ABSTRACT This study models the spatial and spatio-temporal relative risk of Dengue transmission in Bandung using Bayesian inference. Applying the Besag-York-Mollié (BYM) framework, we evaluated separable and inseparable space-time models. Results show that Integrated Nested Laplace Approximation (INLA) produces estimates comparable to Markov chain Monte Carlo (MCMC) but is significantly faster. Evaluated via Deviance Information Criterion (DIC), the INLA-estimated inseparable spatio-temporal model performed best (DIC: 1795.190), effectively identifying high-risk areas like Arcamanik, Lengkong, and southeastern Bandung. This highlights INLA’s computational efficiency and the necessity of space-time interactions in robust disease mapping.

Respiratory syncytial virus (RSV) causes substantial disease burden worldwide, disproportionately affecting infants and young children. Higher susceptibility to RSV infections in young children, interacting with age-varying contact patterns and risk of disease progression, could drive the age-related variations in disease burden, though the extent of the susceptibility differences, and their influence on transmission dynamics and immunisation impact remains unclear. We developed an age-structured deterministic transmission model that integrated virological surveillance data, hospitalisations, and infection rates from the UK. We estimated age-dependent susceptibility coefficients for the 0- < 5years, 5-59year and ≥ 60years by integrating a profile likelihood approach with Markov Chain Monte Carlo (MCMC)-based calibration. Models were fitted to weekly RSV-positive cases in Scotland and infection rate estimates for the UK population. Age-specific infection-hospitalisation ratios (IHRs) were derived by combining modelled infections with RSV-associated hospitalisations. We evaluated multiple paediatric immunisation scenarios by estimating infections and hospitalisations averted, and the number of individuals needed to immunise (NNI) to prevent one RSV hospitalisation at varying coverage and efficacy. We estimated a susceptibility coefficient of 0.38 (95% CI 0.36-0.38) for 5-59years, and 0.38 (0.20-0.40) for ≥ 60years, relative to those under 5years. The overall annual infection rate was 51.8%, with peaked in children aged 12-23months (71.1%) and 0-2months (63.7%) using the best-fitting model, showing a substantial shift in the age distribution compared to the base model. IHRs showed a U-shaped distribution, with the highest rates in infants aged 0-2months and adults aged 75 and above. This model also projected a greater impact from immunisation programmes compared to the base model. For instance, an infant immunisation programme with 80% coverage and 80% efficacy against hospitalisation was projected to prevent 15.2% of hospitalisations, compared to 8.9% in the base model. Broader programmes, such as targeting 0-4-year-olds, resulted in larger reductions in hospitalisations (27.1%), while NNI increased as the programme expanded. The increased RSV susceptibility in children under 5years drives higher baseline transmission rates and disease burden in this subgroup, thereby influencing immunisation programme impact and efficiency.

Data analysis in (2+1)-D $$\Lambda (z)$$ gravity with BAO, Pantheon and Hubble dataset using MCMC method

ABSTRACT A collection of time series are “related” if they follow similar stochastic processes and/or they are statistically dependent. This paper proposes a related time series (RTS) forecasting model that exploits these relationships. The model's foundation is a set of univariate Gaussian autoregressions, one for each series, which are then augmented to incorporate stochastic volatility, heavy‐tailed innovations, additive outliers, time‐varying parameters and common factors. The model is estimated and forecasts are computed using Bayesian methods with hierarchical priors that pool information across series. Computationally efficient MCMC methods are proposed. The RTS model is applied to three datasets and yields encouraging pseudo‐out‐of‐sample forecasting results.

