Bayesian Fitting Research Articles

Editorial for the special issue on advances in forward and inverse surrogate modeling for high‐frequency design

Editorial for the special issue on advances in forward and inverse surrogate modeling for <scp>high‐frequency</scp> design

Accurate intravoxel incoherent motion parameter estimation using Bayesian fitting and reduced number of low b-values.

Intravoxel incoherent motion (IVIM) magnetic resonance imaging is a potential noninvasive technique for the diagnosis of brain tumors. However, perfusion-related parameter mapping is a persistent problem. The purpose of this paper is to investigate the IVIM parameter mapping of brain tumors using Bayesian fitting and low b-values. Bayesian shrinkage prior (BSP) fitting method and different low b-value distributions were used to estimate IVIM parameters (diffusion D, pseudo-diffusion D*, and perfusion fraction F). The results were compared to those obtained by least squares (LSQ) on both simulated and in vivo brain data. Relative error (RE) and reproducibility were used to evaluate the results. The differences of IVIM parameters between brain tumor and normal regions were compared and used to assess the performance of Bayesian fitting in the IVIM application of brain tumor. In tumor regions, the value of D* tended to be decreased when the number of low b-values was insufficient, especially with LSQ. BSP required less low b-values than LSQ for the correct estimation of perfusion parameters of brain tumors. The IVIM parameter maps of brain tumors yielded by BSP had smaller variability, lower RE, and higher reproducibility with respect to those obtained by LSQ. Obvious differences were observed between tumor and normal regions in parameters D (P<0.05) and F (P<0.001), especially F. BSP generated fewer outliers than LSQ, and distinguished better tumors from normal regions in parameter F. Intravoxel incoherent motion parameters clearly allow brain tumors to be differentiated from normal regions. Bayesian fitting yields robust IVIM parameter mapping with fewer outliers and requires less low b-values than LSQ for the parameter estimation.

Timing the earliest quenching events with a robust sample of massive quiescent galaxies at 2 &amp;lt; z &amp;lt; 5

ABSTRACT We present a sample of 151 massive (M* &amp;gt; 1010 M⊙) quiescent galaxies at 2 &amp;lt; z &amp;lt; 5, based on a sophisticated Bayesian spectral energy distribution fitting analysis of the CANDELS UDS and GOODS-South fields. Our sample includes a robust sub-sample of 61 objects for which we confidently exclude low-redshift and star-forming solutions. We identify 10 robust objects at z &amp;gt; 3, of which 2 are at z &amp;gt; 4. We report formation redshifts, demonstrating that the oldest objects formed at z &amp;gt; 6; however, individual ages from our photometric data have significant uncertainties, typically ∼0.5 Gyr. We demonstrate that the UVJ colours of the quiescent population evolve with redshift at z &amp;gt; 3, becoming bluer and more similar to post-starburst galaxies at lower redshift. Based upon this, we construct a model for the time evolution of quiescent galaxy UVJ colours, concluding that the oldest objects are consistent with forming the bulk of their stellar mass at z ∼ 6–7 and quenching at z ∼ 5. We report spectroscopic redshifts for two of our objects at z = 3.440 and 3.396, which exhibit extremely weak Ly α emission in ultra-deep VANDELS spectra. We calculate star formation rates based on these line fluxes, finding that these galaxies are consistent with our quiescent selection criteria, provided their Ly α escape fractions are &amp;gt;3 and &amp;gt;10 per cent, respectively. We finally report that our highest redshift robust object exhibits a continuum break at λ ∼ 7000 Å in a spectrum from VUDS, consistent with our photometric redshift of $z_\mathrm{phot}=4.72^{+0.06}_{-0.04}$. If confirmed as quiescent, this object would be the highest redshift known quiescent galaxy. To obtain stronger constraints on the times of the earliest quenching events, high-SNR spectroscopy must be extended to z ≳ 3 quiescent objects.

