable and accurate carbon emission values.

Interaction-based screening, Monte Carlo Bayesian inference-based de novo design and in vitro verification of adenine-binding peptide

One of the main reasons for hyperuricemia is high purine intake. The primary strategy for treating hyperuricemia is blocking the purine metabolism enzyme. However, by binding the purine bases directly, we suggested a unique therapeutic strategy that might interfere with purine metabolism. There have been numerous reports of extensive interactions between proteins and purine bases. Adenine, constituting numerous protein co-factors, can interact with the adenine-binding motif. Using Bayesian Inference and Markov chain Monte Carlo sampling, we created a novel adenine-binding peptide Ile-Tyr-Val-Thr based on the structure of the adenine-binding motifs. Ile-Tyr-Val-Thr generates a semi-pocket that can clip the adenine within, as demonstrated by docking. Then, using thermodynamic techniques, the interaction between Ile-Tyr-Val-Thr and adenine was confirmed. The KD value is 1.50e−5 (ΔH = −20.2 kJ/mol and ΔG = −27.6 kJ/mol), indicating the high affinity. In brief, the adenine-binding peptide Ile-Tyr-Val-Thr may help lower uric acid level by blocking the absorption of food-derived adenine.

Probabilistic state estimation in district heating grids using deep neural network

Probabilistic state estimation is critical for operating and controlling district heating grids efficiently. However, computational bottlenecks of traditional solvers limit the feasibility of uncertainty-aware Bayesian estimation. This paper proposes using deep neural networks (DNNs) to enable fast and accurate posterior estimation. Fully-connected neural networks (FCNNs), convolutional neural networks (CNNs), and recurrent neural networks (RNNs) are evaluated as candidate approximators of the physical model. Markov chain Monte Carlo sampling in the heat exchange space is leveraged to generate posterior samples. Experiments on a benchmark heating grid demonstrate FCNNs can efficiently learn the mapping from heat exchanges to network states. A FCNN trained on 20 training epochs after hyperparameter optimization provides the best approximation accuracy and uncertainty estimates, outperforming prior methods based on Deep Neural Networks. The results highlight the potential of data-driven deep learning models for probabilistic state estimation. The proposed framework could enable real-time uncertainty-aware control and decision-making for future intelligent district heating grids.

Candl: cosmic microwave background analysis with a differentiable likelihood

We present an automatically differentiable python likelihood for analysing cosmic microwave background (CMB) power spectrum measurements. is powered by JAX, which makes it fast and easy to calculate derivatives of the likelihood. This facilitates, for example, robust Fisher matrices without finite-difference methods. We show the benefits of through a series of example calculations, covering forecasting, robustness tests, and gradient-based Markov chain Monte Carlo sampling. These also include optimising the band power bin width to minimise parameter errors of a realistic mock data set. Moreover, we calculate the correlation of parameter constraints from correlated and partially overlapping subsets of the SPT-3G 2018 data release. In a traditional analysis framework, these tasks are slow and require careful fine-tuning to obtain stable results. As such, a fully differentiable pipeline allows for a higher level of scrutiny; we argue that this is the paradigm shift required to leverage incoming data from ground-based experiments, which will significantly improve the cosmological parameter constraints from the mission. comes with the latest primary and lensing power spectrum data from the South Pole Telescope and Atacama Cosmology Telescope collaborations and will be used as part of the upcoming SPT-3G and data releases. Along with the core code, we release a series of auxiliary tools, which simplify common analysis tasks and interface the likelihood with other cosmological software. is pip-installable and publicly available on Github.

Toward mapping turbulence in the intracluster medium

Future X-ray observatories with high spectral resolution and imaging capabilities will enable measurements and mappings of emission line shifts in the intracluster medium (ICM). Such direct measurements can serve as unique probes of turbulent motions in the ICM. Determining the level and scales of turbulence will improve our understanding of the galaxy cluster dynamical evolution and assembly, together with a more precise evaluation of the non thermal support pressure budget. This will allow for more accurate constraints to be placed on the masses of galaxy clusters, among other potential benfits. In this view, we implemented the methods presented in the previous instalments of our work to characterising the turbulence in the intra-cluster medium in a feasibility study with the X-ray Integral Field Unit (X-IFU) on board the future European X-ray observatory, Athena. From idealized mock observations of a toy model cluster, we reconstructed the second-order structure function built with the observed velocity field to constrain the turbulence. We carefully accounted for the various sources of errors to derive the most realistic and comprehensive error budget within the limits of our approach. With prior assumptions on the dissipation scale and power spectrum slope, we constrained the parameters of the turbulent power spectrum model through the use of Markov chain Monte Carlo (MCMC) sampling. With a very long exposure time, a favourable configuration, and a prior assumption of the dissipation scale, we were able to retrieve the injection scale, velocity dispersion, and power spectrum slope, with 1sigma uncertainties for better than sim 15<!PCT!> of the input values. We demonstrated the efficiency of our carefully set framework to constrain the turbulence in the ICM from high-resolution X-ray spectroscopic observations, paving the way for more in-depth investigation of the optimal required observing strategy within a more restrictive observational setup with the future Athena/X-IFU instrument.