ABSTRACTThe black‐legged kittiwake (Rissa tridactyla, hereafter ‘kittiwake’, conservation status ‘Vulnerable’) is a long‐lived, highly motile and wide‐ranging seabird. Breeding kittiwake colonies are abundant across the northern hemisphere. The kittiwake's life history and the spatial scale of its breeding distribution make understanding colony connectivity a challenge; current species management models kittiwake colonies as closed units. Here, we explored the use of Bayesian analysis of multilocus microsatellite genotypes in the program BayesAss (BA3) to infer dispersal and seasonal summer breeding movements (information‐gathering behaviour; prospecting) (collectively ‘connectivity’) of kittiwakes around the North Atlantic. This approach uses the concept of inheritance by descent (IBD) (the formulation of genotypes within a population mediated by inheritance) and Markov‐chain Monte Carlo (MCMC) resampling to quantify patterns of breeding movements among spatial aggregations of related individuals. Data comprised diploid microsatellites of the kittiwake and the common seabird tick (Ixodes uriae) sampled from the High Arctic to the lower southern boundary of the species between the years of 1992 and 2001. Kittiwake dispersal and summer breeding movements, the latter derived from tick microsatellites, were heterogenous among the sampled colonies. There was an east to west longitudinal trend in dispersal. Summer breeding movements were more localised, although still present at large spatial scales. Connectivity among kittiwake colonies was less likely across the Atlantic Ocean. This study supports the prevailing theory that geographic distance only weakly constrains connectivity among kittiwake colonies. Multimodal relationships between geographic distance and connectivity indicate that other factors, such as colony status and conspecific associations may be more important.

This study addresses the challenge of estimating parameters for two logistic populations that share a common scale parameter but have different location parameters in the presence of fuzzy data. To handle these complexities, both Maximum Likelihood Estimation (MLE) and Bayesian methods are employed. Asymptotic confidence intervals are constructed using ML estimates. For Bayesian estimation, a conjugate prior is utilized, and Bayes estimators are approximated using Lindley’s method due to the lack of closed-form solutions. Furthermore, Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC) techniques, including Hamiltonian Monte Carlo (HMC) and the Metropolis–Hastings (MH) algorithm, are utilized to sample from the posterior distributions and construct Highest Posterior Density (HPD) intervals. A detailed comparative analysis of MLE, Lindley’s approximation, ABC, HMC, and MH is conducted to assess their performance. The effectiveness of the proposed methodology is demonstrated using a real-world dataset under fuzzy conditions.

The continuous-flow technologies in organic synthesis for the production of active pharmaceutical ingredients (APIs) are nowadays more and more applied. In-silico process design is a powerful tool able to support organic synthesis in the field of scale-up and process development. Process design feasibility and reliability depend on the availability of a well-defined chemical reaction kinetic scheme, information which is usually derived from experimental datasets collected on purpose. The latter approach is time-consuming and demanding in terms of resources. Different possibilities are here proposed to valorize widely available experimental data from explorative works with different approaches, depending on the nature, richness, and structure of the datasets. The kinetic parameters (i.e., reaction order, kinetic constant, and activation energy) of some interesting organic reactions have been approximately estimated by applying different computational methodologies, thanks to built-in experimental databases. The numerical algebra approach dealing with linear and non-linear regression analysis for the kinetic parameters has been initially considered and related to the database information for oseltamivir synthesis. The Bayesian statistic was applied to the ibuprofen case through the application of the Markov Chain Monte Carlo (MCMC) method for reaction order estimation. At last, a Machine Learning (ML) approach has been applied to the Rolipram and Pregabalin case study. The in-house developed T-ReX experimental kinetic constant database was exploited, with application of the k-Nearest neighbor algorithm for classification and regular expression pattern recognition. Advantages and limitations of the three approaches are discussed.

