Posteriori Methods Research Articles

A kind regularization method for solving Cauchy problem of the Schrödinger equation

The potential-free field Schrödinger Cauchy problem is the major topic of this research. Because it is gravely ill-posed in the Hadamard sense. The Cauchy problem is modified through an improved boundary method. The regular approximate solution is created based on the priori and posteriori regularization parameter selection rules, and the convergence evidence is provided. The proposed method is practical under the priori and the posteriori regularization methods, according to numerical experiments. It works well and is resistant to data disruption noise.

Comparing the Associations of Dietary Patterns Identified through Principal Component Analysis and Cluster Analysis with Colorectal Cancer Risk: A Large Case-Control Study in China.

Examining the association between dietary patterns and colorectal cancer (CRC) risk can provide valuable insights beyond the assessment of individual foods or nutrients. However, there is a lack of in-depth analysis of dietary patterns and CRC risk in Chinese populations, and few studies have compared dietary patterns derived from different posteriori methods with the aim of predicting disease risk. The aim of this study was to derive dietary patterns using both principal component analysis (PCA) and cluster analysis (CA) and to assess their respective associations with CRC risk. A large-scale case-control study was conducted in Guangdong Province, China, including 2799 incident colorectal cancer cases and an equal number of frequency-matched controls. Dietary intake information was gathered through the use of a validated food frequency questionnaire. PCA and CA were used to derive dietary patterns. A multivariable logistic regression model was used to calculate the adjusted odds ratio (aOR) and 95% confidence interval (CI). Four major dietary patterns were identified by PCA. CA identified two dietary patterns, referred to as the "Balanced dietary pattern" and the "Refined grain dietary pattern". Notably, there were significant inverse associations between the milk-egg-nut-soy dietary pattern (aOR, 0.51; 95% CI, 0.42, 0.62), the vegetable-fruit dietary pattern (aOR, 0.61; 95%CI, 0.51, 0.74), and the poultry-fish dietary pattern (aOR, 0.81; 95%CI, 0.68, 0.97) and CRC risk. However, the red meat-preserved food dietary pattern was associated with an increased risk of CRC (aOR, 2.99; 95%CI, 2.43, 3.67). When compared with the Refined grain dietary pattern, the Balanced dietary pattern showed a decreased risk of CRC (aOR, 0.59; 95%CI, 0.52, 0.66). The results from the comparison of the two methods indicate that both CA and PCA derived remarkably similar patterns. The combined use of PCA and CA identified consistent underlying patterns, showing comparable associations with CRC risk. These findings suggest that individuals who prefer dietary patterns characterized by a high intake of red meat, preserved food, and refined grains should be cautious about their increased CRC risk. Conversely, dietary patterns rich in fruits, vegetables, and high-quality protein sources are advisable for the prevention of CRC in the Chinese population.

Rejection methods for vegetation mapping using hyperspectral airborne data

ABSTRACT Vegetation mapping from remote sensing data has proven useful for monitoring ecosystems at local, regional and global scales. Generally based on supervised classification methods, ecosystem mapping needs representative and consistent labelling. Such completeness is often difficult to achieve and requires the exclusion of minority species poorly represented in the studied scene in the training base. This exclusion leads to wrong predictions in the resulting map. In this study, the use of a posteriori classification rejection methods to limit the errors associated with minority species was evaluated in three different mapping scenarios: classification according to vegetation layers, prediction of genera from various vegetation types from low vegetation to trees and mapping of habitat (assemblages of species). For this purpose, several supervised classification methods based on Support Vector Machines (SVM), Random Forests (RF) and Regularized Logistic Regression (RLR) algorithms were first applied to hyperspectral images covering the reflective domain. On these classifications, the usual evaluation methods (confusion matrix and its derivatives calculated on an independent test set composed of the majority species) showed performances similar to those of the state-of-the-art. However, the introduction of a new score taking into account minority species demonstrated the need to include them in the evaluation process to provide robust performance quantification representing map effectiveness. Three a posteriori rejection methods, based on simple thresholding, K-means and SVM algorithms, were well suited to monitor minority species. The performance gain depended on the mapping scenario, the machine learning model and the rejection method. An increase in performance with the inclusion of minority species of up to 12% could be observed through the new score. These methods also detected a similar proportion of prediction errors associated with predominant species

A Simple, Test-Based Method to Control the Overestimation Bias in the Analysis of Potential Prognostic Tumour Markers