Bayesian approach of elliptical loci and RAPID for damage localization in wind turbine blade

This investigation addresses the issue of damage detection and localization in wind turbine blade laminates. This paper proposes a novel approach that integrates the elliptical trajectory and probabilistic imaging method using the Bayesian framework. This method employs multiple damage-sensitive features to enhance the reliability and robustness of sensor arrays. The algorithm is optimized by analyzing the propagation characteristics of Lamb waves in composite blade laminates. A numerical simulation is conducted on a 1.5 MW wind turbine blade laminate model, incorporating the scattered wave signal, wave arrival time, and correlation coefficient as damage characteristic signals. Markov Chain Monte Carlo sampling method is adopted to obtain the posterior distribution of the damage location and achieve accurate localization of blade delamination damage. The experimental results indicate that the damage localization algorithm, which utilizes the Bayesian approach, achieves an accuracy of approximately 97.04% in localizing delamination damage in blade laminates.

Bayesian Feature Extraction for Two-Part Latent Variable Model with Polytomous Manifestations

Semi-continuous data are very common in social sciences and economics. In this paper, a Bayesian variable selection procedure is developed to assess the influence of observed and/or unobserved exogenous factors on semi-continuous data. Our formulation is based on a two-part latent variable model with polytomous responses. We consider two schemes for the penalties of regression coefficients and factor loadings: a Bayesian spike and slab bimodal prior and a Bayesian lasso prior. Within the Bayesian framework, we implement a Markov chain Monte Carlo sampling method to conduct posterior inference. To facilitate posterior sampling, we recast the logistic model from Part One as a norm-type mixture model. A Gibbs sampler is designed to draw observations from the posterior. Our empirical results show that with suitable values of hyperparameters, the spike and slab bimodal method slightly outperforms Bayesian lasso in the current analysis. Finally, a real example related to the Chinese Household Financial Survey is analyzed to illustrate application of the methodology.

Comparison of three recent discrete stochastic inversion methods and influence of the prior choice

Groundwater flow depends on subsurface heterogeneity, which often calls for categorical fields to represent different geological facies. The knowledge about subsurface is however limited and often provided indirectly by state variables, such as hydraulic heads of contaminant concentrations. In such cases, solving a categorical inverse problem is an important step in subsurface modeling. In this work, we present and compare three recent inverse frameworks: Posterior Population Expansion (PoPEx), Ensemble Smoother with Multiple Data Assimilation (ESMDA), and DREAM-ZS (a Markov chain Monte Carlo sampler). PoPEx and ESDMA are used with Multiple-point statistics (MPS) as geostatistical engines, and DREAM-ZS is used with a Wasserstein generative adversarial network (WGAN). The three inversion methods are tested on a synthetic example of a pumping test in a fluvial channelized aquifer. Moreover, the inverse problem is solved three times with each method, each time using a different training image to check the performance of the methods with different geological priors. To assess the quality of the results, we propose a framework based on continuous ranked probability score (CRPS), which compares single true values with predictive distributions. All methods performed well when using the training image used to create the reference, but their performances were degraded with the alternative training images. PoPEx produced the least geological artifacts but presented a rather slow convergence. ESMDA showed initially a very fast convergence which reaches a plateau, contrary to the remaining methods. DREAM-ZS was overly confident in placing some incorrect geological features but outperformed the other methods in terms of convergence.

Inferring networks from time series: A neural approach.

Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations of the dynamics to which they give rise. In this work, we present a powerful computational method to infer large network adjacency matrices from time series data using a neural network, in order to provide uncertainty quantification on the prediction in a manner that reflects both the degree to which the inference problem is underdetermined as well as the noise on the data. This is a feature that other approaches have hitherto been lacking. We demonstrate our method's capabilities by inferring line failure locations in the British power grid from its response to a power cut, providing probability densities on each edge and allowing the use of hypothesis testing to make meaningful probabilistic statements about the location of the cut. Our method is significantly more accurate than both Markov-chain Monte Carlo sampling and least squares regression on noisy data and when the problem is underdetermined, while naturally extending to the case of nonlinear dynamics, which we demonstrate by learning an entire cost matrix for a nonlinear model of economic activity in Greater London. Not having been specifically engineered for network inference, this method in fact represents a general parameter estimation scheme that is applicable to any high-dimensional parameter space.

Radio-optical synergies at high redshift to constrain primordial non-Gaussianity

We apply the multi-tracer technique to test the possibility of improved constraints on the amplitude of local primordial non-Gaussianity, f NL, in the cosmic large-scale structure. A precise measurement of f NL is difficult because the effects of non-Gaussianity mostly arise on the largest scales, which are heavily affected by the low statistical sampling commonly referred to as cosmic variance. The multi-tracer approach suppresses cosmic variance and we implement it by combining the information from next-generation galaxy surveys in the optical/near-infrared band and neutral hydrogen (Hi) intensity mapping surveys in the radio band. High-redshift surveys enhance the precision on f NL, due to the larger available volume, and Hi intensity mapping surveys can naturally reach high redshifts. In order to extend the redshift coverage of a galaxy survey, we consider different emission-line galaxy populations, focusing on the Hα line at low redshift and on oxygen lines at higher redshift. By doing so, we cover a wide redshift range 1 ≲ z ≲ 4. To assess the capability of our approach, we implement a synthetic-data analysis by means of Markov chain Monte Carlo sampling of the (cosmological+nuisance) parameter posterior, to evaluate the constraints on f NL obtained in different survey configurations. We find significant improvements from the multi-tracer technique: the full data set leads to a precision of σ(f NL) < 1.