Markov Chain Monte Carlo Research Articles

Bayesian quantile inference and order shrinkage for hysteretic quantile autoregressive models

Hysteretic quantile autoregressive model combines the hysteretic patterns and quantile autoregression, which can capture the dynamic relationship and nonlinear characteristics at different quantiles in time series data. In this paper, the Bayesian quantile inference and order shrinkage are studied for a class of hysteretic quantile autoregressive time series models. By using Markov Chain Monte Carlo (MCMC) techniques, the proposed Bayesian quantile method can handle the sparse hysteretic quantile autoregressive model well. It can accurately determine order of the model and estimate non-zero coefficients. Both simulation studies and a data example show that the proposed methods are feasible, reliable and appropriate for analysing the US Gross National Product data set.

Toward mapping turbulence in the intra-cluster medium

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

Breaking the baryon-dark matter degeneracy in a model-independent way through the Sunyaev-Zeldovich effect

Context. In cosmological fits, it is common to fix the baryon density ωb via the cosmic microwave background. We here constrain ωb by means of a model-independent interpolation of the acoustic parameter from correlated baryonic acoustic oscillations. Aims. The proposed technique is used to alleviate the degeneracy between baryonic and dark matter abundances. Methods. We propose a model-independent Bézier parametric interpolation and applied it to intermediate-redshift data. We first interpolated the observational Hubble data to extract cosmic bounds over the (reduced) Hubble constant h0 and interpolated the angular diameter distances, D(z), of the galaxy clusters, inferred from the Sunyaev-Zeldovich effect, to constrain the spatial curvature, Ωk. Through the Hubble points and D(z) determined in this way, we interpolated uncorrelated data of baryonic acoustic oscillations bounding the baryon ωb and total matter ωm densities, reinforcing the constraints on h0 and Ωk with the same technique. Finally, to remove the matter sector degeneracy, we obtained ωb by interpolating the acoustic parameter from correlated baryonic acoustic oscillations. Results. Monte Carlo Markov chain simulations agree at 1σ confidence level with the flat ΛCDM model and are roughly suitable at 1σ with its nonflat extension, while the Hubble constant appears in tension up to the 2σ confidence levels. Conclusions. Our method excludes very small extensions of the standard cosmological model, and on the Hubble tension side, seems to match local constraints slightly.

DIFFUSION MODEL-BASED POSTERIOR DISTRIBUTION PREDICTION FOR KINETIC PARAMETER ESTIMATION IN DYNAMIC PET.

Positron Emission Tomography (PET) is a valuable imaging method for studying molecular-level processes in the body, such as hyperphosphorylated tau (p-tau) protein aggregates, a hallmark of several neurodegenerative diseases including Alzheimer's disease. P-tau density and cerebral perfusion can be quantified from PET data using tracer kinetic modeling techniques. However, noise in PET images leads to uncertainty in the estimated kinetic parameters. This can be quantified in a Bayesian framework by the posterior distribution of kinetic parameters given PET measurements. Markov Chain Monte Carlo (MCMC) techniques can be employed to estimate the posterior distribution, although with significant computational needs. In this paper, we propose to leverage deep learning inference efficiency to infer the posterior distribution. A novel approach using denoising diffusion probabilistic model (DDPM) is introduced. The performance of the proposed method was evaluated on a [18F]MK6240 study and compared to an MCMC method. Our approach offered significant reduction in computation time (over 30 times faster than MCMC) and consistently predicted accurate (< 0.8 % mean error) and precise (< 5.77 % standard deviation error) posterior distributions.

Extended Regression Analysis for Debye-Einstein Models Describing Low Temperature Heat Capacity Data of Solids.

Heat capacity data of many crystalline solids can be described in a physically sound manner by Debye-Einstein integrals in the temperature range from 0K to 300K. The parameters of the Debye-Einstein approach are either obtained by a Markov chain Monte Carlo (MCMC) global optimization method or by a Levenberg-Marquardt (LM) local optimization routine. In the case of the MCMC approach the model parameters and the coefficients of a function describing the residuals of the measurement points are simultaneously optimized. Thereby, the Bayesian credible interval for the heat capacity function is obtained. Although both regression tools (LM and MCMC) are completely different approaches, not only the values of the Debye-Einstein parameters, but also their standard errors appear to be similar. The calculated model parameters and their associated standard errors are then used to derive the enthalpy, entropy and Gibbs energy as functions of temperature. By direct insertion of the MCMC parameters of all 4·105 computer runs the distributions of the integral quantities enthalpy, entropy and Gibbs energy are determined.