Statistical modeling of frequency responses using linear Bayesian vector fitting

AbstractThis article presents a Bayesian extension of the vector fitting (VF) procedure for rational approximation of frequency‐domain responses. The proposed method treats the linear part of VF in a Bayesian way, while propagating distributions through the nonlinear part by sampling. As such, it is capable of providing data‐driven uncertainty information along with the rational fit. The Bayesian VF technique is applied to two realistic design examples, a double folded stub filter and a RAM memory channel, demonstrating its validity and highlighting three potential applications of this novel framework.

Self-consistent Analysis of Stellar Clusters: An Application to HST Data of the Halo Globular Cluster NGC 6752

Abstract The Bayesian isochrone fitting using the Markov chain Monte Carlo algorithm is applied, to derive the probability distribution of the parameters age, metallicity, reddening, and absolute distance modulus. We introduce the SIRIUS code by means of simulated color–magnitude diagrams (CMDs), including the analysis of multiple stellar populations (MPs). The population tagging is applied from the red giant branch to the bottom of the main sequence. Through sanity checks using synthetic Hubble Space Telescope CMDs of globular clusters we verify the code reliability in the context of simple and MPs. In such tests, the formal uncertainties in age or age difference, metallicity, reddening, and absolute distance modulus can reach 400 Myr, 0.03 dex, 0.01 mag, and 0.03 mag, respectively. We apply the method to analyze NGC 6752, using Dartmouth stellar evolutionary models. Assuming a single stellar population, we derive an age of 13.7 ± 0.5 Gyr and a distance of , with the latter in agreement within 3σ with the inverse Gaia parallax. In the analysis of the MPs, three populations are clearly identified. From the Chromosome Map and UV/Optical two-color diagrams inspection, we found a fraction of stars of 25 ± 5, 46 ± 7, and 29 ± 5 %, for the first, second, and third generations, respectively. These fractions are in good agreement with the literature. An age difference of 500 ± 410 Myr between the first and the third generation is found, with the uncertainty decreasing to 400 Myr when the helium enhancement is taken into account.

Bayesian curve fitting for discontinuous functions using an overcomplete system with multiple kernels

We propose a fully Bayesian methodology for estimation of functions that have jump discontinuities. The proposed model is an extension of the LARK model, which enables functions to be represented by the small number of elements from an overcomplete system. In the proposed model, multiple kernels are used as the elements of an overcomplete system. Since these elements are composed of different types of functions such as Haar, Laplacian, and Gaussian kernel, the proposed model can estimate discontinuous as well as smooth functions without model selection. The location of jumps, the number of basis functions, and even the smoothness of the target function are automatically determined by the Levy random measure. A simulation study and a real data analysis illustrate that the proposed model performs better than the standard nonparametric methods for the estimation of discontinuous functions. Finally, we prove prior positivity of the model and show that the prior has sufficiently large support including discontinuous functions with a finite number of jumps.

A novel bayesian approach with conditional autoregressive specification for intravoxel incoherent motion diffusion-weighted MRI.

The Intra-Voxel Incoherent Motion (IVIM) model is largely adopted to estimate slow and fast diffusion coefficients of water molecules in biological tissues, which are used in cancer applications. The most reported fitting approach is a voxel-wise segmented non-linear least square, whereas Bayesian approaches with a direct fit, also considering spatial regularization, were proposed too. In this work a novel segmented Bayesian method was proposed, also in combination with a spatial regularization through a Conditional Autoregressive (CAR) prior specification. The two segmented Bayesian approaches, with and without CAR specification, were compared with two standard least-square and a direct Bayesian fitting methods. All approaches were tested on simulated images and real data of patients with head-and-neck and rectal cancer. Estimation accuracy and maps noisiness were quantified on simulated images, whereas the coefficient of variation and the goodness of fit were evaluated for real data. Both versions of the segmented Bayesian approach outperformed the standard methods on simulated images for pseudo-diffusion (D∗ ) and perfusion fraction (f), whilst the segmented least-square fitting remained the less biased for the diffusion coefficient (D). On real data, Bayesian approaches provided the less noisy maps, and the two Bayesian methods without CAR generally estimated lower values for f and D∗ coefficients with respect to the other approaches. The proposed segmented Bayesian approaches were superior, in terms of estimation accuracy and maps quality, to the direct Bayesian model and the least-square fittings. The CAR method improved the estimation accuracy, especially for D∗ .

