Markov Chain Monte Carlo Research Articles

A comprehensive analysis of observational cosmology in [formula omitted] gravity with deep learning and MCMC method

Our goal in this study is to build FRW cosmological models inside the f(Q) theory of gravity framework by using Bayesian statistics and deep learning method. We investigate the universe’s accelerating behaviour for a specific version of the f(Q) gravity model using a novel, straightforward parameterization of the Hubble parameter in the form H=H0(1+z)1+q0−q1exp(q1z). The corresponding free parameters in H(z) are limited between 1σ and 2σ confidence bounds using the χ2-minimization procedure. The results show that all the numbers we got are in the ballpark of what cosmological observations would predict. In our model, we examined the physical behaviour of the cosmos using characteristics such as energy density, pressure, and equation of state. We analysed kinematic factors including Hubble parameter, acceleration parameter, and universe age in our model. In our concept, the deceleration parameter q(z) represents the universe’s transition from deceleration to acceleration. We employ a novel approach for parameter estimation by utilizing a mixed neural network (MNN) that combines artificial neural networks (ANN) and mixture density networks (MDN). This new methodology leverages the strengths of ANN, MDN, and MNN to enhance the accuracy of parameter estimation.

A virtual anti-scatter grid for multi-energy photon counting detector systems

Photon-counting (PC) systems are the next technological generation of medical computed tomography (CT) imaging and is being worked on by all major system providers. CT devices that are based on PC detectors enable multi-energy data collection. The information-content of this data can be used to obtain more detailed patient data, which improves the quality of reconstructions, compared to conventional detector systems. However, PC CT systems are subject to radiation scatter as just as any other imaging systems is. Conventionally anti-scatter grids (ASG) are used to reduce the scatter effect. These are however an imperfect solution, especially for PC detectors. In this work, a software-based scatter correction method, thus a virtual ASG is proposed. The method is tailoring a new statistical model in the measurement space and combining it with the statistical inversion method called Markov chain Monte Carlo (MCMC). The method can recover the measurement data from dense projections. We present the method on simulated data of a single photon emission computed tomography (SPECT) problem for which only under-sampled data is available. However, our approach can in principle be generalised to CT, PC-CT, Positron emission tomography (PET), radiotherapy, or even digital radiography problems. The results show that the proposed model performs similarly as physical ASGs and for cases where ASGs are not possible. The model further offers a significant improvement in the quality of the reconstruction image compared to the image reconstruction from original under-sampled data.

Efficacy and safety of direct-acting antiviral regimen for patients with hepatitis C virus genotype 2: a systematic review and meta-analysis.

Direct-acting antivirals (DAAs) show high cure rates in treating chronic hepatitis C virus (HCV). However, the effect of DAAs on patients infected with genotype 2 (GT2) is difficult to determine despite the availability of several DAA regimens. A systematic search of six databases (PubMed, Embase, Cochrane Library, Web of Science, CNKI, and Clinicaltrial.gov) was conducted through April 20, 2022. We considered the sustained virological response 12 weeks after treatment (SVR12) as the efficacy outcome, and adverse events (AEs) as the safety outcome. By calculating the mean SVR12 and the proportion of AEs among patients, we considered the intervention effect for each DAA regimen. The random effect model was then used in all meta-analyses. This systematic review and meta-analysis aimed to summarize the evidence on efficacy and safety of DAAs in patients infected with HCV GT2. The Bayesian Markov Chain Monte Carlo (MCMC) network metanalysis was used to indirectly compare regimen in GT2 patients. Among 31 articles included (2,968 participants), consisting of 1,387 treatment-naive patients and 354 patients with cirrhosis. The overall pooled SVR12 rate was 94.62% (95% CI: 92.43-96.52%) among the participants who received all doses of treatment. Meta-analysis results of AEs revealed that fatigue was the most common AE (14.0%, 95% CI: 6.4-21.6%), followed by headache (13.1%, 95% CI: 9.2-17.1%), whereas death and serious adverse events were uncommon. We compared DAA-based treatments indirectly using meta-analysis and found the combination of Sofosbuvir plus Velpatasvir and Glecaprevir plus Pibrentasvir, each administered over a 12-week period, were identified as the most effective and relatively safe in managing chronic hepatitis C virus genotype 2 (HCV GT2) infection. Both treatments achieved a SVR12 of 100% (95% CI 99-100%).