The early evaluation of prognostic tumour markers is commonly performed by comparing the survival of two groups of patients identified on the basis of a cut-off value. The corresponding hazard ratio (HR) is usually estimated, representing a measure of the relative risk between patients with marker values above and below the cut-off. A posteriori methods identifying an optimal cut-off are appropriate when the functional form of the relation between the marker distribution and patient survival is unknown, but they are prone to an overestimation bias. In the presence of a small sample size, which is typical of rare diseases, the external validation sets are hardly available and internal cross-validation could be unfeasible. We describe a new method to obtain an unbiased estimate of the HR at an optimal cut-off, exploiting the simple relation between the HR and the associated p-value estimated by a random permutation analysis. We validate the method on both simulated data and set of gene expression profiles from two large, publicly available data sets. Furthermore, a reanalysis of a previously published study, which included 134 Stage 4S neuroblastoma patients, allowed for the identification of E2F1 as a new gene with potential oncogenic activity. This finding was confirmed by an immunofluorescence analysis on an independent cohort.

The Explanatory Generalized Graded Unfolding Model: Incorporating Collateral Information to Improve the Latent Trait Estimation Accuracy.

Collateral information has been used to address subpopulation heterogeneity and increase estimation accuracy in some large-scale cognitive assessments. The methodology that takes collateral information into account has not been developed and explored in published research with models designed specifically for noncognitive measurement. Because the accurate noncognitive measurement is becoming increasingly important, we sought to examine the benefits of using collateral information in latent trait estimation with an item response theory model that has proven valuable for noncognitive testing, namely, the generalized graded unfolding model (GGUM). Our presentation introduces an extension of the GGUM that incorporates collateral information, henceforth called Explanatory GGUM. We then present a simulation study that examined Explanatory GGUM latent trait estimation as a function of sample size, test length, number of background covariates, and correlation between the covariates and the latent trait. Results indicated the Explanatory GGUM approach provides scoring accuracy and precision superior to traditional expected a posteriori (EAP) and full Bayesian (FB) methods. Implications and recommendations are discussed.

Framework for the comparison of a priori and a posteriori error variance estimation and tuning schemes

AbstractThe performance of an assimilation system is strongly dependent on the quality of the error statistics used. A number of error statistics estimation and tuning methods have previously been developed to better assess and determine these statistics. Many of these are a posteriori methods which make use of quantities calculated during the assimilation procedure, while other a priori methods do not require information from the assimilation. In this study, we develop a conceptual framework that relates these methods when applied to error variance determination, where each method is associated with the minimization of a particular cost function. The minimization of these cost functions describes a fitting procedure that fits parts of the prescribed modelled innovation covariance to its observed values. Each method must in some way separate the innovation covariance into its contributions from the background and the observations, which are then used in the fitting procedure. It is shown that the examined a posteriori methods use the analysis filter to make this separation and that the minimization of their associated cost functions is done implicitly within the tuning procedure. Analytical expressions for the expectation value and variance of estimates for error variance scaling parameters are determined for each method. The expressions for the expectation values of these estimates show that the accuracy of each method is dependent on its ability to separate the background from the observation contributions to the innovation covariance. This separability is quantified by use of the Frobenius inner product between the background‐ and observation‐error covariances, which additionally allows for geometric interpretations of the covariances to be made. Comparisons between variance parameter estimates from different methods are made for the case of a 1D periodic domain.

A Mathematical Blended Learning Model for University Students

The article aims to develop a model for assessing the quality of blended learning for university students. Different viewpoints on blended learning and the quality of learning are summarized and systematized. A model and method for assessing the quality of blended learning are presented. Approaches are developed for obtaining estimates of the quality of learning based on a priori and a posteriori assessment methods.

Learning Bayesian network parameters from small data sets: A further constrained qualitatively maximum a posteriori method

To improve the learning accuracy of the parameters in a Bayesian network from a small data set, domain knowledge is normally incorporated into the learning process as parameter constraints. MAP-based (Maximum a Posteriori) methods that utilize both sample data and domain knowledge have been well studied in the literature. Among all the MAP-based methods, the QMAP (Qualitatively Maximum a Posteriori) method exhibits the best learning performance. However, when the data is insufficient, the estimation given by the QMAP often fails to satisfy all the convex parameter constraints, and this has made the overall QMAP estimation unreliable. To ensure that QMAP estimation does not violate any given parameter constraints and to further improve the learning accuracy, a FC-QMAP (Further Constrained Qualitatively Maximum a Posteriori) algorithm is proposed in this paper. The algorithm regulates QMAP estimation by replacing data estimation with a further constrained estimation via convex optimization. Experiments and theoretical analysis show that the proposed algorithm outperforms most of the existing parameter learning methods (namely, Maximum Likelihood, Constrained Maximum Likelihood, Maximum Entropy, Constrained Maximum Entropy, Maximum a Posteriori, and Qualitatively Maximum a Posteriori).

