Statistical analysis of parameters and adsorption isotherm models.

The present work intends to discuss parameter estimation and statistical analysis in adsorption. The Langmuir and Tóth isotherm models are compared for a set of carbon dioxide adsorption data on 13X zeolite from literature at different temperatures: 303, 323, 373, and 423 K. Statistical analyses were performed under frequentist and Bayesian perspectives. Under the frequentist statistical view, parameters were estimated using Maximum Likelihood estimation (MLE). Statistical analyses of parameters were performed by confidence regions in terms of elliptical approximation and likelihood region, while the evaluation of models was performed by chi-square statistics. The results showed that, for these nonlinear models, the elliptical region offers a poor approximation of the parameter estimates' confidence region, especially for the most correlated parameter pairs. Additionally, the four-parameter Tóth's equation yields less correlated parameters than the three-parameter Langmuir model. From a Bayesian perspective, the Markov chain Monte Carlo (MCMC) technique facilitated the reconstruction of the probability density functions of parameters as well as enabled the propagation of parametric uncertainties in the model responses. Finally, the accurate assessment of experimental uncertainty significantly influences the evaluation of models and their respective parameters.

A Bayesian spatial voting model to characterize the legislative behavior of the Colombian Senate 2010-2014.

This paper characterizes the legislators voting behavior in the Colombian Senate 2010-2014, by implementing a one-dimensional standard Bayesian ideal point estimator via Markov chain Monte Carlo algorithms. Our main goal is to retrieve the political preferences of legislators from their roll-call voting records, which individualizes the electoral behavior of the legislative chamber. Furthermore, we conclude about the nature of the latent trait underlying the deputies voting decisions and the legislators locations in political space. Finally, we also offer several methodological and theoretical tools to guide the analysis of nominal voting data in the context of unbalanced parliaments (multi-party systems), taking as reference the particular case of the Colombian Senate.

Monitoring of SARS-CoV-2 RNA in wastewater: A surveillance tool to foresee infection's evolution in the Mexican Caribbean.

The study aims to determine SARS-CoV-2 RNA in sewage of Cancun wastewater treatment plants, the main touristic destination of Mexico, and to estimate the infected persons during the sampling period. SARS-CoV-2 RNA traces were detected in the inlet of the five plants during almost all the sampling months. However, there is no presence of SARS-CoV-2 RNA traces in the effluent of the five WWTPs during the study period. ANOVA analysis showed differences in the concentrations of RNA traces of SARS-CoV-2 between the sample dates, but no differences were found from one WWTP to another. Estimated infected individuals by Markov chain Monte Carlo simulation are higher (between 77% and 91%) than the cases reported by the health authority. Wastewater monitoring and the estimation of infected individuals are a helpful tool, because estimation provides early warning signs on how broadly SARS-CoV-2 is circulating in the city, and led to the authorities to take measures wisely. PRACTITIONER POINTS: There is no presence of SARS-CoV-2 RNA traces in the effluent of the facilities, suggesting the effectiveness of treatment. Surveillance of viral RNA concentrations at treatment plants revealed presence in the influent of five plants Estimated infected individuals by MCMC simulation are higher than cases reported by health authority Environmental surveillance approach in wastewater influent is helpful to identify the clusters and to take informed decisions.

Phosphate removal using dolomite modified with ultrasound: mathematical and experimental analysis.

We studied the dolomite modified using an ultrasound bath and its application in phosphate removal. The modification was applied to improve the physicochemical properties of the dolomite and then to enhance its suitability as an adsorbent solid. The settings for analyzing the adsorbent modification were bath temperature and sonication time. The modified dolomite was characterized by electron microscopy, N2 adsorption/desorption, pore size, and X-ray diffraction. To grasp the pollutant's adsorption mechanism more precisely, we used experimental research and mathematical model analysis. Design of Experiments was conducted to determine the ideal circumstances. In addition, the Bayesian method of Markov Chain Monte Carlo was used to estimate the isotherm and kinetic model parameters. A thermodynamic study was done to investigate the adsorption mechanism. Results show that the surface area of the modified dolomite was greater, enhancing its adsorption properties. To remove more than 90% of the phosphate, the optimal operational parameters for the adsorption were pH 9, 1.77 g of adsorbent mass, and 55 minutes of contact time. The pseudo-first-order, Redlich-Peterson and Sips models presented a good fit to the experimental data. Thermodynamics suggested a spontaneous and endothermic process. The mechanism suggested that physisorption and chemisorption could be involved in phosphate removal.

