Markov Chain Monte Carlo Research Articles

Modeling key intermediates during anaerobic digestion of lipid rich kitchen waste with an extended ADM1.

Quantitative dynamics of the key intermediates, gases and carbohydrates during anaerobic digestion of different lipid rich kitchen waste and lipid rich model kitchen waste were modeled. Six batch reactors loaded with 25g l ( 39 l ) kitchen waste and model kitchen waste during a batch experiment were considered in simulation. Observed dynamics of carbohydrates, volatile organic acids and gases were described by an extended benchmark simulation model no. 2 (BSM2). In this study the extended BSM2 included a more detailed -oxidation for prediction of caproic acid. Furthermore, the extensions included carbohydrate digestion with an additional intermediate before propionic acid was released. In addition, a novel simplification approach for initial pH estimation was successfully applied. For parameter estimation a Markov Chain Monte Carlo method was used to obtain parameter distributions. With the presented model it was possible even with no calibrated data to predict point of times of intermediates maxima and propionic acid with relative stable concentration over several days for kitchen waste.

Analysis of the spatiotemporal velocity of annual precipitation based on random field

. Changes in precipitation directly impact river runoff volume, subsequently influencing food production, and the security of downstream urban areas. In this study, we introduce a random velocity field (RVF) capable of performing multi-step predictions while providing interpretable insights into precipitation variations. The RVF leverages the gradient of a Gaussian random field to learn spatiotemporal velocity patterns and employs a predictive process to reduce dimensionality and enable multi-step forecasting. Bayesian parameter estimation is obtained using the Markov Chain Monte Carlo (MCMC) method. Our analysis reveals a noticeable shifting trend in annual precipitation based on diverse real datasets. This trend serves as a valuable foundation for further exploration of urban flood control and agricultural development strategies.

Cosmological constraints on f(Q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(Q)$$\\end{document} gravity with redshift space distortion data

In this paper, we explore one of Einstein’s alternative formulations which involves the non-metricity scalar, Q, within the framework of f(Q) theory. Our study focuses on solving the modified Friedmann equations for the case of dust matter, ρ=ρm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho =\\rho _{m}$$\\end{document}, and a form of f(Q)=α+βQn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(Q) = \\alpha + \\beta Q^n$$\\end{document}. We investigate the behavior of our model in both linear (n=1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n=1)$$\\end{document} and nonlinear (n≠1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n\ e 1)$$\\end{document} scenarios at the background and perturbation levels. By employing the Markov chain Monte Carlo (MCMC) method, we constrain our model using observational datasets including redshift space distortion, cosmic chronometers, and Pantheon+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+$$\\end{document}. Without using any parameterization of the growth rate index which quantifies the deviation from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model, both models exhibit good accuracy in describing the redshift space distortion. We further analyze the dynamics of the Universe using cosmography parameters, where our model exhibits a phase transition between deceleration and acceleration phases at z=0.789\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z=0.789$$\\end{document}. Our findings reveal that our model exhibits a phantom-like behavior based on statefinder diagnostic analysis. Interestingly, the model demonstrates a rich variety of behaviors, resembling either a quintessence-like scenario for (n<1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n<1)$$\\end{document} or phantom-like scenario for (n≥1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n\\ge 1)$$\\end{document}. Using the MCMC best fit and parameterizing the growth index, the evolution of the growth index also depends on the parameter n, either remaining constant (in the linear case) or showing a decreasing trend (in the nonlinear case), indicating a weaker growth rate of density perturbations during earlier cosmic times. Finally, we compare our findings of the growth index with the values obtained in the literature.

On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design

Bayesian Experimental Design (BED), which aims to find the optimal experimental conditions for Bayesian inference, is usually posed as to optimize the expected information gain (EIG). The gradient information is often needed for efficient EIG optimization, and as a result the ability to estimate the gradient of EIG is essential for BED problems. The primary goal of this work is to develop methods for estimating the gradient of EIG, which, combined with the stochastic gradient descent algorithms, result in efficient optimization of EIG. Specifically, we first introduce a posterior expected representation of the EIG gradient with respect to the design variables. Based on this, we propose two methods for estimating the EIG gradient, UEEG-MCMC that leverages posterior samples generated through Markov Chain Monte Carlo (MCMC) to estimate the EIG gradient, and BEEG-AP that focuses on achieving high simulation efficiency by repeatedly using parameter samples. Theoretical analysis and numerical studies illustrate that UEEG-MCMC is robust agains the actual EIG value, while BEEG-AP is more efficient when the EIG value to be optimized is small. Moreover, both methods show superior performance compared to several popular benchmarks in our numerical experiments.