The effect of spatial variation for predicting aphid outbreaks

AbstractIn order to improve forecasting of pest epidemics, it is important to know the spatial scale at which specific forecasts are reliable. To investigate the spatial scale of aphid outbreaks, we have developed a spatio‐temporal stochastic aphid population growth model and fitted the model to empirical spatial time series of aphid population data using a Bayesian hierarchical fitting procedure. Furthermore, detailed spatial data of the initial phases of population growth were investigated in semivariograms. Our results suggest that spatial variation is low in the initial occurrence probability at a spatial scale of 10 km. Consequently, the results support the hypothesis that initial aphid population sizes and outbreaks may be predicted in fields within a 10 km radius. For farmers, this may imply that they can rely their decision of whether to spray against aphids on observations made by other nearby farmers or by the consultancy service.

Estimating redshift distributions using hierarchical logistic Gaussian processes

ABSTRACT This work uses hierarchical logistic Gaussian processes to infer true redshift distributions of samples of galaxies, through their cross-correlations with spatially overlapping spectroscopic samples. We demonstrate that this method can accurately estimate these redshift distributions in a fully Bayesian manner jointly with galaxy-dark matter bias models. We forecast how systematic biases in the redshift-dependent galaxy-dark matter bias model affect redshift inference. Using published galaxy-dark matter bias measurements from the Illustris simulation, we compare these systematic biases with the statistical error budget from a forecasted weak gravitational lensing measurement. If the redshift-dependent galaxy-dark matter bias model is mis-specified, redshift inference can be biased. This can propagate into relative biases in the weak lensing convergence power spectrum on the 10–30 per cent level. We, therefore, showcase a methodology to detect these sources of error using Bayesian model selection techniques. Furthermore, we discuss the improvements that can be gained from incorporating prior information from Bayesian template fitting into the model, both in redshift prediction accuracy and in the detection of systematic modelling biases.

Bayesian Spectral Moment Estimation and Uncertainty Quantification

We present a Bayesian spectral fitting method developed for spectroscopic data analysis, particularly (but not solely) in the context of fusion energy research. The presented techniques are particularly valuable to estimating moments and corresponding uncertainties whenever the spectra result from line-integrated measurements in nonuniform plasmas, for which the approximation of atomic line shapes being ideal Gaussians gives poor estimates. We decompose multiple, potentially overlapping spectral lines into a sum of Gauss–Hermite polynomials, whose properties allow efficient truncation and uncertainty quantification, often with only three free parameters per atomic emission line. Tests with both synthetic and experimental data demonstrate the effectiveness and robustness where more standard nonlinear fitting routines may experience difficulties. A parallelized version of our implementation is publicly released under an open source license 1 . 1 https://github.com/Maplenormandy/bsfc

XGASS: The impact of photometric bulges on the scatter of HI scaling relations

ABSTRACT We present a structural decomposition analysis of the galaxies in the extended GALEX Arecibo SDSS Survey (xGASS) using (gri) images from the Sloan Digital Sky Survey. Utilizing the 2D Bayesian light profile fitting code ProFit, we fit single- and double-component models taking advantage of a robust Markov chain Monte Carlo optimization algorithm in which we assume a Sérsic profile for single-component models and a combination of a Sérsic bulge and near-exponential disc (0.5 ≤ n ≤ 1.5) for double-component models. We investigate the effect of bulges on the atomic hydrogen (H i) content in galaxies by revisiting the H i-to-stellar mass scaling relations with the bulge-to-total ratio measured in the ProFit decompositions. We show that, at both fixed total and disc stellar mass, more bulge-dominated galaxies have systematically lower H i masses, implying that bulge-dominated galaxies with large H i reservoirs are rare in the local Universe. We see similar trends when separating galaxies by a bulge-to-total ratio based either on luminosity or stellar mass, however, the trends are more evident with luminosity. Importantly, when controlling for both stellar mass and star formation rate, the separation of atomic gas content reduces to within 0.3 dex between galaxies of different bulge-to-total ratios. Our findings suggest that the presence of a photometric bulge has little effect on the global H i gas reservoirs of local galaxies.