Evaluating deep learning predictions for COVID-19 from X-ray images using leave-one-out predictive densities.

Early detection of the COVID-19 virus is an important task for controlling the spread of the pandemic. Imaging techniques such as chest X-ray are relatively inexpensive and accessible, but its interpretation requires expert knowledge to evaluate the disease severity. Several approaches for automatic COVID-19 detection using deep learning techniques have been proposed. While most approaches show high accuracy on the COVID-19 detection task, there is not enough evidence on external evaluation for this technique. Furthermore, data scarcity and sampling biases make difficult to properly evaluate model predictions. In this paper, we propose stochastic gradient Langevin dynamics (SGLD) to take into account the model uncertainty. Four different deep learning architectures are trained using SGLD and compared to their baselines using stochastic gradient descent. The model uncertainties are also evaluated according to their convergence properties and the leave-one-out predictive densities. The proposed approach is able to reduce overconfidence of the baseline estimators while also retaining predictive accuracy for the best-performing cases.

Flexible Bayesian modelling in dichotomous item response theory using mixtures of skewed item curves.

Most item response theory (IRT) models for dichotomous responses are based on probit or logit link functions which assume a symmetric relationship between the probability of a correct response and the latent traits of individuals taking a test. This assumption restricts the use of those models to the case in which all items behave symmetrically. On the other hand, asymmetric models proposed in the literature impose that all the items in a test behave asymmetrically. This assumption is inappropriate for great majority of tests which are, in general, composed of both symmetric and asymmetric items. Furthermore, a straightforward extension of the existing models in the literature would require a prior selection of the items' symmetry/asymmetry status. This paper proposes a Bayesian IRT model that accounts for symmetric and asymmetric items in a flexible but parsimonious way. That is achieved by assigning a finite mixture prior to the skewness parameter, with one of the mixture components being a point mass at zero. This allows for analyses under both model selection and model averaging approaches. Asymmetric item curves are designed through the centred skew normal distribution, which has a particularly appealing parametrization in terms of parameter interpretation and computational efficiency. An efficient Markov chain Monte Carlo algorithm is proposed to perform Bayesian inference and its performance is investigated in some simulated examples. Finally, the proposed methodology is applied to a data set from a large-scale educational exam in Brazil.

An application of a non-homogeneous Poisson model to study PM2.5 exceedances in Mexico City and Bogota.

It is very important to study the occurrence of high levels of particulate matter due to the potential harm to people's health and to the environment. In the present work we use a non-homogeneous Poisson model to analyse the rate of exceedances of particulate matter with diameter smaller that 2.5 microns (PM 2.5 ). Models with and without change-points are considered and they are applied to data from Bogota, Colombia, and Mexico City, Mexico. Results show that whereas in Bogota larger particles pose a more serious problem, in Mexico City, even though nowadays levels are more controlled, in the recent past PM 2.5 were the ones causing serious problems.

Parameter estimation in high-intensity focused ultrasound therapy.