Bayesian analysis of physiologically based toxicokinetic (PBTK) modeling for pentachlorophenol exposure in pregnant women

Pentachlorophenol (PCP) is a persistent organic compound that is widely present in the environment. The estimation of internal exposure levels for a given external exposure using toxicokinetic models is key to the human health risk assessment of PCP. The present study developed a physiologically based multicompartmental pharmacokinetic (PBTK) model to describe and predict the behavior of pentachlorophenol (PCP) in an organism. The model consists of stomach, intestines, adipose tissue, kidneys and fast- and poorly perfused tissues that are interconnected via blood circulation. We constructed a PBTK model of PCP in rats and extrapolated it to human dietary PCP exposure. The toxicokinetic data of PCP in human tissues and excreta were obtained from the published literature. Based on the collected PCP dietary survey and internal exposure data of pregnant women in Shanghai, Bayesian statistical analysis was performed for the model using Markov chain Monte Carlo (MCMC) simulation. The posterior distributions of the sensitive parameters were estimated, and the model was parameter optimized and validated using the pregnant women's test dataset. The results showed that the root mean square error (RMSE) improved 37.3% compared to the original model, and a systematic literature search revealed that the optimized model achieved acceptable prediction results for other datasets in China. A PCP metabolism model based on the exposure characteristics of pregnant women in China was constructed in the present study. The model provides a theoretical basis for the study of PCP toxicity and risk assessment.

Estimating hydraulic diffusivity in coastal confined aquifer under tidal fluctuation using a frequency domain model

Oceanic tidal propagation into the coastal aquifers is a cost-effective method for estimating hydraulic parameters in coastal aquifers, and identifying the most suitable parameter estimation method for coastal aquifers based on the observations has become an intensively studied subject. In this study, the frequency domain model, LPMLE3 (combination of a local polynomial (LP) signal processing technique with a maximum likelihood estimator (MLE)), was applied to estimate the hydraulic diffusivity (λ) of the coastal aquifer by adjusting the mathematical model in LPMLE3. The mathematical model in LPMLE3 has been adjusted by removing the convective term from the convective diffusion equation within LPMLE3, and a newly developed frequency-domain analytical solution that describes the head changes due to tidal fluctuations in coastal confined aquifers was used to replace the diffusion term. For comparison, an analytical solution in the time domain was also derived by Green’s functions method. After that, the particle swarm optimization algorithm and Markov Chain Monte Carlo method were used to estimate λ. Results show that LPMLE3 performed well in estimating homogeneous or heterogeneous aquifers with complicated boundary conditions. The estimated error of λ is within 10 % in a heterogeneous aquifer when the variance of the natural logarithm of the aquifer hydraulic conductivity is less than 0.05 (σlnK2≤0.05). If the coastal aquifer has a sloping beach, the estimated λ by LPMLE3 method accurately when the sloping beach angle is greater than 65°. As for an inclined coastal aquifer, the dip angle has a greater influence on the offshore areas than the nearshore areas and the estimation errors are relatively small (less than 15 %) when the dip angle is within a range of 0- 15°.

Pore characteristics and microscopic damage mechanism of disintegrated carbonaceous mudstone exposed to dry-wet cycles

Disintegrated carbonaceous mudstone (DCM), derived from pre-disintegration treatments of waste carbonaceous mudstone, is utilized as filler for highway embankments with the aim of conserving resources. However, the mechanical behavior of DCM is greatly influenced by its microstructure, particularly pore characteristics. The aim of this study is to investigate the pore characteristics and microscopic damage mechanisms of DCM subjected to dry-wet cycles. Triaxial tests, along with microscopic observations using scanning electron microscopy and mercury intrusion porosimetry, were performed. Three-dimensional pore models were reconstructed from the microscopic test results via the Markov chain-Monte Carlo method. Subsequently, a finite element method that accounts for the anisotropy of porosity was proposed based on these pore models. Finally, numerical triaxial tests were performed to analyze stress changes in DCM under triaxial loading using the proposed method. The results show that the shear strength and cohesion of the DCM decrease with an increase in dry-wet cycles, stabilizing notably after four cycles. Meanwhile, the porosity and the number of slender pores in the specimen increase, leading to intricate alterations in pore shape and distribution. A comparison between numerical and laboratory triaxial tests demonstrates closely aligned results, with distinct stress concentration behavior related to porosity anisotropy. It is revealed that dry-wet cycles cause an increase in porosity and the occurrence of more irregular-shaped pores, subsequently leading to a decrease in the cohesion. This microscopic mechanism is responsible for the shear strength damage of DCM.