Constraining the Initial Mass Function via Stellar Transients

The stellar initial mass function (IMF) represents a fundamental quantity in astrophysics and cosmology describing the mass distribution of stars from low mass all the way up to massive and very massive stars. It is intimately linked to a wide variety of topics, including stellar and binary evolution, galaxy evolution, chemical enrichment, and cosmological reionization. Nonetheless, the IMF still remains highly uncertain. In this work, we aim to determine the IMF with a novel approach based on the observed rates of transients of stellar origin. We parametrize the IMF with a simple but flexible Larson shape, and insert it into a parametric model for the cosmic UV luminosity density, local stellar mass density, type Ia supernova (SN Ia), core-collapse supernova (CCSN), and long gamma-ray burst (LGRB) rates as a function of redshift. We constrain our free parameters by matching the model predictions to a set of empirical determinations for the corresponding quantities via a Bayesian Markov Chain Monte Carlo method. Remarkably, we are able to provide an independent IMF determination with a characteristic mass mc=0.10−0.08+0.24M⊙ and high-mass slope ξ=−2.53−0.27+0.24 that are in accordance with the widely used IMF parameterizations (e.g., Salpeter, Kroupa, Chabrier). Moreover, the adoption of an up-to-date recipe for the cosmic metallicity evolution allows us to constrain the maximum metallicity of LGRB progenitors to Zmax=0.12−0.05+0.29Z⊙. We also find which progenitor fraction actually leads to SN Ia or LGRB emission (e.g., due to binary interaction or jet-launching conditions), put constraints on the CCSN and LGRB progenitor mass ranges, and test the IMF universality. These results show the potential of this kind of approach for studying the IMF, its putative evolution with the galactic environment and cosmic history, and the properties of SN Ia, CCSN, and LGRB progenitors, especially considering the wealth of data incoming in the future.

Bayesian Updating for Prediction of Scour Depth Using Natural Frequency of Monopiles

Scour is a non-negligible issue of monopiles that profoundly threatens the safety of monopile for offshore wind turbines (OWTs). Accurately predicting the scour depth is essential for the design and operation of OWTs. This study introduces a model aimed at predicting scour depth from the aspect of the natural frequency of monopile. The model is developed using uniform design samples to ensure its applicability across a wider range of OWT monopiles and soil properties. To enhance the model accuracy, a Bayesian framework is employed, incorporating prior information. The three main model coefficients are updated iteratively, allowing the predicted scour depth to converge with the observed values. The Monte Carlo Markov chain (MCMC) simulation is utilized to generate the posterior distribution. The model accuracy is validated through 48 representative samples, and the effectiveness of Bayesian updating in improving the model precision is demonstrated by comparing the results prior to and following Bayesian updating. Additionally, the numerical simulations and monitored data confirm the validity of the proposed prediction model.

A combined Markov Chain Monte Carlo and Levenberg–Marquardt inversion method for heterogeneous subsurface reservoir modeling

In this study, we systematically investigate an inverse method for heterogeneous porous media to obtain porosity and permeability fields considering only production well data. The forward modeling of the input data, namely pressure and saturation fields, is based on the motion equations of a coupled Darcy flow system involving two phases of isothermal fluid flow. We discretize these equations using a multiscale finite volume simulation technique in the spatial domain, and the backward Euler method in time domain. In the inversion procedure, we combine a global optimization method, the Markov Chain Monte Carlo (MCMC) method, with a local optimization method, the Levenberg–Marquardt (LM) method. The MCMC was implemented as the Random Walk algorithm, and to generate the samples of the porosity and permeability fields, we employed Karhunen–Loève (KL) expansion of second-order stationary fields with Gaussian covariance. The coefficients of the KL expansion are estimated by minimizing the norm of the residual dependent on these fields. At the end of the MCMC iterations, we refine the KL coefficients associated with the porosity and permeability fields using the LM method. We verify in the numerical experiments that the accuracy of the porosity and permeability fields is improved by the LM refinement step.

