Objective Bayesian analysis for geostatistical Student-t processes

We develop a Bayesian analysis based on two different Jeffreys priors for the Student-t regression model with unknown degrees of freedom. It is typically difficult to estimate the number of degrees of freedom: improper prior distributions may lead to improper posterior distributions, whereas proper prior distributions may dominate the analysis. We show that Bayesian analysis with either of the two considered Jeffreys priors provides a proper posterior distribution. Finally, we show that Bayesian estimators based on Jeffreys analysis compare favourably to other Bayesian estimators based on priors previously proposed in the literature.

The Generalized Pareto (GP) and Generalized extreme value (GEV) distributions play an important role in extreme value analyses, as models for threshold excesses and block maxima respectively. For each of these distributions we consider Bayesian inference using "reference" prior distributions (in the general sense of priors constructed using formal rules) for the model parameters, specifically a Jeffreys prior, the maximal data information (MDI) prior and independent uniform priors on separate model parameters. We investigate the important issue of whether these improper priors lead to proper posterior distributions. We show that, in the GP and GEV cases, the MDI prior, unless modified, never yields a proper posterior and that in the GEV case this also applies to the Jeffreys prior. We also show that a sample size of three (four) is sufficient for independent uniform priors to yield a proper posterior distribution in the GP (GEV) case.

Bayesian statistical methods have recently been combined with conventional methods for fisheries stock assessment (e.g. catch-age analysis) to provide a conceptually elegant approach for providing fishery management advice under uncertainty. Uncertainties in the advice provided can be conveyed using posterior probability distributions (or “posteriors”) for the potential outcomes of each policy option. Posteriors can be estimated using data (e.g. catch-age data and relative abundance indices) for the fish population of interest and prior probability distributions for population model parameters (e.g. stock-recruit function parameters) based on data from similar fish populations. Despite growing interest, Bayesian methods remain accessible to relatively few. To increase the accessibility of these methods, the conceptual basis for Bayesian statistical estimation is reviewed and set in the context of fisheries stock assessment. The use of Bayesian methods is illustrated by fitting a logistic model to relative abundance indices for Namibian hake (Merlucius capensis and M. paradoxus) and presenting a decision analysis of alternative harvest policy options. Some alternative approaches are outlined for constructing prior and posterior probability distributions and some recent applications in fisheries. Some of the problems that can be encountered while implementing Bayesian methods are also discussed.

Spatial regression models are developed as a complementary alternative to second-order polynomial response surfaces in the context of process optimization. These models provide estimates of design variable effects and smooth, data-faithful approximations to the unknown response function over the design space. The predicted response surfaces are driven by the covariance structures of the models. Several structures, isotropic and anisotropic, are considered and connections with thin plate splines are reviewed. Estimation of covariance parameters is achieved via maximum likelihood and residual maximum likelihood. A feature of the spatial regression approach is the visually appealing graphical summaries that are produced. These allow rapid and intuitive identification of process windows on the design space for which the response achieves target performance. Relevant design issues are briefly discussed and spatial designs, such as the packing designs available in Gosset, are suggested as a suitable design complement. The spatial regression models also perform well with no global design, for example with data obtained from series of designs on the same space of design variables. The approach is illustrated with an example involving the optimization of components in a DNA amplification assay. A Monte Carlo comparison of the spatial models with both thin plate splines and second-order polynomial response surfaces for a scenario motivated by the example is also given. This shows superior performance of the spatial models to the second-order polynomials with respect to both prediction over the complete design space and for cross-validation prediction error in the region of the optimum. An anisotropic spatial regression model performs best for a high noise case and both this model and the thin plate spline for a low noise case. Spatial regression is recommended for construction of response surfaces in all process optimization applications.

Bayesian Analysis of the Pragmatic Airway Resuscitation Trial

Bayesian inference plays an essential role in the development of mathematical theory, as an important component of statistical methods. The prior distribution, the likelihood function and the posterior distribution are used in Bayesian inference. A combination of the prior distribution and the likelihood function will represent the posterior distribution, where the background information decides the prior distribution, and the background information and the observed data together form the likelihood function. This paper presents the background of Bayesian inference, the main developments, and the challenges of computing the posterior distribution. It focuses on six MCMC-based methods, such as the Metropolis-Hastings algorithm, Gibbs sampler, Reversible Jump MCMC, Hamiltonian Monte Carlo, Adaptive Metropolis, and preconditioned Crank-Nicolson. The advantages, limitations and applications of each algorithm are also briefly described.