Covariate-Dependent Clustering of Undirected Networks with Brain-Imaging Data

This article focuses on model-based clustering of subjects based on the shared relationships of subject-specific networks and covariates in scenarios when there are differences in the relationship between networks and covariates for different groups of subjects. It is also of interest to identify the network nodes significantly associated with each covariate in each cluster of subjects. To address these methodological questions, we propose a novel nonparametric Bayesian mixture modeling framework with an undirected network response and scalar predictors. The symmetric matrix coefficients corresponding to the scalar predictors of interest in each mixture component involve low-rankness and group sparsity within the low-rank structure. While the low-rank structure in the network coefficients adds parsimony and computational efficiency, the group sparsity within the low-rank structure enables drawing inference on network nodes and cells significantly associated with each scalar predictor. Being a principled Bayesian mixture modeling framework, our approach allows model-based identification of the number of clusters, offers clustering uncertainty in terms of the co-clustering matrix and presents precise characterization of uncertainty in identifying network nodes significantly related to a predictor in each cluster. Empirical results in various simulation scenarios illustrate substantial inferential gains of the proposed framework in comparison with competitors. Analysis of a real brain connectome dataset using the proposed method provides interesting insights into the brain regions of interest (ROIs) significantly related to creative achievement in each cluster of subjects. Supplementary material shows the convergence rate for the posterior predictive density of the proposed model, additional simulation examples with model misspecification, full conditional distributions to run the Markov chain Monte Carlo (MCMC) algorithm and also presents traceplots for various model parameters to demonstrate convergence of the MCMC algorithm.

Uncertainty assessment of aquifer hydraulic parameters from pumping test data

Data from pumping tests is a noisy process, and therefore, performing the pumping test numerous times will not get the same drawdown values. As a consequence, various pumping experiments lead to different values for aquifer parameter estimates. The data of pumping tests are usually analyzed using traditional methods (aquifer tests and AQtesolv software), which depend on trial and error technique. During these methods, non-unique values of hydraulic parameters are selected, which usually have a high level of uncertainty. Uncertainty must be taken into account in determining aquifer parameters, especially when using groundwater models for decision makers. The main goal of this study is to build a comprehensive tool for quantifying uncertainty associated with hydraulic parameter estimation from different pumping test conditions for fully penetrating wells in confined and semi-confined aquifers. To achieve the previous objective, a FORTRAN code was developed to apply the Markov Chain Monte Carlo (MCMC) algorithm using different likelihood functions (exponential, inverse, and log). This developed tool can be used to detect the most probable range of aquifer parameters that are consistent with pumping test data with a high degree of confidence. The tool was successfully used to several hypothetical cases to demonstrate the uncertainty in the quantification of aquifer parameters and compare the findings to the standard method's results. Also, the concept was verified numerically (using Modflow program) with satisfactory results using a hypothetical case with well-known aquifer parameters. Finally, the tool was applied for actual pumping test data with good results.

Optimising CH4 simulations from the LPJ-GUESS model v4.1 using an adaptive Markov chain Monte Carlo algorithm