Individual random effects model for differences in trait distribution among respondents

The homogeneity hypothesis is a common assumption in classic measurement. However, the item response theory model assumes that different respondents with same ability have the same option probabilities, which may not hold. The aim of this study is to propose a new individual random effect model that accounts for the differences in option probabilities among respondents with same latent traits by using within-person variance. The performance of the new model is evaluated through simulation studies and real data using the PRESUPP scale of PISA. The model parameters are estimated by the MCMC method. The results show that the individual random effect model can provide more accurate parameter estimates and obtain a scale parameter to describe the distribution of respondents’ abilities, under different within-person variances. The new model has lower RMSE and better model fit than the classic IRT model.

Mathematical Modeling Suggests That Monocyte Activity May Drive Sex Disparities during Influenza Infection.

In humans, females of reproductive age often experience a more severe disease during influenza A virus infection, which may be due to differences in their innate immune response. Sex-specific outcomes to influenza infection have been recapitulated in mice, enabling researchers to study viral and immune dynamics in vivo in order to identify immune mechanisms that are differently regulated between the sexes. This study is based on the hypothesis that sex-specific outcomes emerge due to differences in the rates/speeds that select immune components respond. Using publicly available sex-specific murine data, we utilized dynamic mathematical models of the innate immune response to identify candidate mechanisms that may lead to increased disease severity in female mice. We implemented a large computational screen using the Bayesian information criterion (BIC), wherein the goodness of fit of the competing model scenarios is balanced against complexity (i.e., the number of parameters). Our results suggest that having sex-specific rates for proinflammatory monocyte induction by interferon and monocyte inhibition of virus replication provides the simplest (lowest BIC) explanation for the difference observed in the male and female immune responses. Markov-chain Monte Carlo (MCMC) analysis and global sensitivity analysis of the top performing scenario were performed to provide rigorous estimates of the sex-specific parameter distributions and to provide insight into which parameters most affect innate immune responses. Simulations using the top-performing model suggest that monocyte activity could be a key target to reduce influenza disease severity in females. Overall, our Bayesian statistical and dynamic modeling approach suggests that monocyte activity and induction parameters are sex-specific and may explain sex-differences in influenza disease immune dynamics.

Precise Mass, Orbital Motion, and Stellar Properties of the M-dwarf Binary LP 349−25AB

LP 349−25 is a well-studied close stellar binary system comprised of two late M dwarf stars, where both stars are close to the limit between star and brown dwarf. This system was previously identified as a source of gigahertz radio emission. We observed LP 349−25AB over 11 epochs in 2020–2022, detecting both components in this nearby binary system using the Very Long Baseline Array (VLBA). We fit simultaneously the VLBA absolute astrometric positions together with existing relative astrometric observations derived from optical/infrared observations with a set of algorithms that use nonlinear least-squares, genetic algorithm, and Markov Chain Monte Carlo methods to determine the orbital parameters of the two components. We find the masses of the primary and secondary components to be 0.08188 ± 0.00061 M ⊙ and 0.06411 ± 0.00049 M ⊙, respectively, representing one of the most precise mass estimates of any ultracool dwarf (UCD) to date. The primary is a UCD of 85.71 ± 0.64 M Jup, while the secondary has a mass consistent with being a brown dwarf of 67.11 ± 0.51 M Jup. This is one of the very few direct detections of a brown dwarf with VLBA observations. We also find a distance to the binary system of 14.122 ± 0.057 pc. Using stellar evolutionary models, we find the model-derived stellar parameters of both stars. In particular, we obtain a model-derived age of 262 Myr for the system, which indicates that LP 349−25AB is composed of two pre–main-sequence stars. In addition, we find that the secondary star is significantly less evolved than the primary star.

