Bayesian Theory Research Articles

Prospective comparison of temporal myocardial function in men vs women after anterior ST-elevation myocardial infarction

Abstract Background Compared to men, women have been reported to have increased morbidity and mortality after ST-elevation myocardial infarction (STEMI), but sex differences in cardiac function in the acute and subacute phases of STEMI are incompletely understood. Objective To prospectively compare changes in cardiac function over the acute and subacute phases after anterior STEMI with timely reperfusion in women versus men. Methods The Stunning in Takotsubo versus Acute Myocardial Infarction (STAMI) study prospectively enrolled 94 men and 36 women with anterior STEMI. Echocardiography and blood sampling were performed within 4 hours of admission and at 1, 2, 3, 7, 14 and 30 days after admission. The primary outcome was akinesia recovery, defined as the difference in the per cent akinesia observed at baseline versus follow-up. Secondary outcomes included wall motion score index (WMSI), left ventricular ejection fraction (LVEF) and global longitudinal strain (GLS). Mixed effects linear regression or zero-inflated tobit models with random intercepts were used to model echocardiographic parameters over time. Results Baseline patient characteristics were similar in both groups. The difference between women and men in akinesia recovery at 30 days was 8.4% (95% confidence interval [CI] 1.23-14.99). The covariate-adjusted Bayesian posterior probability that akinesia recovery and WMSI improvement at 30 days are more significant in women than men were 95% and 99%, respectively. Similar but less pronounced trends towards greater improvement in women than men were observed for LVEF and GLS. Conclusions After anterior STEMI with timely reperfusion, cardiac dysfunction recovered to a greater extent in women than in men.

Linking quantum discord with Bayesian game theory

Linking quantum discord with Bayesian game theory

Multiple Maternal Lineages of <i>Strauchbufo raddei</i> (Strauch, 1876) in Mongolia Revealed by Mitochondrial DNA

The Mongolian toad Strauchbufo raddei (Strauch, 1876) is one of widely distributed and dominated amphibian species in eastern Asian, including Mongolia. In this study, we amplified and sequenced a total of 50 samples of S. raddei, from three main regions in its Mongolian distribution range namely, Northern, Eastern, and Gobi regions. Our phylogenetic trees (Bayesian inference; BI and time-calibrated) and network analysis clearly support presence of multiple maternal mitochondrial DNA lineages for S. raddei in Mongolia. As expected, samples from these three regions were clustered separately in BI tree (Bayesian posterior probability (BPP 0.52). In addition, the population specific haplotypes, estimated genetic distances (e.g. uncorrelated p distance; ranged from 1% to 25%) and hierarchical AMOVA suggested relatively strong population genetic structure of S. raddei across Mongolia. Time-calibrated tree and ancestral range analysis showed that the first colonization of S. raddei may have occurred in Northern part of Mongolia approximately 9.63 mya, then dispersed over other parts of the country. Estimated approximate time for crossing event of S. raddei over dry steppe and semi-desert regions in Mongolia was 5.02 – 2.50 mya. Finally, high level of genetic diversity (overall; haplotype diversity, Hd = 0.93; nucleotide diversity, π = 0.011) of S. raddei were observed in Mongolia. Importantly, through this study, we contributed to closing sampling gaps in distribution range of S. raddei in Eastern Asia, which is key to better understanding species history, as well as describing cryptic lineages.

Transferability of real-time EVT safety models: an investigation using autonomous vehicles data

Recent research has shown that data from autonomous vehicles (AVs) enables proactive, real-time road safety management. However, with low AV market penetration, it's crucial to assess the transferability of AV-based safety models to other locations. This study transfers real-time safety models from a data-rich to a data-scarce environment using vehicular conflict data collected by AVs. Multi-site Bayesian hierarchical Extreme Value Theory models are developed in two cities, with model transfer evaluated using informative priors and parameter recalibration. Both approaches produce reliable results, though the transferability index favors the informed prior method, while predictive deviance shows similar performance for both. Model sensitivity to temporal data limitations is assessed, revealing that the recalibration approach is more sensitive to block size, whereas the informed prior method remains stable. A novel method mimicking data limitations shows transferred models perform well with data utilizations above 20%, promoting transferability to mitigate data inadequacy.