Estimation of the Hubble constant using Gaussian process regression and viable alternatives

A well-known problem in cosmology is the ‘Hubble tension’ problem, i.e. different estimates for the Hubble constant H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} are not concordant with each other. This work investigates different statistical methods for estimating this value using cosmic chronometer, type Ia supernova and baryonic acoustic data. We start by making use of methods already established in the literature for this purpose, namely Gaussian process regression and Markov chain Monte Carlo (MCMC) methods based on the concordance Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model. We also consider two novel approaches; the first makes use of non-parametric MCMC inference on the hyperparameters of a Gaussian process kernel, independently of any cosmological model. The second approach is Student’s t-process regression, which is a generalised version of Gaussian process regression that makes use of the multivariate Student’s t-distribution instead of the multivariate Gaussian distribution. We also consider variants of these two methods which account for heteroscedasticity within the data. A comparison of the different approaches is made. In particular, the model-independent techniques investigated mostly agree with predictions based on the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model. Moreover, Gaussian process regression is highly sensitive to the prior specification, while Student’s t-process regression and the heteroscedastic variants of both methods are more robust to this. Student’s t-process regression and both heteroscedastic models suggest a lower value of the Hubble constant. Across all the estimates obtained for the Hubble constant within this work, the median value is H^0med=68.85±1.67\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{H}_0^{med} = 68.85 \\pm 1.67$$\\end{document} km s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} Mpc-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}.

Model-independent cosmographic constraints from DESI 2024

Context. We explore model-independent constraints on the Universe kinematics up to the snap and jerk hierarchical terms, considering the latest baryon acoustic oscillation (BAO) release provided by the DESI collaboration. Aims. We intend to place novel and more stringent constraints on the cosmographic series, incorporating three combinations of data catalogs: the first made by BAO and observational cosmic chronometers, the second made by BAO and type Ia supernovae, and the last including all the cited data sets. Methods. Considering the latest BAO data provided by the DESI collaboration and tackling the rd parameter to span within the range [144,152] Mpc, with a fixed step of δrd = 2 Mpc, we employed Monte Carlo Markov chain analyses based on the Metropolis algorithm to fix novel bounds on the cosmographic series, fixing the deceleration, q0 , the jerk, j0 , and the snap, s0, parameters, up to the 2σ level. A comparison between the results of the Planck satellite with those obtained by the DESI collaboration is also reported. Results. Our findings showcase a significant departure in terms of j0 even at the 1σ confidence level, albeit compatible with the ACDM paradigm in regard to q0 and s0 at the 2σ level. Analogously, the h0 tension appears alleviated in the second hierarchy when including snap. Conclusions. Our method excludes models that significantly depart from the standard cosmological model. Particularly, direct comparisons with the ACDM and wCDM models and the Chevallier-Polarski-Linder parameterisation are explored, which definitively favour the wCDM scenario over other approaches, contradicting the findings of the original DESI collaboration.

Circular motion and QPOs near black holes in Kalb–Ramond gravity

General relativity (GR) theory modifications include different scalar, vector, and tensor fields with non-minimal gravitational coupling. Kalb–Ramond (KR) gravity is a modified theory formulated based on the presence of the bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BHs) using observational data. In the present work, we aimed to test KR gravity through theoretical studies of epicyclic frequencies of particle oscillations using quasi-periodic oscillation (QPO) frequency data from microquasars. First, we derive equations of motion and analyze the effective potential for circular orbits. Also, we studied the energy and angular momentum of particles corresponding to circular orbits. In addition, we analyze the stability of circular orbits. It is shown that the radius of the innermost stable circular orbits is inversely proportional to the KR parameter. We are also interested in how the energy and angular momentum of test particles at ISCO behave around the KR BHs. We found that the Keplerian frequency for the test particles in KR gravity is the same as that in GR. Finally, we study the QPOs by applying epicyclic oscillations in the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models. We also analyze QPO orbits in the resonance cases of upper and lower frequencies 3:2, 4:3, and 5:4 in the QPO as mentioned above models. We obtain constraints on the KR gravity parameter and BH mass using a Monte Carlo Markov Chain simulation in the multidimensional parameter space for the microquasars GRO J1655-40 & XTE J1550-564, M82 X-1, and Sgr A*.