A least squares approach for efficient and reliable short-term versus long-term optimization

The uncertainties related to long-term forecasts of oil prices impose significant financial risk on ventures of oil production. To minimize risk, oil companies are inclined to maximize profit over short-term horizons ranging from months to a few years. In contrast, conventional production optimization maximizes long-term profits over horizons that span more than a decade. To address this challenge, the oil literature has introduced short-term versus long-term optimization. Ideally, this problem is solved by a posteriori multi-objective optimization methods that generate an approximation to the Pareto front of optimal short-term and long-term trade-offs. However, such methods rely on a large number of reservoir simulations and scale poorly with the number of objectives subject to optimization. Consequently, the large-scale nature of production optimization severely limits applications to real-life scenarios. More practical alternatives include ad hoc hierarchical switching schemes. As a drawback, such methods lack robustness due to unclear convergence properties and do not naturally generalize to cases of more than two objectives. Also, as this paper shows, the hierarchical formulation may skew the balance between the objectives, leaving an unfulfilled potential to increase profits. To promote efficient and reliable short-term versus long-term optimization, this paper introduces a natural way to characterize desirable Pareto points and proposes a novel least squares (LS) method. Unlike hierarchical approaches, the method is guaranteed to converge to a Pareto optimal point. Also, the LS method is designed to properly balance multiple objectives, independently of Pareto front’s shape. As such, the method poses a practical alternative to a posteriori methods in situations where the frontier is intractable to generate.

Towards quantitative mesh pre-optimization for finite element analysis

ABSTRACTIn a previous research work, we introduced the concept of automatic mesh pre-optimization, also referred to as a priori mesh adaptation. Indeed, the basic idea underlying mesh pre-optimization is providing finite element analysis with meshes that have been adapted before analysis itself. It consists in automatically deriving mesh sizing functions from geometric features of the analysis domain. This allows providing the analyst with meshes that feature a certain degree of adaptation around sensitive zones or sensitive shapes (high curvature zones, narrow regions, sources of stress concentration, etc.) before any analysis, which also means before any a posteriori mesh adaptation. So far, mesh pre-optimization could not be considered as a quantitative adaptation since it does not explicitly target accuracy objectives, contrary to a posteriori mesh adaptation methods. This paper brings about new concepts in mesh pre-optimization that tend to make pre-optimization not only qualitative. It shows that, f...

An a priori analytical method for the determination of operating reserve requirements

Power balance is one of the key requirements for reliable power system operation. However, factors, such as net load variability and forecast errors, impose practical limitations on matching the scheduled generation and the real-time demand. Normally, potential power imbalances are mitigated by scheduling additional generation capacity called operating reserves. However, reserves are a costly commodity and their requirements should be accurately assessed to avoid unnecessary expense. Currently, the reserve requirements are determined using a posteriori methods based upon operator’s experience and established assumptions. While these assumptions are made out of a level of engineering practicality, they may not be formally true given the numerical evidence. This paper presents a formal mathematical framework for the a priori determination of three types of operating reserve requirements, namely load following, ramping and regulation. Validation of the methodology is performed by a set of extensive simulations that model the power system operations for different scenarios. This methodology is used to study the sensitivity of each type of reserve requirement to the net load and power system parameters.

Variance difference between maximum likelihood estimation method and expected A posteriori estimation method viewed from number of test items

The aim of this study is to determine variance difference between maximum likelihood and expected A posteriori estimation methods viewed from number of test items of aptitude test. The variance presents an accuracy generated by both maximum likelihood and Bayes estimation methods. The test consists of three subtests, each with 40 multiple-choice items of 5 alternatives. The total items are 102 and 3159 respondents which were drawn using random matrix sampling technique, thus 73 items were generated which were qualified based on classical theory and IRT. The study examines 5 hypotheses. The results are variance of the estimation method using MLE is higher than the estimation method using EAP on the test consisting of 25 items with F= 1.602, variance of the estimation method using MLE is higher than the estimation method using EAP on the test consisting of 50 items with F= 1.332, variance of estimation with the test of 50 items is higher than the test of 25 items, and variance of estimation with the test of 50 items is higher than the test of 25 items on EAP method with F=1.329. All observed F values ≥ 1.00. 5 RMSE in items 10, 15, 20, and 25 are different in both MLE and EAP, with t = 3.060, , thereby meaning that statistical null hypothesis are rejected. The study concludes that variance of MLE method is higher than EAP, and the test with 50 items has higher variance than that with 25 items, the accuracy of EAP estimate higher than that of MLE in item 10, 15, 20, and 25. Key words: Variance, RMS of estimation, maximum likelihood, expected A posteriori.