Abstract. The processes responsible for methane (CH4) emissions from boreal wetlands are complex; hence, their model representation is complicated by a large number of parameters and parameter uncertainties. The arctic-enabled dynamic global vegetation model LPJ-GUESS (Lund–Potsdam–Jena General Ecosystem Simulator) is one such model that allows quantification and understanding of the natural wetland CH4 fluxes at various scales, ranging from local to regional and global, but with several uncertainties. The model contains detailed descriptions of the CH4 production, oxidation, and transport controlled by several process parameters. Complexities in the underlying environmental processes, warming-driven alternative paths of meteorological phenomena, and changes in hydrological and vegetation conditions highlight the need for a calibrated and optimised version of LPJ-GUESS. In this study, we formulated the parameter calibration as a Bayesian problem, using knowledge of reasonable parameters values as priors. We then used an adaptive Metropolis–Hastings (MH)-based Markov chain Monte Carlo (MCMC) algorithm to improve predictions of CH4 emission by LPJ-GUESS and to quantify uncertainties. Application of this method on uncertain parameters allows for a greater search of their posterior distribution, leading to a more complete characterisation of the posterior distribution with a reduced risk of the sample impoverishment that can occur when using other optimisation methods. For assimilation, the analysis used flux measurement data gathered during the period from 2005 to 2014 from the Siikaneva wetlands in Southern Finland with an estimation of measurement uncertainties. The data are used to constrain the processes behind the CH4 dynamics, and the posterior covariance structures are used to explain how the parameters and the processes are related. To further support the conclusions, the CH4 flux and the other component fluxes associated with the flux are examined. The results demonstrate the robustness of MCMC methods to quantitatively assess the interrelationship between objective function choices, parameter identifiability, and data support. The experiment using real observations from Siikaneva resulted in a reduction in the root-mean-square error (RMSE), from 0.044 to 0.023 gC m−2 d−1, and a 93.89 % reduction in the cost function value. As a part of this work, knowledge about how CH4 data can constrain the parameters and processes is derived. Although the optimisation is performed based on a single site's flux data from Siikaneva, the algorithm is useful for larger-scale multi-site studies for a more robust calibration of LPJ-GUESS and similar models, and the results can highlight where model improvements are needed.

Mutations make pandemics worse or better: modeling SARS-CoV-2 variants and imperfect vaccination.

COVID-19 is a respiratory disease triggered by an RNA virus inclined to mutations. Since December 2020, variants of COVID-19 (especially Delta and Omicron) continuously appeared with different characteristics that influenced death and transmissibility emerged around the world. To address the novel dynamics of the disease, we propose and analyze a dynamical model of two strains, namely native and mutant, transmission dynamics with mutation and imperfect vaccination. It is also assumed that the recuperated individuals from the native strain can be infected with mutant strain through the direct contact with individual or contaminated surfaces or aerosols. We compute the basic reproduction number, , which is the maximum of the basic reproduction numbers of native and mutant strains. We prove the nonexistence of backward bifurcation using the center manifold theory, and global stability of disease-free equilibrium when , that is, vaccine is effective enough to eliminate the native and mutant strains even if it cannot provide full protection. Hopf bifurcation appears when the endemic equilibrium loses its stability. An intermediate mutation rate leads to oscillations. When increases over a threshold, the system regains its stability and exhibits an interesting dynamics called endemic bubble. An analytical expression for vaccine-induced herd immunity is derived. The epidemiological implication of the herd immunity threshold is that the disease may effectively be eradicated if the minimum herd immunity threshold is attained in the community. Furthermore, the model is parameterized using the Indian data of the cumulative number of confirmed cases and deaths of COVID-19 from March 1 to September 27 in 2021, using MCMC method. The cumulative cases and deaths can be reduced by increasing the vaccine efficacies to both native and mutant strains. We observe that by considering the vaccine efficacy against native strain as 90%, both cumulative cases and deaths would be reduced by 0.40%. It is concluded that increasing immunity against mutant strain is more influential than the vaccine efficacy against it in controlling the total cases. Our study demonstrates that the COVID-19 pandemic may be worse due to the occurrence of oscillations for certain mutation rates (i.e., outbreaks will occur repeatedly) but better due to stability at a lower infection level with a larger mutation rate. We perform sensitivity analysis using the Latin Hypercube Sampling methodology and partial rank correlation coefficients to illustrate the impact of parameters on the basic reproduction number, the number of cumulative cases and deaths, which ultimately sheds light on disease mitigation.

Monte Carlo on manifolds in high dimensions

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018) [53]), where the manifold is defined by the level set of constraint functions, and the probability distribution may involve the pseudodeterminant of the Jacobian of the constraints, as arises in physical sampling problems. The algorithm is easy to implement and scales well to problems with thousands of dimensions and with complex sets of constraints provided their Jacobian retains sparsity. The algorithm uses direct linear algebra and requires a single matrix factorization per proposal point, which enhances its efficiency over previously proposed methods but becomes the computational bottleneck of the algorithm in high dimensions. We test the algorithm on several examples inspired by soft-matter physics and materials science to study its complexity and properties.