The purpose of this study was to assess the spatial distribution of malaria prevalence rates among selected rural part of woredas in SNNPR, Ethiopia. This work is based on data available from the 2011 malaria indicator survey (MIS 2011) of Ethiopian Public Health Institution. ESDA, Spatial regression model and Bayesian Spatial analysis were employed for data analysis. From ESDA, we found positive spatial autocorrelation in malaria prevalence rate. Relying on specification diagnostics and measures of fit; Spatial lag model was found to be the best model for modeling malaria prevalence rate data. The relationship between malaria prevalence and its risk factors was assessed using spatial models. The spatial models also showed an increase of malaria prevalence with a number of factors. From results, increase in the proportion of households sprayed in 12 months and the average altitude in the woreda estimated to decrease the average malaria prevalence. The result also demonstrated that increase in the House hold size of the district, proportion of households having access to piped water, proportion of households having access to radio, proportion of households having access to radio and Main construction material of the room’s wall are estimated to raise the average malaria prevalence rate. Finally, the study concluded that malaria is spatially clustered in space and the risk factors exhibit effect on the malaria prevalence in the study area. Based on the results of the study, We recommend for policy makers on the way to reduce malaria prevalence in the rural part of woreda of SNNPR using spatial information.

An empirical evaluation of spatial regression models

Leprosy, a highly contagious disease caused by the bacterium Mycobacterium leprae, can result in permanent disability if left untreated. It remains a significant public health issue in many regions, particularly tropical countries like Indonesia. Despite ongoing control efforts, incidence rates are still high in some areas. In 2023, East Java had the highest number of leprosy cases in Indonesia, with 2,124 out of 7,166. To understand the factors contributing to these cases, this study explores various influences and offers policy recommendations to reduce leprosy in East Java. The study uses spatial modeling with a weighting scheme based on queen contiguity, selected because leprosy spreads through human interactions and movement, creating spatial dependencies. It examines spatial, social, economic, educational, and environmental factors based on cross-sectional data from 38 regencies/cities in East Java for 2023. Among the regression models tested, the spatial error regression model proved most effective, showing an R-Square value of 67.14% and an AIC of 213.023. Key findings identified () average years of schooling and () healthcare worker ratios as significant factors influencing leprosy cases. These results aim to guide policymakers in developing stronger leprosy control strategies and offer a basis for further research in East Java.

At the start of new operation, a production process is commonly unstable. Then, a process condition is into being stable gradually over time. For the purpose of shifting to mass production, the stability in a process should be evaluated. This paper proposes a method of evaluating the process stability based on Bayesian statistics and information theory. In Bayesian statistics, the knowledge for a process is renewed by deriving posterior distribution based on current prior distribution and observations. Here, equivalency between prior and posterior distributions could be considered to be a criterion for the stability in a process. It is needed to define difference between prior and posterior distributions in order to evaluate the equivalency between prior and posterior distributions. We first formulate the relation between the prior distribution and the posterior distribution for process mean using Bayesian statistics. Secondly, we evaluate the difference between the both distributions based on Kullback‐Leibler (K‐L) divergence in information theory. Finally, some numerical examples in the method of evaluating the stability in process mean are illustrated. Also, we discuss about a decision rule for the stability in process mean through the numerical investigation.

Bayesian system reliability assessment method with maximum entropy as prior distribution is developed in the present analysis. The system reliability assessment model is established, and the method and process of system reliability assessment are put forward. The method is based on the theory of information entropy. The probability density function and distribution function of system reliability parameters are given by using maximum entropy method. Prior distribution of Bayesian analysis method is the distribution function. Likelihood function is given by a small amount of field test data. According to Bayesian methods, posterior distribution is determined by using prior distribution and likelihood function. The point estimation and interval estimation of system reliability parameters are calculated in order to evaluate the system reliability. The method solves better the problem of system reliability assessment for small sample cases, and is an optimum method for reliability assessment of large and complex systems.

In this study, we investigated the relation- ship between watershed characteristics and hydrology using high spatial resolution impervious surface area (ISA), hydrologic simulations and spatial regression. We selected 20 watersheds at HUC 12 level with different degrees of urbanization and performed hydro- logic simulation using a distributed object-oriented rainfall and runoff simulation model. We extracted the discharge per area and ratio of runoff to base flow from simulation results and used them as indicators of hydrology pattern. We derived percentage of ISA, distance from ISA to streams, and stream density as the watershed characteristics to evaluate the relationship with hydrology pattern in watersheds using ordinary least square, spatial error and spatial lag regression models. The comparison indicates that spatial lag regression model can achieve better performance for the evaluation of relationship between ratio of runoff to base flow and watershed characteristics, and that three models provide similar performance for the evaluation of relationship between discharge per area and watershed characteristics. The results from regression analyses demonstrate that ISA plays an important role in watershed hydrology. Ignorance of spatial dependence in analyses will likely cause inaccurate evaluation for relationship between ISA and watershed hydrology. The hydrologic model, regression methods and relationships between watershed characteristics and hydrology pat- tern provide important tools and information for deci- sion makers to evaluate the effect of different scenarios in land management.

Strange bayes indeed: uniform topological priors imply non-uniform clade priors

Estimating spatial logistic model: A deterministic approach or a heuristic approach?

Thermodynamic modeling and uncertainty quantification of CO2-loaded aqueous MEA solutions