The diffusion of cholera epidemics and the emergence of drug-resistant strain pose significant challenges to cholera control and treatment, emphasizing the need for more effective interventions. By establishing a reaction-diffusion model of cholera with vaccination and two strains (wild and drug-resistant), we study the spatiotemporal dynamics of cholera transmission in this paper. In a spatially heterogeneous case, we derive and establish a threshold result: the disease-free steady state is globally stable if , and the disease persists if . In addition, we prove the global stability of the endemic equilibrium by constructing a Lyapunov functional in a spatially homogeneous case. Our model is successfully validated by the cholera data in Zimbabwe via Markov Chain Monte Carlo (MCMC). Using COMSOL Multiphysics software, we display the spatial transmission of cholera in the two-dimensional geographic map via demographic data in Zimbabwe. This offers a novel perspective for investigating the spatiotemporal dynamics of cholera transmission. Our findings indicate that restricted local population diffusion may contribute to the persistence and localized transmission of cholera in certain regions of Zimbabwe. Simulations further indicate that vaccination can serve as an effective intervention under such spatial dynamics.

Bayesian seabed geoacoustic inverse problems are commonly addressed using Markov chain Monte Carlo (McMC) methods or their variants, which are computationally expensive. This study proposes an efficient Bayesian geoacoustic inversion approach based on mixture density networks (MDNs). Rather than training separate networks for each parameter, this approach models the joint posterior probability distribution of all parameters. Moreover, the classical Bayesian geoacoustic inversion framework is enhanced by utilizing the MDN theory to analytically deduce essential geoacoustic statistics from the multidimensional posterior probability density (PPD). This approach not only eliminates the computationally intensive numerical integration typically required for Bayesian inversion but also provides deeper insight into the statistical characteristics of the Bayesian PPD. Comparisons of MDN and McMC inversion results across various cases reveal that the inversion using MDN (MDN inversion) produces PPD approximations that align well with the McMC method in terms of overall trends, despite some local discrepancies. Analysis of inter-parameter correlations indicates that the MDN can capture key trade-offs between parameters. This approach offers an efficient method for solving seabed geoacoustic inverse problems within the Bayesian inference framework, making it a promising technique for real-time inversion.

The Bayesian analysis of infectious disease surveillance data from multiple locations typically involves building and fitting a spatio-temporal model of how the disease spreads in the structured population. Here we present new generally applicable methodology to perform this task. We introduce a parsimonious representation of seasonality and a biologically informed specification of the outbreak component to avoid parameter identifiability issues. We develop a computationally efficient Bayesian inference methodology for the proposed models, including techniques to detect outbreaks by computing marginal posterior probabilities at each spatial location and time point. We show that it is possible to efficiently integrate out the discrete parameters associated with outbreak states, enabling the use of dynamic Hamiltonian Monte Carlo (HMC) as a complementary alternative to a hybrid Markov chain Monte Carlo (MCMC) algorithm. Furthermore, we introduce a robust Bayesian model comparison framework based on importance sampling to approximate model evidence in high-dimensional space. The performance of our methodology is validated through systematic simulation studies, where simulated outbreaks were successfully detected, and our model comparison strategy demonstrates strong reliability. We also apply our new methodology to monthly incidence data on invasive meningococcal disease from 28 European countries. The results highlight outbreaks across multiple countries and months, with model comparison analysis showing that the new specification outperforms previous approaches. The accompanying software is freely available as a R package at https://github.com/Matthewadeoye/DetectOutbreaks.

Abstract In this work, we study two scalar field driven dark energy models characterized by the axion potential and the inverse power-law potential, each coupled to dark matter through momentum exchange. By formulating the dynamics as an autonomous system, we identify the equilibrium points and analyze their stability. To constrain these models, we utilize observational data from Pantheon Plus Type Ia Supernovae, DES Y5, DESI DR2 BAO, and Planck 2018 CMB compressed likelihood, employing Markov Chain Monte Carlo (MCMC) methods. Both potentials exhibit weak to strong preference over the $$\Lambda $$ Λ CDM model, with a particularly strong preference for the momentum-coupled scenario when Supernova data are included in the analysis. Furthermore, we find the coupling parameter to be negative, with no lower bound, for both potentials. This finding agrees with previous studies and suggests that momentum-exchange coupling between the dark sectors cannot be ruled out. From the stability analysis, we observe that for both potentials, the late-time attractor corresponds to a dark energy–dominated phase, and the scalar field can behave as a stiff fluid during the early epoch. According to the model selection criteria, the inverse power-law potential is favoured over the axion potential.