Long-term waning of vaccine-induced immunity to measles in England: a mathematical modelling study

Among people infected with measles in England between 2010 and 2019, the proportion of cases who had previously received two doses of vaccine has increased, especially among young adults. Possible explanations include rare infections in vaccinated individuals who did not gain immunity upon vaccination, made more common because fewer individuals in the population were born in the endemic era, before vaccination was introduced, and exposed as part of endemic transmission, or the waning of vaccine-induced immunity, which would present new challenges for measles control in near-elimination settings. We aimed to evaluate whether measles dynamics observed in England between 2010 and 2019 were in line with a waning of vaccine-induced immunity. We used a compartmental mathematical model stratified by age group, region, and vaccine status, fitted to individual-level case data reported in England from 2010 to 2019 and collected by the UK Health Security Agency. The deterministic model was fitted using Monte Carlo Markov Chains under three scenarios: without the waning of vaccine-induced immunity, with waning depending on time since vaccination, and with waning depending on time since vaccination, starting in 2000. We generated stochastic simulations from the fitted parameter sets to evaluate which scenarios could replicate the transmission dynamics observed in vaccinated cases in England. The scenario without waning overestimated the number of one-dose recipients among measles cases, and underestimated the number of two-dose recipients among cases older than 15 years (median 75 cases [95% simulation interval (SI) 44-124] in simulations without waning, 196 [95% SI 122-315] in simulations when waning was included, 188 [95% SI 118-301] in simulations when waning started in 2000, and 202 observed cases). The number of onward transmissions from vaccinated cases was 83% (95% credible interval 72-91%) of the number of transmissions from unvaccinated cases. The estimated waning rate was slow (0·039% per year of age; 95% credible interval 0·034-0·044% per year in the best-fitting scenario with waning starting in 2000), but sufficient to increase measles burden. Measles case dynamics in England are consistent with scenarios assuming the waning of vaccine-induced immunity. Since measles is highly infectious, slow waning leads to a heightened burden in outbreaks, increasing the number of measles cases in people who are both vaccinated and unvaccinated. Our findings show that although the vaccine remains highly protective against measles infections for decades and most transmission is connected to people who are unvaccinated, breakthrough infections are increasingly frequent for individuals aged 15 years and older who have been vaccinated twice. National Institute for Health and Care Research and Wellcome Trust.

Phenomenological emergent dark energy in the light of DESI Data Release 1

This manuscript revisits the phenomenological emergent dark energy model (PEDE) by confronting it with recent cosmological data from early and late times. In particular we analyze PEDE model by using the baryon acoustic oscillation (BAO) measurements coming from both Dark Energy Spectroscopy Instrument (DESI) data release 1 and Sloan Digital Sky Survey (SDSS). Additionally, the measurements from cosmic chronometers, supernovae type Ia (Pantheon+), quasars, hydrogen II galaxies and cosmic background radiation distance priors are considered. By performing a Bayesian analysis based on Monte Carlo Markov Chain, we find consistent results on the constraints when SDSS and DESI are considered. However, we find higher values on the Hubble constant than Supernova H0 for the Equation of State (SH0ES) does although it is still in agreement, within 1σ confidence level, when BAO measurements are added. Furthermore, we estimate the age of the Universe younger ∼3% than the one predicted by the standard cosmology. Additionally, we report values of q0=−0.771−0.007+0.007, zT=0.764−0.011+0.011 for the deceleration parameter today and the deceleration–acceleration transition redshift, respectively. However, PEDE cosmology is disfavored by the combined samples.

Multivariate moment least-squares variance estimators for reversible Markov chains

Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for multivariate functions of a Markov chain, it is important to estimate not only the auto-correlation for each component but also to estimate cross-correlations, in order to better assess sample quality, improve estimates of effective sample size, and use more effective stopping rules. Berg and Song (2023) introduced the moment least squares (momentLS) estimator, a shape-constrained estimator for the autocovariance sequence from a reversible Markov chain, for univariate functions of the Markov chain. Based on this sequence estimator, they proposed an estimator of the asymptotic variance of the sample mean from MCMC samples. In this study, we propose novel autocovariance sequence and asymptotic variance estimators for Markov chain functions with multiple components, based on the univariate momentLS estimators from Berg and Song (2023). We demonstrate strong consistency of the proposed auto(cross)-covariance sequence and asymptotic variance matrix estimators. We conduct empirical comparisons of our method with other state-of-the-art approaches on simulated and real-data examples, using popular samplers including the random-walk Metropolis sampler and the No-U-Turn sampler from STAN. Supplemental materials for this article are available online.