Stochastic acceleration in extreme TeV BL Lacs through MCMC

Extreme TeV BL Lacs are a class of blazars with unique spectral and temporal features that are not easily reproducible using standard one-zone models based on single shock acceleration. To account for their peculiar properties, we elaborated a two-step acceleration model in which a recollimation shock and the subsequent downstream turbulence energize non-thermal electrons. We applied the model to a sample of extreme TeV BL Lacs with well-characterized spectral energy distributions. Since we used several sources, we automatized the exploration of the parameter space. This allowed us to derive the parameter distributions and study the correlations among them. We numerically solved a system of two coupled nonlinear differential equations to obtain the non-thermal particles and turbulence spectra. We calculated the spectral energy distribution via the synchrotron self-Compton emission model. The automatization of the parameter space exploration is possible through a Markov chain Monte Carlo (MCMC) ensemble sampler, in our case emcee We derived well-defined posterior distributions for the parameters, showing that the model is well constrained by available data and demonstrating the suitability of our method. The cross-correlations among some of the physical parameters are not trivial.\ Therefore, we conclude that MCMC sampling is a key instrument for characterizing the complexity of our multiparameter phenomenological model.

Bayesian cross-validation by parallel Markov chain Monte Carlo

Brute force cross-validation (CV) is a method for predictive assessment and model selection that is general and applicable to a wide range of Bayesian models. Naive or ‘brute force’ CV approaches are often too computationally costly for interactive modeling workflows, especially when inference relies on Markov chain Monte Carlo (MCMC). We propose overcoming this limitation using massively parallel MCMC. Using accelerator hardware such as graphics processor units, our approach can be about as fast (in wall clock time) as a single full-data model fit. Parallel CV is flexible because it can easily exploit a wide range data partitioning schemes, such as those designed for non-exchangeable data. It can also accommodate a range of scoring rules. We propose MCMC diagnostics, including a summary of MCMC mixing based on the popular potential scale reduction factor (R^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{\ extrm{R}}$$\\end{document}) and MCMC effective sample size (ESS^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{\ extrm{ESS}}$$\\end{document}) measures. We also describe a method for determining whether an R^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{\ extrm{R}}$$\\end{document} diagnostic indicates approximate stationarity of the chains, that may be of more general interest for applications beyond parallel CV. Finally, we show that parallel CV and its diagnostics can be implemented with online algorithms, allowing parallel CV to scale up to very large blocking designs on memory-constrained computing accelerators.

System-Level Offshore Wind Energy and Hydrogen Generation Availability and Operations and Maintenance Costs

With the current trends of wind energy already playing a major part in the Scottish energy supply, the capacity of wind farms is predicted to grow exponentially and reach further depths offshore. However, a key challenge that presents itself is the integration of large producing assets into the current UK grid. One potential solution to this is green hydrogen production, which is being heavily researched in industry, with many concepts being investigated for large-scale purposes. However, the operations and maintenance (O&amp;M) costs and availability of green hydrogen systems need to be quantified to ensure economical and technical viability, which is sparse in the available literature. The study presented in this paper investigated the availability and O&amp;M costs of coupled wind–hydrogen systems by attempting to quantify the failure rates, repair times, repair costs and number of technicians required for key green hydrogen components. This study also utilised an O&amp;M model created by the University of Strathclyde, which uses Monte Carlo Markov chain simulations to produce the O&amp;M outputs. A number of assumptions were made throughout the study in relation to the O&amp;M model inputs, and the baseline availability for the coupled wind–hydrogen system was 85.24%. Whilst the wind turbine still contributed a major part to the downtime seen in the simulations, the combined hydrogen system also contributed a significant amount, a total of 37%, which could have been due to the technology readiness levels of some the components included in the hydrogen system.

Bayesian Inference Based on Monte Carlo Technique for Multiplier of Performance Shaping Factor

Abstract The Human Error Probabilities (HEP) can be estimated using multipliers that correspond to the level of Performance Shaping Factors (PSFs) in the Human Reliability Analysis (HRA). This paper focuses on the adjustment of multipliers through Bayesian inference based on Monte Carlo techniques using the experimental results from simulators. Markov Chain Monte Carlo (MCMC) and Bayesian Monte Carlo (BMC) are used as Bayesian inference methods based on Monte Carlo techniques. MCMC is utilized to obtain the posterior distribution of the multipliers. BMC is used for the estimation of the moments of the posterior distribution such as the mean and variance. The results obtained by MCMC and that by BMC well agree with the reference results. As a case study, the data assimilation was performed using the results of the simulator experiment of Halden reactor. The results show that the multiplier changes by the result of a particular scenario and HEP of another scenario that uses the same multiplier also changes by data assimilation. Also, in the case study, the correlation between multipliers is obtained by the data assimilation and the correlation contributes to the reduction of uncertainty of HEP.