A catalog of 159,238 white dwarf ages

AbstractWe employ Pan-STARRS photometry, Gaia trigonometric parallaxes, modern stellar evolution and atmosphere models, and our Bayesian fitting approach to determine cooling and total ages for 159,238 white dwarfs. In many cases we are able to derive precise ages (better than 5%) for individual white dwarfs. These results are meant for broad use within the white dwarf and stellar astrophysics communities and we plan to make available on-line the posterior distributions for cooling age, total age, initial stellar mass, and other parameters.

JINGLE V: Dust properties of nearby galaxies derived from hierarchical Bayesian SED fitting

Abstract We study the dust properties of 192 nearby galaxies from the JINGLE survey using photometric data in the 22-850$\mu$m range. We derive the total dust mass, temperature T and emissivity index β of the galaxies through the fitting of their spectral energy distribution (SED) using a single modified black-body model (SMBB). We apply a hierarchical Bayesian approach that reduces the known degeneracy between T and β. Applying the hierarchical approach, the strength of the T-β anti-correlation is reduced from a Pearson correlation coefficient R = −0.79 to R = −0.52. For the JINGLE galaxies we measure dust temperatures in the range 17 − 30 K and dust emissivity indices β in the range 0.6 − 2.2. We compare the SMBB model with the broken emissivity modified black-body (BMBB) and the two modified black-bodies (TMBB) models. The results derived with the SMBB and TMBB are in good agreement, thus applying the SMBB, which comes with fewer free parameters, does not penalize the measurement of the cold dust properties in the JINGLE sample. We investigate the relation between T and β and other global galaxy properties in the JINGLE and Herschel Reference Survey (HRS) sample. We find that β correlates with the stellar mass surface density (R = 0.62) and anti-correlates with the HI mass fraction (MHI/M*, R = −0.65), whereas the dust temperature correlates strongly with the SFR normalized by the dust mass (R = 0.73). These relations can be used to estimate T and β in galaxies with insufficient photometric data available to measure them directly through SED fitting.

Working with Gaussian Random Noise for Multi-Sensor Archaeological Prospection: Fusion of Ground Penetrating Radar Depth Slices and Ground Spectral Signatures from 0.00 m to 0.60 m below Ground Surface

The integration of different remote sensing datasets acquired from optical and radar sensors can improve the overall performance and detection rate for mapping sub-surface archaeological remains. However, data fusion remains a challenge for archaeological prospection studies, since remotely sensed sensors have different instrument principles, operating in different wavelengths. Recent studies have demonstrated that some fusion modelling can be achieved under ideal measurement conditions (e.g., simultaneously measurements in no hazy days) using advance regression models, like those of the nonlinear Bayesian Neural Networks. This paper aims to go a step further and investigate the impact of noise in regression models, between datasets obtained from ground-penetrating radar (GPR) and portable field spectroradiometers. Initially, the GPR measurements provided three depth slices of 20 cm thickness, starting from 0.00 m up to 0.60 m below the ground surface while ground spectral signatures acquired from the spectroradiometer were processed to calculate 13 multispectral and 53 hyperspectral indices. Then, various levels of Gaussian random noise ranging from 0.1 to 0.5 of a normal distribution, with mean 0 and variance 1, were added at both GPR and spectral signatures datasets. Afterward, Bayesian Neural Network regression fitting was applied between the radar (GPR) versus the optical (spectral signatures) datasets. Different regression model strategies were implemented and presented in the paper. The overall results show that fusion with a noise level of up to 0.2 of the normal distribution does not dramatically drop the regression model between the radar and optical datasets (compared to the non-noisy data). Finally, anomalies appearing as strong reflectors in the GPR measurements, continue to provide an obvious contrast even with noisy regression modelling.