Communicating with parents of obese children: which channels are most effective?

BackgroundOne of the strategies proven most successful in curbing rising rates of childhood obesity involves targeting parents as agents of change. Prior studies have focused on what messages to communicate, but few have investigated how they should be communicated.ObjectiveTo identify the channels most effective for communicating with parents of overweight and obese children and understand whether their use of parenting information sources differs from others in the community.Design/settingThis study utilizes data from the Longitudinal Study of Australian Children (LSAC). Families were included if weight and height information was available for parents and children at three data collection points: Waves 1, 2 and 4 (collected 2004, 2006 and 2010, respectively, n = 5107).Analysis A priori and a posteriori segmentation methods identified groups of parents that were similar in the sources used to obtain information about parenting, and examined whether some segments were more likely to have obese children.ResultsFour segments were identified that differed in their information source use: the ‘personal networks’, ‘books’, ‘official sources’ and ‘mixed approach’ segments. The ‘official sources’ and ‘mixed approach’ segments were most likely to have obese children, and they used doctors, government/community organizations and friends to obtain information on parenting. These segments were also less educated and had lower employment.ConclusionsMessages are most likely to reach families with obese children if communicated through doctors, government publications and community organizations. Further, messages targeting social groupings of parents will leverage the power of advice from friends, which is another valuable information source for this group.

Nutrient Patterns and Their Food Sources in Older Persons from France and Quebec: Dietary and Lifestyle Characteristics.

Background: Dietary and nutrient patterns have been linked to health outcomes related to aging. Food intake is influenced by environmental and genetic factors. The aim of the present study was to compare nutrient patterns across two elderly populations sharing a common ancestral cultural background, but living in different environments. Methods: The diet quality, lifestyle and socioeconomic characteristics of participants from the Three-City Study (3C, France, n = 1712) and the Québec Longitudinal Study on Nutrition and Successful Aging (NuAge, Quebec, Canada, n = 1596) were analyzed. Nutrient patterns and their food sources were identified in the two samples using principal component analysis. Diet quality was compared across sample-specific patterns by describing weekly food intake and associations with the Canadian Healthy Eating Index (C-HEI). Results: Three nutrient patterns were retained in each study: a healthy, a Western and a more traditional pattern. These patterns accounted for 50.1% and 53.5% of the total variance in 3C and NuAge, respectively. Higher education and non-physical occupations over lifetime were associated with healthy patterns in both studies. Other characteristics such as living alone, having a body mass index lower than 25 and being an ex-smoker were associated with the healthy pattern in NuAge. No association between these characteristics and the nutrient patterns was noted in 3C. The healthy and Western patterns from each sample also showed an inverse association with C-HEI. Conclusion: The two healthy patterns showed important similarities: adequate food variety, consumption of healthy foods and associations with common sociodemographic factors. This work highlights that nutrient patterns derived using a posteriori methods may be useful to compare the nutritional quality of the diet of distinct populations.

The Relationship Between Dietary Patterns and Carotid Intima Media Thickness, as an Early Biomarker of Cardiovascular Disease: A Systematic Review and Narrative Synthesis