In this study, we explored the cosmological implications of the modified gravity framework f(R,Lm), taking the specific form f(R,Lm)=R2+Lmn, where n denotes the model parameter. The analysis was carried out within a spatially flat FLRW background by adopting the Barboza–Alcaniz (BA) parametrization for the dark energy equation of state, expressed as ω(z)=w0+w1z(1+z)1+z2. Based on this setup, an expression for the Hubble parameter H(z) was derived. The parameters (H0,n,w0,w1) were estimated using a Bayesian Markov Chain Monte Carlo (MCMC) technique, implemented via the emcee package, with Cosmic Chronometers (CC), Pantheon Plus &amp; SH0ES (PPS) and DESI BAO datasets. For the CC+PPS+DESI BAO combination, the best-fit Hubble constant was obtained as H0=72.08−0.24+0.30kms−1Mpc−1, which shows better consistency with the local SH0ES measurement than with the Planck ΛCDM result, thereby reducing the Hubble tension. Furthermore, the dynamical evolution of the equation of state parameter ω, the deceleration parameter, the impact of various energy conditions, and the optimal model parameters were thoroughly examined. The study also investigated the behavior of the (Om) diagnostic and determined the present age of the universe predicted by this model.

Abstract In this work we derive empirical models of the fast solar wind by applying a Monte Carlo Markov Chain technique to in situ measurements of the wind charge state distributions to determine the wind’s electron temperature, electron density, and bulk speed from the source region to the freeze-in point. We utilize 6 month averages of ACE/SWICS measurements carried out at seven different times along the solar cycle, to monitor whether the solar cycle causes any changes in the results. We use the results to estimate several wind plasma properties as well as the wave pressure and energy needed to power the solar wind in the 1-temperature wind model by S. R. Cranmer et al. We find that the bulk of the momentum and energy is injected between 1.5 and 3.0 solar radii and that the solar cycle does not qualitatively affect the results. However, the plasma acceleration predicted by our empirical model occurs much closer to the Sun than indicated by SoHO/UVCS measurements: we discuss this discrepancy as well as other approximations and limitations of the present work.

Appearing as secondary higher-velocity absorption components, high-velocity features (HVFs) have been observed in several absorption lines in many Type Ia supernovae (SNe Ia). The frequency and ubiquity of these components in silicon and calcium features specifically indicates that the mechanism through which they form must be a common occurrence among the majority of SNe Ia. Here we present the modelling of the HVF evolution in a sample of six well-observed SNe Ia with the radiative-transfer code TARDIS . A base model is derived for each of the SNe to reproduce the photospheric-velocity components, followed by a grid of simulations with Gaussian enhancements to the density profile at high velocities. We trained a set of neural networks to emulate the impact of these density enhancements upon the simulated silicon line profile. These networks were subsequently used within a Markov chain Monte Carlo (MCMC) framework to infer the density enhancement parameters that most closely reproduce the HVF evolution. While we obtain good matches for the silicon profile, we find that a single density enhancement alone cannot simultaneously produce the observed silicon and calcium HVF evolution. Our findings indicate that neither the delayed-detonation mechanism nor the double-detonation mechanism can produce these HVFs, which suggests that something may be missing from the models.