L1495 revisited: a ppmap view of a star-forming filament

ABSTRACT We have analysed the Herschel and SCUBA-2 dust continuum observations of the main filament in the Taurus L1495 star-forming region, using the Bayesian fitting procedure ppmap. (i) If we construct an average profile along the whole length of the filament, it has FWHM $\simeq 0.087\pm 0.003\, {\rm pc};\,\,$ but the closeness to previous estimates is coincidental. (ii) If we analyse small local sections of the filament, the column-density profile approximates well to the form predicted for hydrostatic equilibrium of an isothermal cylinder. (iii) The ability of ppmap to distinguish dust emitting at different temperatures, and thereby to discriminate between the warm outer layers of the filament and the cold inner layers near the spine, leads to a significant reduction in the surface-density, $\varSigma$, and hence in the line-density, μ. If we adopt the canonical value for the critical line-density at a gas-kinetic temperature of $10\, {\rm K}$, $\mu _{{\rm CRIT}}\simeq 16\, {\rm M_{\odot }\, pc^{-1}}$, the filament is on average trans-critical, with ${\bar{\mu }}\sim \mu _{{\rm CRIT}};\,\,$ local sections where μ &gt; μCRIT tend to lie close to prestellar cores. (iv) The ability of ppmap to distinguish different types of dust, i.e. dust characterized by different values of the emissivity index, β, reveals that the dust in the filament has a lower emissivity index, β ≲ 1.5, than the dust outside the filament, β ≳ 1.7, implying that the physical conditions in the filament have effected a change in the properties of the dust.

93 Host genetics help shape the rumen microbiome in beef cattle

Abstract In this study, we investigated the degree to which host genetics shape the rumen microbiome. Complex and diverse microbial communities can alter the nutrient profile available to the animal and subsequent performance. Studies of the gut microbiome have demonstrated that host genotype influences gut microbial species composition. Therefore, microbial species composition in the rumen may be a complex trait that manifests through the convergence of host-genetics and environmental factors. To test this hypothesis, we collected rumen contents and blood samples from 586 beef cattle on different diets from two locations. The rumen samples were used to sequence the V4 region of the 16S rDNA on an Illumina MiSeq platform. Animals were genotyped with various platforms and a common set of 61,974 SNP were used to conduct a genome-wide association study (GWAS) using the microbiome (OTUs, families and phyla) as response variables. The GWAS was performed using Bayesian GBLUP fitting fixed effects of cohort (location and date), and the first 2 principle components to account for population stratification. Median posterior genomic heritability estimates were 0.110, 0.124, and 0.141 at the OTU, family and phylum taxonomic level, respectively. The top 8 1-Mb windows for OTUs, families and phyla were located on 7 different chromosomes. These regions affect the rumen microbiota in multiple ways; some (chromosome 19; position 3.0–4.0 Mb) are associated with closely related taxa (Prevotellaceae, Paraprevotellaceae, and RF16), some (chromosome 27; position 3.0–4.0 Mb) are associated with distantly related taxa (Prevotellaceae, Fibrobacteraceae, RF16, RFP12, S24-7, Lentisphaerae, and Tenericutes) and others (chromosome 23; position 0.0–1.0) controlling both related and unrelated taxa. Overall, the 8 regions identified control 11 different families and 6 different phyla. This study shows that host genetics can affect rumen bacterial community members and points towards the possibility that genomics can be used to manipulate the rumen microbiome.

Nonparametric Star Formation History Reconstruction with Gaussian Processes. I. Counting Major Episodes of Star Formation