A Comparative Study of Single-Chain and Multi-Chain MCMC Algorithms for Bayesian Model Updating-Based Structural Damage Detection

Bayesian model updating has received considerable attention and has been extensively used in structural damage detection. It provides a rigorous statistical framework for realizing structural system identification and characterizing uncertainties associated with modeling and measurements. The Markov Chain Monte Carlo (MCMC) is a promising tool for inferring the posterior distribution of model parameters to avoid the intractable evaluation of multi-dimensional integration. However, the efficacy of most MCMC techniques suffers from the curse of parameter dimension, which restricts the application of Bayesian model updating to the damage detection of large-scale systems. In addition, there are several MCMC techniques that require users to properly choose application-specific models, based on the understanding of algorithm mechanisms and limitations. As seen in the literature, there is a lack of comprehensive work that investigates the performances of various MCMC algorithms in their application of structural damage detection. In this study, the Differential Evolutionary Adaptive Metropolis (DREAM), a multi-chain MCMC, is explored and adapted to Bayesian model updating. This paper illustrates how DREAM is used for model updating with many uncertainty parameters (i.e., 40 parameters). Furthermore, the study provides a tutorial to users who may be less experienced with Bayesian model updating and MCMC. Two advanced single-chain MCMC algorithms, namely, the Delayed Rejection Adaptive Metropolis (DRAM) and Transitional Markov Chain Monte Carlo (TMCMC), and DREAM are elaborately introduced to allow practitioners to understand better the concepts and practical implementations. Their performances in model updating and damage detection are compared through three different engineering applications with increased complexity, e.g., a forty-story shear building, a two-span continuous steel beam, and a large-scale steel pedestrian bridge.

Kinetics of Viral Shedding for Outbreak Surveillance of Emerging Infectious Diseases: Modeling Approach to SARS-CoV-2 Alpha and Omicron Infection.

Previous studies have highlighted the importance of viral shedding using cycle threshold (Ct) values obtained via reverse transcription polymerase chain reaction to understand the epidemic trajectories of SARS-CoV-2 infections. However, it is rare to elucidate the transition kinetics of Ct values from the asymptomatic or presymptomatic phase to the symptomatic phase before recovery using individual repeated Ct values. This study proposes a novel Ct-enshrined compartment model to provide a series of quantitative measures for delineating the full trajectories of the dynamics of viral load from infection until recovery. This Ct-enshrined compartment model was constructed by leveraging Ct-classified states within and between presymptomatic and symptomatic compartments before recovery or death among people with infections. A series of recovery indices were developed to assess the net kinetic movement of Ct-up toward and Ct-down off recovery. The model was applied to (1) a small-scale community-acquired Alpha variant outbreak under the "zero-COVID-19" policy without vaccines in May 2021 and (2) a large-scale community-acquired Omicron variant outbreak with high booster vaccination rates following the lifting of the "zero-COVID-19" policy in April 2022 in Taiwan. The model used Bayesian Markov chain Monte Carlo methods with the Metropolis-Hastings algorithm for parameter estimation. Sensitivity analyses were conducted by varying Ct cutoff values to assess the robustness of the model. The kinetic indicators revealed a marked difference in viral shedding dynamics between the Alpha and Omicron variants. The Alpha variant exhibited slower viral shedding and lower recovery rates, but the Omicron variant demonstrated swifter viral shedding and higher recovery rates. Specifically, the Alpha variant showed gradual Ct-up transitions and moderate recovery rates, yielding a presymptomatic recovery index slightly higher than 1 (1.10), whereas the Omicron variant had remarkable Ct-up transitions and significantly higher asymptomatic recovery rates, resulting in a presymptomatic recovery index much higher than 1 (152.5). Sensitivity analysis confirmed the robustness of the chosen Ct values of 18 and 25 across different recovery phases. Regarding the impact of vaccination, individuals without booster vaccination had a 19% higher presymptomatic incidence rate compared to those with booster vaccination. Breakthrough infections in boosted individuals initially showed similar Ct-up transition rates but higher rates in later stages compared to nonboosted individuals. Overall, booster vaccination improved recovery rates, particularly during the symptomatic phase, although recovery rates for persistent asymptomatic infection were similar regardless of vaccination status once the Ct level exceeded 25. The study provides new insights into dynamic Ct transitions, with the notable finding that Ct-up transitions toward recovery outpaced Ct-down and symptom-surfacing transitions during the presymptomatic phase. The Ct-up against Ct-down transition varies with variants and vaccination status. The proposed Ct-enshrined compartment model is useful for the surveillance of emerging infectious diseases in the future to prevent community-acquired outbreaks.