Hyperthermia using High-Intensity Focused Ultrasound (HIFU) is an acoustic therapy for cancer treatment. This technique consists of an increase in the temperature field of the tumor to achieve coagulative necrosis and immediate cell death. Therefore, for having a successful treatment, the physical problem requires to know several properties due to the high variability from individual to individual, or even for the same individual under different physiological conditions. This article presents a numerical simulation of hyperthermia therapy for cancer treatment using HIFU, as well as the estimation of parameters that influence the physical problem. Two mathematical models were considered to solve the forward problem. The acoustic model based on acoustic pressure performs a frequency-domain study, and the bioheat transfer model a time-dependent study. These models were solved using Comsol Multiphysics® software in a 2D-axisymmetric rectangular domain to determine the temperature field. Parameter estimation was coded in Matlab Mathworks® environment using a Bayesian approach. The Markov Chain Monte Carlo method by the Metropolis-Hastings algorithm was implemented, and the simulated temperature measurements were considered. Results suggest that specific HIFU therapy can be performed for each patient by estimating appropriate parameters for cancer treatment and provides the possibility to define procedures before and during the treatment.

Modelling diagnostics for Echinococcus granulosus surveillance in sheep using Latent Class Analysis: Argentina as a case study.

Echinococcus granulosus sensu lato is a globally prevalent zoonotic parasitic cestode leading to cystic echinococcosis (CE) in both humans and sheep with both medical and financial impacts, whose reduction requires the application of a One Health approach to its control. Regarding the animal health component of this approach, lack of accurate and practical diagnostics in livestock impedes the assessment of disease burden and the implementation and evaluation of control strategies. We use of a Bayesian Latent Class Analysis (LCA) model to estimate ovine CE prevalence in sheep samples from the Río Negro province of Argentina accounting for uncertainty in the diagnostics. We use model outputs to evaluate the performance of a novel recombinant B8/2 antigen B subunit (rEgAgB8/2) indirect enzyme-linked immunosorbent assay (ELISA) for detecting E. granulosus in sheep. Necropsy (as a partial gold standard), western blot (WB) and ELISA diagnostic data were collected from 79 sheep within two Río Negro slaughterhouses, and used to estimate individual infection status (assigned as a latent variable within the model). Using the model outputs, the performance of the novel ELISA at both individual and flock levels was evaluated, respectively, using a receiver operating characteristic (ROC) curve, and simulating a range of sample sizes and prevalence levels within hypothetical flocks. The estimated (mean) prevalence of ovine CE was 27.5% (95%Bayesian credible interval (95%BCI): 13.8%-58.9%) within the sample population. At the individual level, the ELISA had a mean sensitivity and specificity of 55% (95%BCI: 46%-68%) and 68% (95%BCI: 63%-92%), respectively, at an optimal optical density (OD) threshold of 0.378. At the flock level, the ELISA had an 80% probability of correctly classifying infection at an optimal cut-off threshold of 0.496. These results suggest that the novel ELISA could play a useful role as a flock-level diagnostic for CE surveillance in the region, supplementing surveillance activities in the human population and thus strengthening a One Health approach. Importantly, selection of ELISA cut-off threshold values must be tailored according to the epidemiological situation.

Interrelations between productive, vegetative, and fruit quality traits in Tahiti acid lime through Bayesian inference / Inter-relações entre características produtivas, vegetativas e de qualidade de fruto em lima ácida Tahiti através de inferência Bayesiana

Although the fruit yield has a core importance in Tahiti acid lime breeding programs, other traits stand out among the quality fruit and vegetative traits as ones that still need to be improved in selection of superior genotypes. Appling efficient tools aiming selection, such as the Bayesian inference, becomes an alternative in perennial crops. This study applied Bayesian inference in the genetic evaluation of Tahiti acid lime genotypes and estimated the interrelation between vegetative, productive and fruit quality traits. Twenty-four acid lime genotypes were evaluated for number of fruits, fruit yield, canopy volume, stem diameter, soluble solids content, shell thickness, and juice yield traits. The genotypic values were estimated through Bayesian inference and models with different residual structure were tested via deviance information criterion. Pearson's correlation and the path analysis were estimated, removing the multicollinearity effect. The Bayesian inference estimates genotypic values with high selective accuracy. The correlations obtained between traits from different groups can be useful in selection strategies for improvement of Tahiti acid lime. The Bayesian inference demonstrated to be an important tool and should be considered in perennial breeding programs.