Deep generative networks for multivariate fullstack seismic data inversion using inverse autoregressive flows

The simultaneous prediction of the subsurface distribution of facies and acoustic impedance (IP) from fullstack seismic data requires solving an inverse problem and is fundamental in natural resources exploration, carbon capture and storage, and environmental risk management. In recent years, deep generative models (DGM), such as variational autoencoders (VAE) and generative adversarial networks (GAN), were proposed to reproduce complex facies patterns honoring prior geological information. Variational Bayesian inference using inverse autoregressive flows (IAF) can be performed to infer the solution to a geophysical inverse problem from the encoded latent space of such pre-trained DGM. Successful applications of such approach on crosshole ground-penetrating radar synthetic data inversion demonstrated that the technique's accuracy is comparable to that of Markov chain Monte Carlo (MCMC) inference methods, while significantly reducing the computational cost. Nonetheless, these application examples did not account for the spatial uncertainty affecting the facies-dependent continuous physical property, from which the geophysical data are calculated. This uncertainty can significantly affect the inversion accuracy and its applicability to real data. In this work, specific VAE and GAN architectures are proposed to simultaneously predict facies and co-located IP, while accounting for their spatial uncertainties. The two types of generative networks are used in Bayesian inversion with IAF for the inversion of seismic data. The results are found to reproduce the statistics of the training images and solve the seismic inversion problem accurately, comparably to MCMC inversion. Furthermore, advantages and limitations of the two DGMs are evaluated by comparing the results obtained.

Bayesian inference for the onset time and epidemiological characteristics of emerging infectious diseases.

Emerging infectious diseases pose a significant threat to global public health. Timely detection and response are crucial in mitigating the spread of such epidemics. Inferring the onset time and epidemiological characteristics is vital for accelerating early interventions, but accurately predicting these parameters in the early stages remains challenging. We introduce a Bayesian inference method to fit epidemic models to time series data based on state-space modeling, employing a stochastic Susceptible-Exposed-Infectious-Removed (SEIR) model for transmission dynamics analysis. Our approach uses the particle Markov chain Monte Carlo (PMCMC) method to estimate key epidemiological parameters, including the onset time, the transmission rate, and the recovery rate. The PMCMC algorithm integrates the advantageous aspects of both MCMC and particle filtering methodologies to yield a computationally feasible and effective means of approximating the likelihood function, especially when it is computationally intractable. To validate the proposed method, we conduct case studies on COVID-19 outbreaks in Wuhan, Shanghai and Nanjing, China, respectively. Using early-stage case reports, the PMCMC algorithm accurately predicted the onset time, key epidemiological parameters, and the basic reproduction number. These findings are consistent with empirical studies and the literature. This study presents a robust Bayesian inference method for the timely investigation of emerging infectious diseases. By accurately estimating the onset time and essential epidemiological parameters, our approach is versatile and efficient, extending its utility beyond COVID-19.

A comparison of computational algorithms for the Bayesian analysis of clinical trials.