Efficiency of reversible MCMC methods: elementary derivations and applications to composite methods

Abstract We review criteria for comparing the efficiency of Markov chain Monte Carlo (MCMC) methods with respect to the asymptotic variance of estimates of expectations of functions of state, and show how such criteria can justify ways of combining improvements to MCMC methods. We say that a chain on a finite state space with transition matrix P efficiency-dominates one with transition matrix Q if for every function of state it has lower (or equal) asymptotic variance. We give elementary proofs of some previous results regarding efficiency dominance, leading to a self-contained demonstration that a reversible chain with transition matrix P efficiency-dominates a reversible chain with transition matrix Q if and only if none of the eigenvalues of $Q-P$ are negative. This allows us to conclude that modifying a reversible MCMC method to improve its efficiency will also improve the efficiency of a method that randomly chooses either this or some other reversible method, and to conclude that improving the efficiency of a reversible update for one component of state (as in Gibbs sampling) will improve the overall efficiency of a reversible method that combines this and other updates. It also explains how antithetic MCMC can be more efficient than independent and identically distributed sampling. We also establish conditions that can guarantee that a method is not efficiency-dominated by any other method.

Fast Computer Model Calibration using Annealed and Transformed Variational Inference

Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While Bayesian inference is the standard approach for this task, employing Markov chain Monte Carlo methods often encounters computational hurdles due to the costly evaluation of likelihood functions and slow mixing rates. Although variational inference (VI) can be a fast alternative to traditional Bayesian approaches, VI has limited applicability due to boundary issues and local optima problems. To address these challenges, we propose flexible VI methods based on deep generative models that do not require parametric assumptions on the variational distribution. We embed a surjective transformation in our framework to avoid posterior truncation at the boundary. Additionally, we provide theoretical conditions that guarantee the success of the algorithm. Furthermore, our temperature annealing scheme and fine-tuning can prevent being trapped in local optima through a series of intermediate posteriors and weight adjustment. We apply our method to infectious disease models and a geophysical model, illustrating that the proposed method can provide fast and accurate inference compared to its competitors.

Comparative Analysis of Perturbed $f(R)$ Gravity and Perturbed Rastall Gravity Models in Describing Cosmic Evolution from Early to Late Universe Relative to the $\Lambda$CDM Model

Abstract This study conducts a meticulous examination of the cosmological implications inherent in Rastall gravity and $f(R)$ gravity models, assessing their efficacy across distinct cosmic epochs, from early universe structure formation to late-time acceleration. In the initial stages, both models exhibit commendable compatibility with observed features of structure formation, aligning with the established $\Lambda$CDM model. The derived Jeans' wavenumbers for each model support their viability. However, as the cosmic timeline progresses into the late universe, a discernible disparity surfaces. Utilizing the Markov Chain Monte Carlo method, we reconstruct the deceleration parameter $(q)$ and identify Deceleration - Acceleration redshift transition values. For $f(R)$ gravity, our results align closely with previous studies, emphasizing its superior ability to elucidate the recent cosmic acceleration. In contrast, Rastall gravity exhibits distinct redshift transition values. Our rigorous analysis underscores the prowess of $f(R)$ gravity in capturing the observed cosmic acceleration, positioning it as a compelling alternative to the conventional $\Lambda$CDM model. The discernible shifts observed in the peaks of the CMB power spectrum and evolution of deceleration parameter (q) for both $f(R)$ gravity and Rastall gravity models in the Early and Late universe, in relation to the $\Lambda $CDM model, provide compelling evidence supporting the proposition that these alternative gravity models can account for the anisotropy of the universe without invoking the need for dark energy.