Quantifying the Tension between Cosmological Models and JWST Red Candidate Massive Galaxies

We develop a Python tool to estimate the tail distribution of the number of dark matter halos beyond a mass threshold and in a given volume in a light-cone. The code is based on the extended Press–Schechter model and is computationally efficient, typically taking a few seconds on a personal laptop for a given set of cosmological parameters. The high efficiency of the code allows a quick estimation of the tension between cosmological models and the red candidate massive galaxies released by the James Webb Space Telescope, as well as scanning the theory space with the Markov Chain Monte Carlo method. As an example application, we use the tool to study the cosmological implication of the candidate galaxies presented in Labbé et al. The standard Λ cold dark matter (ΛCDM) model is well consistent with the data if the star formation efficiency can reach ∼0.3 at high redshift. For a low star formation efficiency ϵ ∼ 0.1, the ΛCDM model is disfavored at ∼2σ–3σ confidence level.

High accuracy ranging for space debris with spaceborne single photon Lidar.

The increasing risk posed by space debris highlights the need for accurate localization techniques. Spaceborne single photon Lidar (SSPL) offers a promising solution, overcoming the limitations of traditional ground-based systems by providing expansive coverage and superior maneuverability without being hindered by weather, time, or geographic constraints. This study introduces a novel approach leveraging non-parametric Bayesian inference and the Dirichlet process mixture model (DPMM) to accurately determine the distance of space debris in low Earth orbit (LEO), where debris exhibits nonlinear, high dynamic motion characteristics. By integrating extended Kalman filtering (EKF) for range gating, our method captures the temporal distribution of reflected photons, employing Markov chain Monte Carlo (MCMC) for iterative solutions. Experimental outcomes demonstrate our method's superior accuracy over conventional statistical techniques, establishing a clear correlation between radial absolute velocity and ranging error, thus significantly enhancing monostatic space debris localization.

Resolving heterogeneous fluxes from tundra halves the growing season carbon budget

Abstract. Landscapes are often assumed to be homogeneous when interpreting eddy covariance fluxes, which can lead to biases when gap-filling and scaling up observations to determine regional carbon budgets. Tundra ecosystems are heterogeneous at multiple scales. Plant functional types, soil moisture, thaw depth, and microtopography, for example, vary across the landscape and influence net ecosystem exchange (NEE) of carbon dioxide (CO2) and methane (CH4) fluxes. With warming temperatures, Arctic ecosystems are changing from a net sink to a net source of carbon to the atmosphere in some locations, but the Arctic's carbon balance remains highly uncertain. In this study we report results from growing season NEE and CH4 fluxes from an eddy covariance tower in the Yukon–Kuskokwim Delta in Alaska. We used footprint models and Bayesian Markov chain Monte Carlo (MCMC) methods to unmix eddy covariance observations into constituent land-cover fluxes based on high-resolution land-cover maps of the region. We compared three types of footprint models and used two land-cover maps with varying complexity to determine the effects of these choices on derived ecosystem fluxes. We used artificially created gaps of withheld observations to compare gap-filling performance using our derived land-cover-specific fluxes and traditional gap-filling methods that assume homogeneous landscapes. We also compared resulting regional carbon budgets when scaling up observations using heterogeneous and homogeneous approaches. Traditional gap-filling methods performed worse at predicting artificially withheld gaps in NEE than those that accounted for heterogeneous landscapes, while there were only slight differences between footprint models and land-cover maps. We identified and quantified hot spots of carbon fluxes in the landscape (e.g., late growing season emissions from wetlands and small ponds). We resolved distinct seasonality in tundra growing season NEE fluxes. Scaling while assuming a homogeneous landscape overestimated the growing season CO2 sink by a factor of 2 and underestimated CH4 emissions by a factor of 2 when compared to scaling with any method that accounts for landscape heterogeneity. We show how Bayesian MCMC, analytical footprint models, and high-resolution land-cover maps can be leveraged to derive detailed land-cover carbon fluxes from eddy covariance time series. These results demonstrate the importance of landscape heterogeneity when scaling carbon emissions across the Arctic.