Embora a produtividade seja uma característica fundamental em programas de melhoramento da lima ácida Tahiti, outras características se destacam por proporcionar uma seleção mais eficiente ou mesmo influenciar na expressão de atributos produtivos. A aplicação de inferência Bayesiana, pode tornar o processo de identificação de indivíduos superiores e o estudo das correlações entre as características ainda mais acurado. Objetivou-se, por meio deste estudo, estimar valores genéticos em genótipos de lima ácida Tahiti através de inferência Bayesiana e estimar coeficientes de correlação e de trilha entre características vegetativas, produtivas e de qualidade de frutos. Vinte e quatro genótipos de lima ácida foram avaliados durante dois anos para peso e número de frutos, volume de copa, diâmetro de caule, teor de sólidos solúveis dos frutos, espessura de casca e rendimento de suco. Os valores genéticos foram estimados por meio de inferência Bayesiana e modelos com diferentes estruturas residuais foram testados via critério de informação de deviance. Coeficiente de correlação de Pearson e de análise de trilha foram determinados, removendo o efeito de multicolinearidade. A estimação de valores genéticos via inferência Bayesiana apresentou alta acurácia seletiva. As correlações obtidas entre caracteres de diferentes grupos podem ser úteis em estratégias de seleção para melhoramento da lima ácida Tahiti. A inferência Bayesiana demonstrou ser uma ferramenta importante e deve ser considerada em programas de melhoramento de culturas perenes.

Evaluation of zinc adsorption through batch and continuous scale applying Bayesian technique for estimate parameters and select model.

This work aims to study the efficiency of zinc adsorption onto granular-activated carbon, predicting the mathematical models that best describe the adsorption behavior in a fixed bed column. First, batch scale experiments were performed to evaluate the influence of pH (3 to 6), contact time (5 to 60 min), and absorbent concentration (5 to 25 g L-1) using synthetic effluent. Fixed bed column experiments were performed by varying the adsorbent concentration (10, 13, 20, and 40 g L-1) and the effluent flow rate (15 and 20 mL min-1). Markov Chain Monte Carlo and Bayesian criteria information were applied to describe the phenomena using Langmuir, Freundlich, Temkin, Redlich-Peterson, Sips, Toth, Khan, Radke-Prausnitz, for isotherm models, and Thomas; Yoon-Nelson; Yan; Clark models for breakthrough curve. Adsorption operating best conditions were pH 5, 20 g L-1 of solid, and 50 min of contact time. These parameters allowed 80% of Zn removal, being better described by the Tempki model. In tests on a pilot plant, the Yan model was able to predict the second-order kinetic model, with an increase in the effluent flow and a 50% increase in the bed saturation time with a greater amount of adsorbent solid.

Bivariate lifetime models in presence of cure fraction: a comparative study with many different copula functions.

In time-to-event studies it is common the presence of a fraction of individuals not expecting to experience the event of interest; these individuals who are immune to the event or cured for the disease during the study are known as long-term survivors. In addition, in many studies it is observed two lifetimes associated to the same individual, and in some cases there exists a dependence structure between them. In these situations, the usual existing lifetime distributions are not appropriate to model data sets with long-term survivors and dependent bivariate lifetimes. In this study, it is proposed a bivariate model based on a Weibull standard distribution with a dependence structure based on fifteen different copula functions. We assumed the Weibull distribution due to its wide use in survival data analysis and its greater flexibility and simplicity, but the presented methods can be adapted to other continuous survival distributions. Three examples, considering real data sets are introduced to illustrate the proposed methodology. A Bayesian approach is assumed to get the inferences for the parameters of the model where the posterior summaries of interest are obtained using Markov Chain Monte Carlo simulation methods and the Openbugs software. For the data analysis considering different real data sets it was assumed fifteen different copula models from which is was possible to find models with satisfactory fit for the bivariate lifetimes in presence of long-term survivors.

Modeling Overdispersion, Autocorrelation, and Zero-Inflated Count Data Via Generalized Additive Models and Bayesian Statistics in an Aphid Population Study.