Sequential model identification with reversible jump ensemble data assimilation method

In data assimilation (DA) schemes, the form representing the processes in the evolution models are pre-determined except some parameters to be estimated. In some applications, such as the contaminant solute transport model and the gas reservoir model, the modes in the equations within the evolution model cannot be predetermined from the outset and may change with the time. We propose a framework of sequential DA method named Reversible Jump Ensemble Filter (RJEnF) to identify the governing modes of the evolution model over time. The main idea is to introduce the Reversible Jump Markov Chain Monte Carlo (RJMCMC) method to the DA schemes to fit the situation where the modes of the evolution model are unknown and the dimension of the parameters is changing. Our framework allows us to identify the modes in the evolution model and their changes, as well as estimate the parameters and states of the dynamic system. Numerical experiments are conducted and the results show that our framework can effectively identify the underlying evolution models and increase the predictive accuracy of DA methods.

Simulation of Discovering Market Opportunities Using AI Methods

Due to the strong turbulence that exists in the business environment, the view is sometimes articulated that the time horizon of decisions is no longer a hallmark of strategic management. Opposing views argue that a turbulent environment changes the trajectory of reaching future objectives determined by strategic decisions. Such trajectories require the company to be agile, which is manifested by seizing opportunities. Opportunities arise because the environment is volatile. An example of market opportunity is the unsatisfied demand for products. Buyers are driven by different motives when choosing between products that are alternative to them. From the producer's point of view, the purchase is therefore random. As a consequence, the alignment of the offered product portfolio with the actual purchasing decisions of customers is undetermined. In this article, we address the problem of determining the product portfolio structure expected by customers, i.e. one that is consistent with their future purchasing decisions. We hypothesise that this problem can be represented by a model of flows between alternative resources. Problems of this type are solved using Markov Chain Monte Carlo (MCMC) methods. In order to discover the expected demand (opportunity), we simulated the flow model we developed using the Metropolis-Hastings algorithm, which is a special case of the MCMC method used in AI. Due to operating on numerical data, such simulations fall under quantitative research. In the article, we present a model of customer flows between alternative products and then the simulation result, which is the expected value of these flows (stationary point). We convert this value into the structure of the product portfolio using a model of customer purchasing decisions that we have developed. The obtained results confirm the effectiveness of our method and have significant practical value, especially for SMEs. It also enables the assessment of the company's product strategy based on real sales data. The application of our methodology is limited to discovering opportunities in situations where purchasing decisions are influenced by variable environmental factors, causing irregular purchases by individual customers. It is useful, for example, in discovering opportunities in markets such as Household Articles, Furniture, Vehicles, Equipment Repairs, Construction, and many others.

Bayesian Inference and Condition Assessment Based on the Deflection of Aging Reinforced Concrete Hollow Slab Bridges

This paper presents a Bayesian inference framework for updating the structural rigidity ratio of aging hollow slab RC bridges using deflection measurements. The framework models the structural rigidity ratio as a stochastic field along the hollow RC slabs, using the Karhunen–Loeve (KL) transform to capture spatial correlation and variation. Bayesian inference is then applied using deflection data from static loading tests, supported by a finite element model (FEM) and a Kriging surrogate model to enhance computational efficiency. The posterior distribution of the structural rigidity ratio is derived using a Markov chain Monte Carlo (MCMC) sampler. The proposed method was tested on an RC bridge with hollow slabs, using deflection measurements taken before and after reinforcement. The Bayesian updates indicated increased structural rigidity ratios after reinforcement, validating the effectiveness of the reinforcement. The deflection predictions from the updated models closely matched the measurements, with the 95% confidence bounds encompassing most of the data. This demonstrates the method’s validity and robustness in capturing the structural improvements post-reinforcement.