A game-based decision-making method for multi-ship collaborative collision avoidance reflecting risk attitudes in open waters

To accurately reflect risk attitudes towards ship intentions in multi-ship encounters, this paper develops a novel two-stage collaborative collision avoidance decision-making (CADM) model by incorporating intention prediction and real-time decision-making. We acquire prior knowledge of risk attitudes by analyzing Automatic Identification System (AIS) data and further estimate the probability distributions of encountering ship's risk attitude using Bayesian reasoning. By treating collision avoidance procedure as a static game with incomplete information, a predictive model for collision avoidance intentions is developed by taking account into risk attitude probabilities. Real-time decisions are then implemented according to different stages, and a collaborative CADM model is established by a game-decision cycle. Finally, a multi-ship encounter scenario is simulated under all combinations of risk attitudes, and the results are compared with those obtained under complete information. The results demonstrate that the proposed model can formulate avoidance actions that meet safety requirements under all combinations of risk attitudes. Further comparison with complete information proves the effectiveness of the risk attitude probability model, which is conducive to improving the decision-making flexibility and reducing complexity. The research findings enhance the collaborative decision-making, contributing to the development of autonomous navigation in open waters.

A comparison of imprecise Bayesianism and Dempster–Shafer theory for automated decisions under ambiguity

Abstract Ambiguity occurs insofar as a reasoner lacks information about the relevant physical probabilities. There are objections to the application of standard Bayesian inductive logic and decision theory in contexts of significant ambiguity. A variety of alternative frameworks for reasoning under ambiguity have been proposed. Two of the most prominent are Imprecise Bayesianism and Dempster–Shafer theory. We compare these inductive logics with respect to the Ambiguity Dilemma, which is a problem that has been raised for Imprecise Bayesianism. We develop an agent-based model comparison that isolates the difference between the two inductive logics in their updating methods. We find that Dempster–Shafer theory does not avoid the Ambiguity Dilemma. We discuss the implications of this result.

The Development and Piloting of an Early Youth-Engagement (EYE) Model to Improve Engagement of Young People in First Episode Psychosis Services: A Mixed Methods Study.

Psychosis is associated with significant health and societal costs. Early intervention in psychosis services (EIP) are highly effective in promoting recovery, yet substantial proportions of young people disengage. The current study aimed to develop and evaluate a novel engagement intervention in EIP services. A qualitative investigation of facilitators and barriers to engagement in 68 first episode psychosis patients, family members and young people, and a Delphi consultation with 27 regional and national youth and psychosis service leads informed the development of the intervention. A mixed-methods feasibility-pilot study then compared engagement outcomes in 298 EIP service users in two cohorts: standard EIP versus standard EIP plus the novel early youth-engagement (EYE) intervention. A qualitative study explored intervention experiences in 22 randomly selected service users, carers and clinicians. A process evaluation explored delivery. Disengagement was 24% in the standard EIP cohort compared to 14.5% in the standard EIP plus EYE intervention cohort. A 95% Bayesian credibility interval revealed a 95% probability that the true reduction in disengagement lay somewhere between 0% and 18%. The number needed to treat was 11, 95% CI [5, 242]. Use of the EYE resources was associated with engagement. Qualitiative feedback supported effects on communication, social network engagement, service user goals, mental health and well-being outcomes. The EYE intervention was designed from a service user, young person and carer perspective. Both qualitative and quantitative data support impacts on engagement. We now need to evaluate effectiveness, cost-effectiveness and implementation in a multi-site randomised controlled trial.