ObjectiveTo systematically review current literature on the association between empirically derived dietary patterns and carotid‐intima media thickness, an early marker of cardiovascular disease.BackgroundDietary pattern analysis has emerged as a complementary approach to single‐nutrient analysis for examining the relationship between diet and the risk of chronic diseases like cardiovascular disease (CVD). Carotid intima‐media thickness (CIMT) has been established as a robust early marker of CVD on the atherosclerotic pathway. Although a wealth of literature links dietary factors and traditional CVD markers, a limited number have investigated the relationship between dietary patterns, derived using empirical data, and CIMT, a novel CVD marker. This is a unique systematic review and narrative synthesis which investigates the association between dietary patterns and CIMT.MethodsA systematic search of MEDLINE, CINAHL and Web of Science (2000 to 2015) supplemented by manual searches of bibliographies was conducted. Studies that derived dietary patterns using a posteriori methods (principal component analysis (PCA)/factor analysis (FA)), a priori methods (investigator‐defined) or a combination (reduced rank regression (RRR)) were included with CIMT as the outcome. Most papers studied healthy adults (≥18 years) except two. The Critical Appraisal Skills Programme (CASP) checklist was adapted to assess each study for validity, methodology, and relevance. The narrative synthesis discusses the findings from each study according to the method used to derive the dietary patterns.ResultsOut of a total of 1582 papers, 15 papers were eligible for review. Six papers used empirical methods (PCA n=4, FA n=1, RRR n=1), while 9 papers used investigator‐defined methods to determine dietary patterns (refer to the figure). In general, of the papers using empirical methods, four reported a statistically significant association with increased CIMT. Overall, the dietary patterns identified in those studies were characterized by high consumption in ‘unhealthful’ food groups such as processed and red meat, soda and meal replacement drinks, refined grain and starchy foods. While two studies that identified dietary patterns empirically were associated with a decrease in CIMT, characterized by high consumption of ‘healthful’ foods namely fruits and vegetables, fish, and rice and low in the ‘unhealthful’ foods. Of the papers using investigator‐defined methods, four cross sectional studies showed that adherence to lacto‐vegetarian/low‐calorie vegan diets is associated with a decrease in CIMT. Dietary patterns derived from each study varied depending on derivation method and study design. When assessed for quality, RCTs scored the lowest, and cross sectional studies failed to provide sufficient information on the measurement of exposure variables. Cohort studies proved to be the most robust study design when assessed using the CASP criteria.ConclusionsFindings from this review are generally supportive of an association between greater adherence to dietary patterns characterised by higher consumption of ‘healthful’ foods and lower consumption of ‘unhealthful’ foods, and decreased CIMT. However, the evidence is heterogeneous as seen from the differences in CIMT measures with varying dietary patterns. Large‐scale prospective observational and interventional studies are needed to evaluate the association between dietary patterns and CIMT.Support or Funding Informationnone

Improving of Energy Measurements Reliability Using Weighted and Normalized Residual Analysis

The article considers the possibility of a posteriori methods implementation for energy measurements verification. Posteriori methods are developed in the framework of state estimation theory. The new approach to calculate the parameters of electric conditions using electrical energy measurements is discussed. Test scheme with different measurements sets is considered. Results demonstrate the implementation of a posteriori analysis.

Low complexity joint estimation of synchronization impairments in sparse channel for MIMO–OFDM system

Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO–OFDM system is presented in this paper. Based on a system model that takes into account the effects of synchronization impairments such as carrier frequency offset, sampling frequency offset, and symbol timing error, and channel, a Maximum Likelihood (ML) algorithm for the joint estimation is proposed. To reduce the complexity of ML grid search, the number of received signal samples used for estimation need to be reduced. The conventional channel estimation techniques using Least-Squares (LS) or Maximum a posteriori (MAP) methods fail for the reduced sample under-determined system, which results in poor performance of the joint estimator. The proposed ML algorithm uses Compressed Sensing (CS) based channel estimation method in a sparse fading scenario, where the received samples used for estimation are less than that required for an LS or MAP based estimation. The performance of the estimation method is studied through numerical simulations, and it is observed that CS based joint estimator performs better than LS and MAP based joint estimator.

The Effect of Muscle Contraction Level on the Cervical Vestibular Evoked Myogenic Potential (cVEMP): Usefulness of Amplitude Normalization