Bayesian mixed model inference for genetic association under related samples with brain network phenotype.

Genetic association studies for brain connectivity phenotypes have gained prominence due to advances in noninvasive imaging techniques and quantitative genetics. Brain connectivity traits, characterized by network configurations and unique biological structures, present distinct challenges compared to other quantitative phenotypes. Furthermore, the presence of sample relatedness in the most imaging genetics studies limits the feasibility of adopting existing network-response modeling. In this article, we fill this gap by proposing a Bayesian network-response mixed-effect model that considers a network-variate phenotype and incorporates population structures including pedigrees and unknown sample relatedness. To accommodate the inherent topological architecture associated with the genetic contributions to the phenotype, we model the effect components via a set of effect network configurations and impose an inter-network sparsity and intra-network shrinkage to dissect the phenotypic network configurations affected by the risk genetic variant. A Markov chain Monte Carlo (MCMC) algorithm is further developed to facilitate uncertainty quantification. We evaluate the performance of our model through extensive simulations. By further applying the method to study, the genetic bases for brain structural connectivity using data from the Human Connectome Project with excessive family structures, we obtain plausible and interpretable results. Beyond brain connectivity genetic studies, our proposed model also provides a general linear mixed-effect regression framework for network-variate outcomes.

Statistical inference for a two-parameter Rayleigh distribution under generalized progressive hybrid censoring scheme

The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose.

Uncertainty analysis of greenhouse gas emissions of monorail transit during the construction.

This paper examines the uncertainty of greenhouse gas (GHG) emissions during monorail construction. Firstly, a deterministic analysis is conducted. Subsequently, the obtained data are evaluated using the data quality indicator (DQI), and a Markov chain Monte Carlo (MCMC) simulation method is employed to assume different parameter distributions. The results of the deterministic calculation indicate that the calculated emissions per unit area of the station amount to 1.97 ton CO2e/m2, while the calculated emissions per unit section length reach 7.55 ton CO2e/m2. To simulate parameter distribution, we utilize a Beta distribution with good shape applicability. Furthermore, we establish scenarios involving system boundary reduction, low-emission factors, and reduced material and energy inputs in order to analyze scenario uncertainties. Regarding model uncertainty, this paper assumes that the material and energy quantity data conform to the normal, log-normal, uniform, and triangular distributions, respectively, subsequently analyzing the uncertainty distributions. This paper analyzes the GHG emission uncertainty evaluation of 16 monorail stations and sections during the construction period, which is divided into parameter, scenario, and model uncertainty. We provide a concrete framework for studying uncertainties related to GHG emissions at stations and sections during the monorail construction period. The scenario analysis results will help to make decisions about the choice of parameters, system boundaries, and other settings. It provides new guidance for emission reduction policies, such as reducing the use of steel-related products or using alternative environmentally friendly materials, considering emission reduction factors more comprehensively and setting emission reduction factors according to uniform distribution principle as far as possible.

Global optimization of multilayer dielectric coatings for precision measurements.

We describe the design of optimized multilayer dielectric coatings for precision laser interferometry. By setting up an appropriate cost function and then using a global optimizer to find a minimum in the parameter space, we were able to realize coating designs that meet the design requirements for spectral reflectivity, thermal noise, absorption, and tolerances to coating fabrication errors. We also present application of a Markov-Chain Monte Carlo (MCMC) based parameter estimation algorithm that can infer thicknesses of dielectric layers in a coating, given a measurement of the spectral reflectivity. This technique can be a powerful diagnostic tool for both commercial coating manufacturers, and the community using dielectric mirrors for precision metrology experiments.

21 cm intensity mapping cross-correlation with galaxy surveys: Current and forecasted cosmological parameters estimation for the SKAO