OS09.7.A GBM AGILE PLATFORM TRIAL FOR NEWLY DIAGNOSED AND RECURRENT GBM: RESULTS OF FIRST EXPERIMENTAL ARM, REGORAFENIB

Abstract BACKGROUND GBM AGILE (NCT03970447;https://www.gcaresearch.org/research/gbm-agile) is a phase 3 Bayesian adaptive platform trial that efficiently tests multiple arms against common control, with 6 arms included to date. Primary endpoint is overall survival (OS). Stage 1 experimental arms are adaptively randomized against other arms. Demonstrated efficacy in stage 1 leads to fixed randomization stage 2. Stages 1 and 2 are combined for registration. Control randomization is fixed. Regorafenib, a multikinase-inhibitor, entered into GBM AGILE as the first arm and therefore was equally randomized against control. Regorafenib showed OS benefit in recurrent disease (RD) in randomized phase 2 REGOMA trial. MATERIAL AND METHODS Patient subtypes in GBM AGILE are newly diagnosed unmethylated (NDU), RD, and—not considered for regorafenib—ND methylated (NDM). Arm indications (signatures) are combinations of subtypes. Control is temozolomide (ND) and lomustine (RD). Efficacy is assessed by OS hazard ratio(HR), arm/control. Efficacy is demonstrated when Bayesian probability of benefit (HR< 1.00) ≥ 98% (roughly analogous P-value: 0.02). Futility occurs at any monthly analysis when Bayesian predictive power (PP) is < 25% for all signatures. Follow-up continues for 12 months after arm’s accrual stops. RESULTS When PP for all 3 pre-defined signatures was < 25%, regorafenib’s accrual was stopped for futility. Regorafenib/control sample sizes were 49/51, 127/128, 176/179 for signatures NDU, RD, and both. Respective PPs: 0.138, 0.030, 0.025—none close to 0.25. Respective mean HRs: 1.26, 1.25, 1.23. Probabilities of benefit (HR< 1.00): 0.35, 0.18, 0.17. At final analysis, mean HRs were 1.07, 1.08, 1.08 with final probabilities of benefit (HR< 1.00) equal to 0.421, 0.312, 0.296—none close to 0.98. CONCLUSION GBM AGILE efficiently and compellingly addressed regorafenib’s role in GBM, in RD and NDU. These findings are germane as they fail to confirm the REGOMA results in RD. GBM AGILE continues to efficiently assess other therapies, including utilizing concurrent and previously accrued controls. This abstract was accepted and previously presented at the 2023 SNO Annual Meeting and published in Neuro-Oncology, Volume 25, Issue Supplement_5, November 2023, Pages v97-v98.

An algorithm for belief rule induction with partial ignorance

Belief rules are an extension of fuzzy rules that consider belief degrees. They are widely applied due to their traceability, interpretability, and flexibility. However, current belief rules only consider residual support and global ignorance while ignoring partial ignorance. In this paper, we proposed a novel belief rule-based classification system called partial ignorance belief rule induction algorithm (PIBRIA). The consequent part of belief rules takes into account not only the residual support and global ignorance but also partial ignorance of evidence. The belief degrees in the consequent part of each belief rule collectively form a genuine basic probability assignment (BPA). Based on fuzzy unordered rule induction algorithm (FURIA), we propose the learning algorithm for belief rules with partial ignorance, which helps the novel proposed PRIBIA achieve a balance between accuracy and complexity. The inference method employs the Dempster’s combination rule and Shafer’s discounting operation, where the discounting operation can resolve evidence conflicts in the combination rule. The effectiveness and superiority of PIBRIA in handling classification tasks have been validated by comparing it to some state-of-the-art rule-based models. The results of statistical tests show that PIBRIA outperforms all other methods in terms of classification accuracy. Whereas its computational complexity and model complexity are moderate.

Penalized Bayesian D-Optimal Designs for Regression Models of Continuous Response

We propose extending the use of desirability functions in Bayesian optimal designs for regression models. This technique generates experimental designs with good statistical inference properties according to Bayesian optimal design theory and practical features, as defined by an investigator. These practical features are defined by a penalty function, using an overall desirability function, which is added to a Bayesian $D$-optimal design criterion to penalize impractical experimental designs. This methodology is illustrated by two examples of regression models: quadratic and exponential. Then, we compare designs obtained for different prior distributions of unknown parameters by efficiency calculations and simulation study. Results show that the $D$-efficiencies of the penalized designs relative to the non-penalized Bayesian D-optimal designs are competitive.

Leaf Rust Pathogens on Hypericum pseudohenryi: Describing Melampsora danbaensis sp. nov. and M. hyperici-pseudohenryi sp. nov. from China.