Count variables are often positively skewed and may include many zero observations, requiring specific statistical approaches. Interpreting abiotic factor changes in insect populations of crop pests, under this condition, can be difficult. The analysis becomes even more complicated because of possible temporal or spatial correlation, irregularly spaced data, heterogeneity over time, and zero inflation. Generalized additive models (GAM) are important tools to evaluate abiotic factors. Moreover, Markov chain Monte Carlo (MCMC) techniques can be used to fit a model that contains a temporal correlation structure, based on Bayesian statistics (BGAM). We compared methods of modeling the effects of temperature, precipitation, and time for the Brevicoryne brassicae (L.) population in Uberlândia, Brasil. We applied the proposed BGAM to the data, comparing this to the GAM model with and without autocorrelation for time, using the statistical programming language R. Analysis of deviance identified significant effects of the smoothers for precipitation and time on the frequentist models. With BGAM, the problem in variance estimations for precipitation and temperature from the previous models was solved. Furthermore, trace and density plots for population-level effects for all parameters converged well. The estimated smoothing curves showed a linear effect with an increase of precipitation, where lower precipitation indicated no presence of the aphid. The average temperature did not affect the aphid incidence. Autocorrelation was solved with ARMA structures, and the excess of zero was solved with zero-inflation models. The example of B. brassicae incidence showed how well abiotic (and biotic) factors can be modeled and analyzed using BGAM.

Fully Bayesian analysis of allele-specific RNA-seq data.

Diploid organisms have two copies of each gene, called alleles, that can be separately transcribed. The RNA abundance associated to any particular allele is known as allele-specific expression (ASE). When two alleles have polymorphisms in transcribed regions, ASE can be studied using RNA-seq read count data. ASE has characteristics different from the regular RNA-seq expression: ASE cannot be assessed for every gene, measures of ASE can be biased towards one of the alleles (reference allele), and ASE provides two measures of expression for a single gene for each biological samples with leads to additional complications for single-gene models. We present statistical methods for modeling ASE and detecting genes with differential allelic expression. We propose a hierarchical, overdispersed, count regression model to deal with ASE counts. The model accommodates gene-specific overdispersion, has an internal measure of the reference allele bias, and uses random effects to model the gene-specific regression parameters. Fully Bayesian inference is obtained using the fbseq package that implements a parallel strategy to make the computational times reasonable. Simulation and real data analysis suggest the proposed model is a practical and powerful tool for the study of differential ASE.

Quantifying personal exposure to air pollution from smartphone-based location data.

Personal exposure assessment is a challenging task that requires both measurements of the state of the environment as well as the individual's movements. In this paper, we show how location data collected by smartphone applications can be exploited to quantify the personal exposure of a large group of people to air pollution. A Bayesian approach that blends air quality monitoring data with individual location data is proposed to assess the individual exposure over time, under uncertainty of both the pollutant level and the individual location. A comparison with personal exposure obtained assuming fixed locations for the individuals is also provided. Location data collected by the Earthquake Network research project are employed to quantify the dynamic personal exposure to fine particulate matter of around 2500 people living in Santiago (Chile) over a 4-month period. For around 30% of individuals, the personal exposure based on people movements emerges significantly different over the static exposure. On the basis of this result and thanks to a simulation study, we claim that even when the individual location is known with nonnegligible error, this helps to better assess personal exposure to air pollution. The approach is flexible and can be adopted to quantify the personal exposure based on any location-aware smartphone application.

Estimation of the kidney metabolic heat generation rate.

Thermogenesis results from the cellular metabolism and has a fundamental role for body thermoregulation in endothermic species. The motivation for this work is the analysis of the kidneys' contribution for thermoregulation. An inverse problem is solved for the estimation of the heat generation rate that results from the metabolic activities in the kidney, by using transient temperature measurements of the urine. The Markov chain Monte Carlo (MCMC) method is applied for the solution of the inverse problem, which presents inherent difficulties associated with low sensitivity of the parameters of main interest that represent the transient heat source term and strong correlation of the remaining model parameters. Such difficulties are dealt with in this work by using a version of the Metropolis-Hastings algorithm that samples the parameters in blocks. Simulated temperature measurements are used for the inverse problem solution, and the convergence of the Markov chains is verified with two different techniques.