Abstract The star formation histories (SFHs) of galaxies contain imprints of the physical processes responsible for regulating star formation during galaxy growth and quenching. We improve the Dense Basis SFH reconstruction method of Iyer &amp; Gawiser, introducing a nonparametric description of the SFH based on the lookback times at which a galaxy assembles certain quantiles of its stellar mass. The method uses Gaussian processes to create smooth SFHs independent of any functional form, with a flexible number of parameters that is adjusted to extract the maximum amount of information from the SEDs being fit. Applying the method to reconstruct the SFHs of 48,791 galaxies with H &lt; 25 at 0.5 &lt; z &lt; 3.0 across the five Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey fields, we study the evolution of galaxies over time. We quantify the fraction of galaxies that show multiple major episodes of star formation, finding that the median time between two peaks of star formation is , where t univ is the age of the universe at a given redshift and remains roughly constant with stellar mass. Correlating SFHs with morphology allows us to compare the timescales on which the SFHs decline for different morphological classifications, ranging from for galaxies with spiral arms to for spheroids at 0.5 &lt; z &lt; 1.0 with 1010 &lt; M * &lt; 1010.5 M ⊙. The Gaussian process–based SFH description provides a general approach to reconstruct smooth, flexible, nonparametric SFH posteriors for galaxies that can be incorporated into Bayesian SED fitting codes to minimize the bias in estimating physical parameters due to SFH parameterization.

Modeling Glycan Processing Reveals Golgi-Enzyme Homeostasis upon Trafficking Defects and Cellular Differentiation

SummaryThe decoration of proteins by carbohydrates is essential for eukaryotic life yet heterogeneous due to a lack of biosynthetic templates. This complex carbohydrate mixture—the glycan profile—is generated in the compartmentalized Golgi, in which level and localization of glycosylation enzymes are key determinants. Here, we develop and validate a computational model for glycan biosynthesis to probe how the biosynthetic machinery creates different glycan profiles. We combined stochastic modeling with Bayesian fitting that enables rigorous comparison to experimental data despite starting with uncertain initial parameters. This is an important development in the field of glycan modeling, which revealed biological insights about the glycosylation machinery in altered cellular states. We experimentally validated changes in N-linked glycan-modifying enzymes in cells with perturbed intra-Golgi-enzyme sorting and the predicted glycan-branching activity during osteogenesis. Our model can provide detailed information on altered biosynthetic paths, with potential for advancing treatments for glycosylation-related diseases and glyco-engineering of cells.

A Thermodynamic Model of Auto-regulated Protein Assembly by a Supramolecular Scaffold.

Ligand-mediated regulation of protein assembly occurs frequently in different cellular contexts. Auto-regulated assembly, where a ligand acts as its own competitive inhibitor, provides a mechanism for exquisite control of assembly. Unlike simple protein-ligand systems a quantification of the binding thermodynamics is not straightforward. Here, we characterize the interactions of a recently identified model system in which the oligomerization of cytochrome c is controlled by sulfonato-calix[8]arene, an anionic supramolecular scaffold. Isothermal titration calorimetry and thermodynamic modelling, in combination with Bayesian fitting, were used to quantify the ligand binding and assembly equilibria for this system. The approach and variations of this model may prove useful for the analysis of auto-regulated protein assembly in general.

Assessment of a clinically feasible Bayesian fitting algorithm using a simplified description of Chemical Exchange Saturation Transfer (CEST) imaging.

Fitting a model based on the Bloch-McConnell (BM) equations to Chemical Exchange Saturation Transfer (CEST) spectra allows for the quantification of metabolite concentration and exchange rate as well as simultaneous correction of field inhomogeneity, direct water saturation and magnetization transfer. Employing a Bayesian fitting approach permits the integration of prior information into the analysis to incorporate expected parameter distributions and to prevent over-fitting. However, the analysis can be time consuming if a general numerical solution of the BM equations is applied. In this study, we combined a Bayesian fitting algorithm with approximate analytical solutions of the BM equations to achieve feasible computational times. To evaluate the accuracy and speed of the suggested approach, phantoms including Iodipamide, Taurine and Creatine were tested in addition to simulated data with continuous-wave (CW) and pulsed saturation with Gaussian pulses. A significant reduction of computational time was achieved when fitting CW data (about 50-fold) and pulsed saturation data (more than 100-fold) with the analytical model while the estimated parameters were largely consistent with the parameters from the general numerical solution. The increased speed of the algorithm facilitates the Bayesian analysis of CEST data within clinically feasible processing times. Other analytical models valid for different parameter regimes may be employed to extend the applicability to a wider range of CEST agents.