Based on morphological and phylogenetic evidence, two novel species of Melampsora were discovered on Hypericum pseudohenryi in China and have been thoroughly characterized. One of these species, designated as M. danbaensis, exhibits distinct features such as aecia of Uredo-type, typically appearing in gregarious or grouped arrangements, and presenting a shallowly pulvinate structure. Aeciospores exhibit tremendous variations in size, ranging in shape from globose to ellipsoidal and bearing pronounced verrucose texture. Telia resemble crusts one-spore deep, covering nearly the entire abaxial leaf surface, with sessile teliospores reaching sizes of up to 65.8 µm, and exhibiting a clavate to cylindrical shape. Another species, designated as M. hyperici-pseudohenryi, is distinguished by Uredo-type uredinia, which are hypophyllous, scattered or grouped, and interspersed with numerous paraphyses. Its urediniospores tend to be globose, ellipsoidal or obovoid, echinulate, and are accompanied by clavate to capitate paraphyses reaching lengths up to 77.6 µm. Phylogenetically, both species form a novel monophyletic clade within the Melampsora genus, with robust support demonstrated by a high Maximum likelihood bootstrap support (MLBS) value of 100% and a Bayesian posterior probability (BPP) of 1. This study enriches our understanding of the diversity and geographical distribution of Melampsora species that infect Hypericum plants in China.

Cyanobacterial blooms prediction in China’s large hypereutrophic lakes based on MODIS observations and Bayesian theory

Cyanobacterial harmful algal blooms (HABs) pose a significant threat to aquatic ecosystems, water quality, and public health, particularly in large hypereutrophic lakes. Developing accurate short-term prediction models is essential for early warning and effective management of HABs. This study introduces a Bayesian-based model aimed at predicting HABs in three of China’s large hypereutrophic lakes: Lake Taihu, Lake Chaohu, and Lake Hulunhu. By integrating MODIS data from the Terra and Aqua satellites with meteorological data spanning from 2010 to 2018, the model forecasts HABs distributions 1, 4, and 7 days in advance. Validation with meteorological data from 2019 to 2020 showed high accuracy, with 0.83 at the pixel level, 0.74 for zonal predictions, and 0.64 for lake-wide HABs area forecasts. Further evaluation using 2023 weather forecast data yielded similar accuracies of 0.78, 0.57, and 0.62, respectively. In addition to predicting the spatial extent of HABs, the model provides binary HABs maps, outbreak areas, and HABs status within lake zones. This method for building prediction models significantly enhances early warning and management capabilities for HABs, providing a scalable framework that can be adapted to other regions facing similar threats from HABs.

Late acute stress effects on decision-making: The magnified attraction to immediate gains in the iowa gambling task

Previous literature indicates that the later phases of the acute stress response may promote poor decision-making, characterized by riskier choices and a likely inclination towards immediate reward-seeking. However, all studies addressing the effect of this phase have treated decisional capacity as a singular dimension, without analyzing the underlying processes under decision-making. Employing the Value-Plus-Perseveration (VPP) RL model, based on Bayesian logic, this study aims to gain specific insights into how late phase of acute stress impacts the cognitive processes underpinning decision-making in the Iowa Gambling Task (IGT), deciphering whether, as expected, gains are processed in a magnified manner. Seventy-three participants were randomly assigned to two groups, stress (N = 35) and control (N = 38). A virtual version of The Trier Social Stress Test (TSST-VR) was employed as a laboratory stressor. Decision-making was evaluated 35 minutes after the stressor onset, by means of the IGT. Results showed that stressed participants, in comparison to control group, displayed more perseverant and consistent decision-making, enhanced memory, and reinforcement learning capabilities, yet were guided by a greater attraction to decks offering immediate high gains. These results are analyzed with the understanding that in the IGT, short-term decisions focused on instant rewards are seen as counterproductive. This suggests that stress could limit the ability to switch to strategies that are more cautious and offer greater long-term benefits.