Knowledge and risk perceptions of foodborne disease by consumers and food handlers at restaurants with different food safety profiles.

Food handlers and consumers are responsible for avoiding foodborne diseases (FBD). Considering the meals consumed away from home, can the consumer identify the FBD risk level of the food that he/she consumes in restaurants? This study aimed to evaluate the knowledge, risk perception, and optimistic bias of food handlers and consumers of restaurants and the relationship of these variables with the FBD risk of these establishments. Sixty-four handlers and 265 consumers of 14 restaurants in the city of Limeira - São Paulo, Brazil participated in the study. A validated checklist was used to evaluate the food safety profile of restaurants with a score ranging from zero to 2565.95. A structured questionnaire was employed to assess knowledge of food safety and the risk perception of FBD. The food handlers indicated their own risk and their peers' risk of causing a FBD. Consumers evaluated their own risk and the risk of their peers of contracting a FBD after making their own meals, consuming meals at the studied restaurants and consuming meals in other food establishments. The answers were based on a structured scale with seven options. The difference between their risk perception levels (risk attributed to itself and to a peer) indicated the optimistic bias of FBD risk. The mean food safety risk score of the food service establishments was 105.51. The restaurants were classified into two groups, higher or lower FBD risk. The mean score of knowledge (percentage of correct answers) of food safety was 61.7% for handlers and 59% for consumers, showing a nonsignificant difference (p = .29). Both food handlers and consumers stated that they were less at risk for FBD than their peers (p < .001). A direct effect of consumers' optimistic bias on food service FBD risk was observed through multivariate analysis. Optimistic bias may lead consumers to choose restaurants with a higher FDB risk. A direct negative effect of food handlers' knowledge of food service FBD risk was observed. These results show that consumers may have incorporated a sense of affection and identity to a place, associating it with making their own meals at home. Therefore, the consumer may not differentiate restaurants with regard to food safety. This result reinforces the need for governments and health agencies to protect the health of the population.

Developing a Hierarchical Model for the Spatial Analysis of PM10 Pollution Extremes in the Mexico City Metropolitan Area.

We implemented a spatial model for analysing PM 10 maxima across the Mexico City metropolitan area during the period 1995-2016. We assumed that these maxima follow a non-identical generalized extreme value (GEV) distribution and modeled the trend by introducing multivariate smoothing spline functions into the probability GEV distribution. A flexible, three-stage hierarchical Bayesian approach was developed to analyse the distribution of the PM 10 maxima in space and time. We evaluated the statistical model's performance by using a simulation study. The results showed strong evidence of a positive correlation between the PM 10 maxima and the longitude and latitude. The relationship between time and the PM 10 maxima was negative, indicating a decreasing trend over time. Finally, a high risk of PM 10 maxima presenting levels above 1000 µ g/m 3 (return period: 25 yr) was observed in the northwestern region of the study area.

Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student's t-distribution.

A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor's 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model.

Spatial generalised linear mixed models based on distances.

Risk models derived from environmental data have been widely shown to be effective in delineating geographical areas of risk because they are intuitively easy to understand. We present a new method based on distances, which allows the modelling of continuous and non-continuous random variables through distance-based spatial generalised linear mixed models. The parameters are estimated using Markov chain Monte Carlo maximum likelihood, which is a feasible and a useful technique. The proposed method depends on a detrending step built from continuous or categorical explanatory variables, or a mixture among them, by using an appropriate Euclidean distance. The method is illustrated through the analysis of the variation in the prevalence of Loa loa among a sample of village residents in Cameroon, where the explanatory variables included elevation, together with maximum normalised-difference vegetation index and the standard deviation of normalised-difference vegetation index calculated from repeated satellite scans over time.