ABSTRACT We present a comprehensive set of forecasts for the cross-correlation signal between 21 cm intensity mapping and galaxy redshift surveys. We focus on the data sets that will be provided by the SKAO for the 21 cm signal, DESI and Euclid for galaxy clustering. We build a likelihood which takes into account the effect of the beam for the radio observations, the Alcock–Paczynski effect, a simple parametrization of astrophysical nuisances, and fully exploit the tomographic power of such observations in the range z = 0.7–1.8 at linear and mildly non-linear scales (k &amp;lt; 0.25h Mpc−1). The forecasted constraints, obtained with Monte Carlo Markov Chains techniques in a Bayesian framework, in terms of the six base parameters of the standard ΛCDM model, are promising. The predicted signal-to-noise ratio for the cross-correlation can reach ∼50 for z ∼ 1 and k ∼ 0.1h Mpc−1. When the cross-correlation signal is combined with current Cosmic Microwave Background (CMB) data from Planck, the error bar on $\Omega _{\rm c}\, h^2$ and H0 is reduced by factors 3 and 6, respectively, compared to CMB only data, due to the measurement of matter clustering provided by the two observables. The cross-correlation signal has a constraining power that is comparable to the autocorrelation one and combining all the clustering measurements a sub-per cent error bar of 0.33 per cent on H0 can be achieved, which is about a factor 2 better than CMB only measurements. Finally, as a proof of concept, we test the full pipeline on the real data measured by the MeerKat collaboration (Cunnington et al. 2022) presenting some (weak) constraints on cosmological parameters.

The Relevance of Dynamical Friction for the MW/LMC/SMC Triple System

Simulations of structure formation in the standard cold dark matter cosmological model quantify the dark matter halos of galaxies. Taking into account dynamical friction between dark matter halos, we investigate the past orbital dynamical evolution of the Magellanic Clouds in the presence of the Galaxy. Our calculations are based on a three-body model of rigid Navarro–Frenk–White profiles for dark matter halos but were verified in a previous publication by comparison to high-resolution N-body simulations of live self-consistent systems. Under the requirement that the LMC and SMC had an encounter within 20 kpc between 1 and 4 Gyr ago in order to allow the development of the Magellanic Stream, using the latest astrometric data, the dynamical evolution of the MW/LMC/SMC system is calculated backwards in time. With the employment of the genetic algorithm and a Markov-Chain Monte-Carlo method, the present state of this system is unlikely, with a probability of &lt;10−9 (6σ complement), because the solutions found do not fit into the error bars for the observed plane-of-sky velocity components of the Magellanic Clouds. This implies that orbital solutions that assume dark matter halos, according to cosmological structure formation theory, to exist around the Magellanic Clouds and the Milky Way are not possible with a confidence of more than 6 sigma.

Modeling high-frequency financial data using R and Stan: A bayesian autoregressive conditional duration approach

In econometrics, Autoregressive Conditional Duration (ACD) models use high-frequency economic or financial duration data, which mostly exhibit irregular time intervals. The ACD model is widely used to examine the duration of transaction volume and duration of price variations in stock markets. In this work, our goal is to devise testing that will aid in the identification of the best potential duration model among a set of four models using Bayesian approach. We test three models that rely on conditional mean duration (Weibull ACD, Log Weibull ACD, Generalized Gamma ACD) and one conditional median duration model (Birnbaum-Saunders ACD), and are being compared each other. The study was done in Rstan, a programming language for statistical inference, and the simulation uses the Hamiltonian Monte Carlo (HMC) algorithm of Markov Chain Monte Carlo (MCMC) to sample from the posterior distribution. Our findings show that Log Weibull ACD (second-generation model) as best among the four models followed by Birnbaum-Saunders ACD (third-generation model). The result offers methodological implications for algorithmic trading (algo-trading), high-frequency trading and risk management.

A new selection criteria to optimize growth in animal breeding programs

Pedigree records and longitudinal measurements of live weight from 2628 buffaloes were analyzed. The aim of this research was to propose a new selection criteria, the Area Under the Growth Curve (AUGC), derived from a growth curve-based model. A hierarchical Bayesian approach with two levels was employed. In the first level, the growth trajectory was modeled using a fourth-degree polynomial, while in the second level, each parameter of the polynomial function was treated as a dependent variable influenced by environmental and genetic effects. The animal model included sex, dams’ parity and contemporary group (herd-year-season) as fixed effects, and relationships among animals as a random effect. Inference was conducted using Markov Chain Monte Carlo (MCMC) simulation algorithm. The proposed AUGC is interesting for use in selection programs because it allows breeders to identify heavier animals with lower risk in the production system. Additionally, that trait showed moderate to high heritabilities from weaning onwards, providing a useful new tool for cattle selection in the post-weaning phases.