Fuzzy-Bayesian Expert System for Suggesting Personalized Training Plans with Exercises and Routines with a Model Driven Architecture (MDA)

In the dynamic world of fitness, the quest for tailor-made exercise plans has never been more critical. Expert systems are stepping up to this challenge, offering a promise of personalized routines for both seasoned athletes and newcomers. In this article, we introduce an ingenious fuzzy-Bayesian expert system, armed with fuzzy and Bayesian logic, that tackles the uncertainties lurking within fitness data. It's a system with a dual focus: for fitness veterans, it conducts a meticulous analysis of their training history, past achievements, and current ambitions. Guided by the nuanced power of fuzzy and Bayesian logic, it makes decisions rooted in probabilities. As for beginners, the system builds a strong foundation, considering your present fitness status and your future aspirations. This forward-thinking approach speaks directly to the increasing demand for adaptable fitness solutions. For seasoned athletes, it paves the way to peak performance and injury prevention. Meanwhile, beginners embark on their fitness journey with gradual and secure steps. The Fuzzy-Bayesian Expert System offers a comprehensive answer that embraces data diversity and individual fitness aspirations in both scenarios. Furthermore, the seamless integration of the UPAFuzzySystem (Montes Rivera et al., 2023) library and Twilio elevates the system's functionality and its connection with users, turning it into a personal fitness enhancement tool. Dive into a world where fitness meets technology for a custom-made future of health and well-being.

Adaptation and validation of an inventory for assessing subjective task value beliefs regarding the decision to pursue postgraduate studies

The desire to pursue postgraduate studies is motivated by several interrelated and multifaceted factors ranging from intrinsic to extrinsic. However, little consensus exists in the literature regarding an instrument that assesses an individual’s motivation for pursuing postgraduate education. In this study, we adapted and validated a pre-existing inventory that evaluates the individuals’ motives for pursuing postgraduate studies using the subjective task value beliefs framework. The study, in particular, focused on assessing the factor structure, construct validity, and reliability of the adapted scale. Study participation invitations were sent to a pool of postgraduate students in two higher education institutions, of which 501 students finally responded to the online questionnaire. The exploratory and confirmatory factor analyses were used to analyse the data to address the research objectives. The results revealed a five-factor structure for the adapted scale with excellent construct validity and reliability indicators. The findings of the research add value to the psychometric literature and also provide a useful instrument for use among instructors, researchers, and university administrators in their line of duty.

Outcomes with revascularisation versus conservative management of participants with 3-vessel coronary artery disease in the ISCHEMIA trial.

Whether revascularisation (REV) improves outcomes in patients with three-vessel coronary artery disease (3V-CAD) is uncertain. Our objective was to evaluate outcomes with REV (percutaneous coronary intervention [PCI] or coronary artery bypass graft surgery [CABG]) versus medical therapy in patients with 3V-CAD. ISCHEMIA participants with 3V-CAD on coronary computed tomography angiography without prior CABG were included. Outcomes following initial invasive management (INV) with REV (PCI or CABG) versus initial conservative management (CON) with medical therapy alone were evaluated. Regression modelling was used to estimate the outcomes if all participants were to undergo prompt REV versus those assigned to CON. Outcomes were cardiovascular (CV) death/myocardial infarction (MI), death, CV death, and quality of life. Bayesian posterior probability for benefit (Pr [benefit]) for 1 percentage point lower 4-year rates with REV versus CON were evaluated. Among 1,236 participants with 3V-CAD (612 INV/624 CON), REV was associated with lower 4-year CV death/MI (adjusted 4-year difference: -4.4, 95% credible interval [CrI] -8.7 to -0.3 percentage points, Pr [benefit]=94.8%) when compared with CON, with similar results for PCI versus CON (-5.8, 95% CrI: -10.8 to -0.5 percentage points, Pr [benefit]=96.4%) and CABG versus CON (-3.7, 95% CrI: -8.8 to 1.5 percentage points, Pr [benefit]=84.7%). Adjusted 4-year REV versus CON differences were as follows: death -1.2 (95% CrI: -4.7 to 2.2) percentage points, CV death -2.3 (95% CrI: -5.5 to 0.8) percentage points, with similar results for PCI and for CABG. The Pr (benefit) for death with REV (PCI or CABG) versus CON was 49-63%. The adjusted 12-month Seattle Angina Questionnaire-7 summary score differences favoured REV: REV versus CON 4.6 (95% CrI: 2.7-6.4) percentage points; PCI versus CON 3.6 (95% CrI: 1.2-5.8) percentage points and CABG versus CON 4.3 (95% CrI: 1.5-6.9) percentage points with high Pr (benefit). In participants with 3V-CAD, REV (either PCI or CABG) was associated with a lower 4-year CV death/MI rate and improved quality of life, with similar results for PCI versus CON and CABG versus CON. The differences in all-cause mortality between REV and CON were small with wide confidence intervals. (ClinicalTrials.gov: NCT01471522).