The cervical vestibular evoked myogenic potential (cVEMP) is a reflexive change in sternocleidomastoid (SCM) muscle contraction activity thought to be mediated by a saccular vestibulo-collic reflex. CVEMP amplitude varies with the state of the afferent (vestibular) limb of the vestibulo-collic reflex pathway, as well as with the level of SCM muscle contraction. It follows that in order for cVEMP amplitude to reflect the status of the afferent portion of the reflex pathway, muscle contraction level must be controlled. Historically, this has been accomplished by volitionally controlling muscle contraction level either with the aid of a biofeedback method, or by an a posteriori method that normalizes cVEMP amplitude by the level of muscle contraction. A posteriori normalization methods make the implicit assumption that mathematical normalization precisely removes the influence of the efferent limb of the vestibulo-collic pathway. With the cVEMP, however, we are violating basic assumptions of signal averaging: specifically, the background noise and the response are not independent. The influence of this signal-averaging violation on our ability to normalize cVEMP amplitude using a posteriori methods is not well understood. The aims of this investigation were to describe the effect of muscle contraction, as measured by a prestimulus electromyogenic estimate, on cVEMP amplitude and interaural amplitude asymmetry ratio, and to evaluate the benefit of using a commonly advocated a posteriori normalization method on cVEMP amplitude and asymmetry ratio variability. Prospective, repeated-measures design using a convenience sample. Ten healthy adult participants between 25 and 61 yr of age. cVEMP responses to 500 Hz tone bursts (120 dB pSPL) for three conditions describing maximum, moderate, and minimal muscle contraction. Mean (standard deviation) cVEMP amplitude and asymmetry ratios were calculated for each muscle-contraction condition. Repeated measures analysis of variance and t-tests compared the variability in cVEMP amplitude between sides and conditions. Linear regression analyses compared asymmetry ratios. Polynomial regression analyses described the corrected and uncorrected cVEMP amplitude growth functions. While cVEMP amplitude increased with increased muscle contraction, the relationship was not linear or even proportionate. In the majority of cases, once muscle contraction reached a certain "threshold" level, cVEMP amplitude increased rapidly and then saturated. Normalizing cVEMP amplitudes did not remove the relationship between cVEMP amplitude and muscle contraction level. As muscle contraction increased, the normalized amplitude increased, and then decreased, corresponding with the observed amplitude saturation. Abnormal asymmetry ratios (based on values reported in the literature) were noted for four instances of uncorrected amplitude asymmetry at less than maximum muscle contraction levels. Amplitude normalization did not substantially change the number of observed asymmetry ratios. Because cVEMP amplitude did not typically grow proportionally with muscle contraction level, amplitude normalization did not lead to stable cVEMP amplitudes or asymmetry ratios across varying muscle contraction levels. Until we better understand the relationships between muscle contraction level, surface electromyography (EMG) estimates of muscle contraction level, and cVEMP amplitude, the application of normalization methods to correct cVEMP amplitude appears unjustified.

Treatment of Not-Administered Items on Individually Administered Intelligence Tests

In administration of individually administered intelligence tests, items are commonly presented in a sequence of increasing difficulty, and test administration is terminated after a predetermined number of incorrect answers. This practice produces stochastically censored data, a form of nonignorable missing data. By manipulating four factors (i.e., treatment of nonresponses, ability estimation method, test length, and stopping rule), this study investigated how accurately ability parameters are recovered under these conditions. The results suggest that there might be a complex interaction among these manipulated factors with respect to parameter estimation bias. The worst estimates occur when nonadministered items are treated as incorrect. Treating nonadministered items as not presented or fractionally correct appears to produce more accurate ability estimates. Among the ability estimation methods examined in this study, the Expected A Posterior and Maximum A posteriori methods tend to produce less estimation error in the presence of censored data. The differences in missing data treatment methods tend to have greater impact on ability estimate under maximum likelihood estimation than Bayesian methods.

A Bayesian generalized multiple group IRT model with model-fit assessment tools

The multiple group IRT model (MGM) proposed by Bock and Zimowski (1997) provides a useful framework for analyzing item response data from clustered respondents. In the MGM, the selected groups of respondents are of specific interest such that group-specific population distributions need to be defined. The main goal is to explore the potentials of an MCMC estimation procedure and Bayesian model-fit tools for the MGM. We develop a full Gibbs sampling algorithm (FGSA) for estimation as well as a Metropolis-Hastings within Gibss sampling algorithm (MHWGS) in order to use non-conjugate priors. The FGSA is compared with Bilog–MG, which uses marginal maximum likelihood (MML) and marginal maximum a posteriori (MMAP) methods. That is; Bilog–MG provides maximum likelihood (ML) and expected a posteriori (EAP) estimates for both item and population parameters, and maximum a posteriori (MAP) estimates for the latent traits. We conclude that, in general, the results from our approach are slightly better than Bilog–MG. Besides a simultaneous MCMC estimation procedure, model-fit assessment tools are developed. Furthermore, the prior sensitivity is investigated with respect to the parameters of the latent population distributions. It will be shown that the FGSA provides a wide set of model-fit tools. The proposed model assessment tools can evaluate important model assumptions of (1) the item response function (IRF) and (2) the latent trait distributions. The utility of the proposed estimation and model-fit assessment methods will be shown using data from a longitudinal data study concerning first to fourth graders of sampled Brazilian public schools.