Dengue fever poses a growing public health challenge in tropical and subtropical regions, with transmission driven by complex interactions among viral and host. Computational models, often expressed as ordinary differential equations (ODEs), are widely used to understand complex systems such as dengue fever transmission dynamics. However, traditional parameter estimation methods such as Markov chain Monte Carlo (MCMC) often require complex setups and are computationally expensive. In this study, we choose a compartmental model extended to human and mosquito populations, estimate its parameters using neural parameter calibration (NPC), and validate the approach using datasets collected from South America and Southeast Asia. The extended compartment model (ECM) is expressed using seven ODEs, describing dengue transmission dynamics between humans and mosquitoes. NPC involves using a neural network to learn the posterior distribution of parameters and initial conditions of the model in consideration. We analyzed six surveillance datasets on cumulative dengue cases, comprising data from three cities (Bello, Iquitos, and San Juan) and three Southeast Asian countries (Vietnam, the Philippines, and Cambodia). NPC achieved significantly faster run times than MCMC: 408 seconds on average versus 2616.01 seconds for city-level analyses and 368 seconds on average versus 2998.83 seconds for country-level analyses. Meanwhile, it delivers comparable accuracy: mean squared error (MSE) 0.00678 versus 0.01638 for the city datasets; and 0.00605 versus 0.01897 for the country datasets. The experimental results demonstrate that combining ECM with NPC enables accurate dengue outbreak forecasts at substantially lower computational cost, offering a practical tool that supports timely response, especially in low-resource environments such as Southeast Asia.

Abstract We present the first observational analysis of the totally eclipsing binary WISE J095035.2+354215 (hereafter J095035), a system whose mass ratio lies near the theoretical stability limit for binary stars. Fundamental stellar parameters of the system were determined through spectral energy distribution (SED) fitting, yielding a surface gravity of \( \log g = 4.16^{+0.34}_{-0.29} \, \text{cm}\,\text{s}^{-2} \), a metallicity of \( [\text{Fe/H}] = 0.05^{+0.08}_{-0.06} \, \text{dex} \), and an effective temperature of \( T_{\text{eff}} = 6262^{+43}_{-34} \, \text{K} \). Employing the PHOEBE 2.4 software package with a Markov Chain Monte Carlo (MCMC) sampling technique, we derived photometric parameters from multiband observations, confirming that J095035 is an overcontact binary with an ultra-low mass ratio ($q \approx 0.064$) and a contact degree of $47\%$. Synthesizing eclipse timing data from our observations and multiple astronomical surveys, we determined that J095035’s orbital period is experiencing a secular decline at \(\frac{dP}{dt} = -3.70 \times 10^{-7} \, \text{day yr}^{-1}\). This secular orbital period variation is most likely driven by the joint influence of two key physical processes: mass exchange between the binary’s constituent stars and angular momentum leakage from the entire system. The sustained orbital period reduction triggers shrinkage of the critical Roche lobes, thereby enhancing the contact depth and ultimately directing the system toward coalescence into a fast-rotating merger product.

Electrochemical biosensors and microfluidics have an inherently synergistic relationship which can allow unparalleled levels of signal enhancement, automation and scalability. In spite of this, the full advantages of fluidic automation remain underexplored with most works automating some but not all biosensor fabrication steps. In this work, we present for the first time the Wee Ally for Flow Functionalisation of Low-cost Electrodes (WAFFLE) - an automated platform designed specifically for researchers to standardise the fabrication of electrochemical biosensors and enhance their performance, and a novel data analysis scheme based on the Markov chain Monte Carlo (MCMC) method for increasing the robustness of data fitting. We first discuss the design of the WAFFLE which features a modular construction, off-the-shelf components (ESP32 microcontroller, Bartels mp-6 μ-pump and memetis μ-valves), an easy-to-manufacture fluidic cartridge, and web interface that can be accessed from any Wi-Fi enabled device. The entire platform can be manufactured for approximately £1 k, less than the cost of a single standard syringe pump. We showcase the sensing benefits of the WAFFLE using two electrochemical immunoassays of high clinical relevance for interleukin-6 (IL-6) and cardiac troponin I (TnI), and one aptamer-based impedimetric assay for cortisol. As well as unilaterally enhancing the sensitivity of those sensors and decreasing sensor variability, the WAFFLE also highlighted some key insights into the assembly of the bioactive surface layer under flow. Finally, we demonstrate how MCMC-integration into impedance fitting algorithms can resolve the issue of local minima trapping.