Clinical trials are increasingly using Bayesian methods for their design and analysis. Inference in Bayesian trials typically uses simulation-based approaches such as Markov Chain Monte Carlo methods. Markov Chain Monte Carlo has high computational cost and can be complex to implement. The Integrated Nested Laplace Approximations algorithm provides approximate Bayesian inference without the need for computationally complex simulations, making it more efficient than Markov Chain Monte Carlo. The practical properties of Integrated Nested Laplace Approximations compared to Markov Chain Monte Carlo have not been considered for clinical trials. Using data from a published clinical trial, we aim to investigate whether Integrated Nested Laplace Approximations is a feasible and accurate alternative to Markov Chain Monte Carlo and provide practical guidance for trialists interested in Bayesian trial design. Data from an international Bayesian multi-platform adaptive trial that compared therapeutic-dose anticoagulation with heparin to usual care in non-critically ill patients hospitalized for COVID-19 were used to fit Bayesian hierarchical generalized mixed models. Integrated Nested Laplace Approximations was compared to two Markov Chain Monte Carlo algorithms, implemented in the software JAGS and stan, using packages available in the statistical software R. Seven outcomes were analysed: organ-support free days (an ordinal outcome), five binary outcomes related to survival and length of hospital stay, and a time-to-event outcome. The posterior distributions for the treatment and sex effects and the variances for the hierarchical effects of age, site and time period were obtained. We summarized these posteriors by calculating the mean, standard deviations and the 95% equitailed credible intervals and presenting the results graphically. The computation time for each algorithm was recorded. The average overlap of the 95% credible interval for the treatment and sex effects estimated using Integrated Nested Laplace Approximations was 96% and 97.6% compared with stan, respectively. The graphical posterior densities for these effects overlapped for all three algorithms. The posterior mean for the variance of the hierarchical effects of age, site and time estimated using Integrated Nested Laplace Approximations are within the 95% credible interval estimated using Markov Chain Monte Carlo but the average overlap of the credible interval is lower, 77%, 85.6% and 91.3%, respectively, for Integrated Nested Laplace Approximations compared to stan. Integrated Nested Laplace Approximations and stan were easily implemented in clear, well-established packages in R, while JAGS required the direct specification of the model. Integrated Nested Laplace Approximations was between 85 and 269 times faster than stan and 26 and 1852 times faster than JAGS. Integrated Nested Laplace Approximations could reduce the computational complexity of Bayesian analysis in clinical trials as it is easy to implement in R, substantially faster than Markov Chain Monte Carlo methods implemented in JAGS and stan, and provides near identical approximations to the posterior distributions for the treatment effect. Integrated Nested Laplace Approximations was less accurate when estimating the posterior distribution for the variance of hierarchical effects, particularly for the proportional odds model, and future work should determine if the Integrated Nested Laplace Approximations algorithm can be adjusted to improve this estimation.

Study on the assessment of illegal wildlife trade projects based on LSTM model and Monte Carlo simulation

The aim of this paper is to conduct an assessment study of illegal wildlife trade projects using LSTM models and Monte Carlo simulation techniques. Firstly, based on the data from 1994-2023, we predicted the number of illegal animal and plant trade in the next five years using LSTM model, and the results showed that although the number was on a decreasing trend, it was still high, indicating that the problem still needs to attract global attention. Subsequently, we used the Kendall correlation coefficient to analyse the relationship between the number of illegal trade counts and economic, environmental and climate indicators, and found a positive correlation with the economic losses from natural disasters and the number of extreme weather events. Finally, we identified seven key parameters affecting project success and simulated the posterior distributions of these parameters using the Markov Chain Monte Carlo method, and then conducted Monte Carlo simulations to estimate the probability of project success as 93.12%. Sensitivity analyses indicate that project success is most sensitive to the level of financial support and monitoring technology. Overall, using a data-driven approach, this paper provides an important reference for assessing illegal wildlife trade projects.

Impossibility result for Markov chain Monte Carlo sampling from microcanonical bipartite graph ensembles.

Markov Chain Monte Carlo (MCMC) algorithms are commonly used to sample from graph ensembles. Two graphs are neighbors in the state space if one can be obtained from the other with only a few modifications, e.g., edge rewirings. For many common ensembles, e.g., those preserving the degree sequences of bipartite graphs, rewiring operations involving two edges are sufficient to create a fully connected state space, and they can be performed efficiently. We show that, for ensembles of bipartite graphs with fixed degree sequences and number of butterflies (k_{2,2} bicliques), there is no universal constant c such that a rewiring of at most c edges at every step is sufficient for any such ensemble to be fully connected. Our proof relies on an explicit construction of a family of pairs of graphs with the same degree sequences and number of butterflies, with each pair indexed by a natural c, and such that any sequence of rewiring operations transforming one graph into the other must include at least one rewiring operation involving at least c edges. Whether rewiring this many edges is sufficient to guarantee the full connectivity of the state space of any such ensemble remains an open question. Our result implies the impossibility of developing efficient, graph-agnostic, MCMC algorithms for these ensembles, as the necessity to rewire an impractically large number of edges may hinder taking a step on the state space.