Bayesian methods offer an intuitive and coherent statistical framework for updating probabilistic beliefs by integrating prior knowledge-whether from existing data or expert consensus-with new evidence via likelihood functions to generate posterior probability distributions. This approach yields clinically meaningful outputs, such as credible intervals and probabilities of treatment benefit, and can incorporate thresholds relevant to practice, like the region of practical equivalence (ROPE). Recent advances in computation-including Markov chain Monte Carlo (MCMC) sampling, Hamiltonian Monte Carlo algorithms, and probabilistic programming languages like Stan and JAGS- have made Bayesian approaches feasible even for complex hierarchical models. In perioperative medicine, these methods are particularly valuable for (1) complementing trial results by quantifying clinically important effects in the context of statistically nonsignificant findings or modest probabilities of benefit despite statistical significance, (2) enhancing meta-analyses through coherent integration of heterogeneous studies and sparse data, and (3) enabling adaptive and platform trial designs through continuous evidence synthesis. The ability to incorporate informative priors can complement existing knowledge, especially in small-sample studies, which are common in perioperative medicine, where traditional approaches provide insufficient precision. Although concerns remain regarding subjectivity in prior specification, these are increasingly addressed through structured guidelines, benchmark priors, and comprehensive sensitivity analyses. Altogether, Bayesian methods provide a flexible and powerful alternative for generating actionable insights in complex clinical settings, including in perioperative care.

Addressing the challenge of tracing hidden and transient cross-connections in urban drainage networks, this study develops a SWMM–Bayesian coupled model based on the Py SWMM interface using the Daming Lake area in Jinan as a case study. By employing a Markov Chain Monte Carlo (MCMC) algorithm to drive the interaction between dynamic simulation and statistical inference, the model achieves multidimensional joint posterior estimation of pollution source location (Jx), discharge intensity (M), and discharge timing (T). The results indicate: (1) Model accuracy: The coupled model demonstrates strong source tracing capability, with mean absolute errors below 0.6% in single-parameter inversion. Under multi-parameter joint inversion, the true values of all parameters consistently fall within the 95% confidence intervals. (2) Parameter sensitivity: The influence of MCMC step size on the uncertainty of pollution tracing results is systematically clarified. Discrete source location estimates (Jx) exhibit high robustness to step size variation due to spatial heterogeneity in hydraulic responses, whereas continuous physical parameters (M and T) show strong dependence on the selected step size scale. (3) Practical application: The impact of spatial monitoring network configuration on pollution tracing performance is examined. By deploying a complementary monitoring system integrating trunk and branch pipelines, the inversion accuracy for mass (M) and time (T) parameters is significantly improved by 84.2% and 88.5%, respectively. Overall, the proposed pollution source tracing method for urban drainage networks effectively overcomes the multi-solution challenge in complex network inversion, providing critical technical support for refined urban water environment management.

ABSTRACT This article explores the estimation of unknown parameters and reliability characteristics under the assumption that the lifetimes of the testing units follow an Inverted Exponentiated Pareto (IEP) distribution. Here, both point and interval estimates are calculated by employing the classical maximum likelihood method, a pivotal estimation method and a hierarchical Bayesian estimation method. Also, existence and uniqueness of the maximum likelihood estimates are verified. Further, asymptotic confidence intervals are derived by using the asymptotic normality property of the maximum likelihood estimator. Moreover, generalized confidence intervals are obtained by utilizing the pivotal quantities. Also, the 95 % highest posterior density (HPD) intervals are constructed based on a Markov chain Monte Carlo (MCMC) algorithm within the Bayesian estimation context. Additionally, some mathematical developments of the IEP distribution are discussed based on the concept of order statistics. Furthermore, all the estimations are performed on the basis of the block censoring procedure, where an adaptive progressive Type-II censoring is employed to every block. In this regard, the performances of the three estimation methods, namely, maximum likelihood estimation, pivotal estimation and the hierarchical Bayesian estimation are evaluated and compared through a simulation study. Finally, a real data is illustrated to demonstrate the flexibility of the proposed IEP model.