Deep learning coupled Bayesian inference method for measuring the elastoplastic properties of SS400 steel welds by nanoindentation experiment

Nanoindentation experiment has shown broad application prospects due to its ability to measure the mechanical properties of various materials at multiple scales. In this paper, a deep learning coupled Bayesian inverse approach is proposed for measuring the elastoplastic parameters of SS400 steel welds by nanoindentation experiment. The nanoindentation experiments were performed on the SS400 steel welds, including base metal (BM), weld zone (WZ), and heat affected zone (HAZ), and the experiment load–displacement (P-h) curves were obtained. The hyper-parameters tunable artificial neural network (ANN) was established to correlate elastoplastic parameters with indentation P-h curves. Based on Bayesian inference theory, the posterior density function for estimating the unknown material parameters was established. Transitional Markov chain Monte Carlo was used for sampling from the posterior density function, and the elastoplastic properties in different regions of SS400 steel welds were identified. The advantage of the established measuring method is that the hyper-parameters optimized ANN model can provide the very accurate forward relationship between material properties and indentation P-h curves. Besides, the inverse Bayesian framework can quantify the potential uncertainty of the identified elastoplastic parameters. The measured elastoplastic properties of the base metal of SS400 steel show good agreement with tensile experiment data, of which the maximum measuring error is less than 12%. The measured elastoplastic properties in WZ and HAZ are also proved to be effective. The uncertainty of the identified elastoplastic parameters of SS400 steel welds can be quantified by posterior marginal distribution, using Mean and Variance values. The results proved that the proposed inverse measuring method is reliable and effective.

Bayesian statistical concepts with examples from rodent toxicology studies.

The theory and practice of statistics comprises two main schools of thought: frequentist statistics and Bayesian statistics. Frequentist methods are most commonly used to analyze animal-based laboratory data, while Bayesian statistical methods have been implemented less widely and may be relatively unfamiliar to practitioners in experimental science. This paper provides a high-level overview of Bayesian statistics and how they compare with frequentist methods. Using examples in rodent toxicity research, we argue that Bayesian methods have much to offer laboratory animal researchers. We advocate for increased attention to and adoption of Bayesian methods in laboratory animal research. Bayesian statistical theory, methods, software, and education have advanced significantly in the last 30 years, making these tools more accessible than ever.

Customizing Bayesian multivariate generalizability theory to mixed-format tests.

Mixed-format tests, which typically include dichotomous items and polytomously scored tasks, are employed to assess a wider range of knowledge and skills. Recent behavioral and educational studies have highlighted their practical importance and methodological developments, particularly within the context of multivariate generalizability theory. However, the diverse response types and complex designs of these tests pose significant analytical challenges when modeling data simultaneously. Current methods often struggle to yield reliable results, either due to the inappropriate treatment of different types of response data separately or the imposition of identical covariates across various response types. Moreover, there are few software packages or programs that offer customized solutions for modeling mixed-format tests, addressing these limitations. This tutorial provides a detailed example of using a Bayesian approach to model data collected from a mixed-format test, comprising multiple-choice questions and free-response tasks. The modeling was conducted using the Stan software within the R programming system, with Stan codes tailored to the structure of the test design, following the principles of multivariate generalizability theory. By further examining the effects of prior distributions in this example, this study demonstrates how the adaptability of Bayesian models to diverse test formats, coupled with their potential for nuanced analysis, can significantly advance the field of psychometric modeling.

Interpretable large-scale belief rule base for complex industrial systems modeling with expert knowledge and limited data

Complex system modeling technology is a hot topic. Nowadays, many complex industrial systems present three characteristics: multiple input indicators, limited data and interpretability requirements. With good interpretability, belief rule base (BRB) serves as an efficient tool for modeling complex systems. However, as the number of input indicators of industrial systems increases, BRB suffers from the combinatorial explosion problem, which makes it hard to generate large-scale BRB and optimize it while maintaining its interpretability. For this purpose, an interpretable large-scale BRB is proposed for complex systems with limited data, where expert knowledge can be utilized effectively. First, a framework for generating an initial large-scale BRB using expert knowledge and limited data is developed, including the determination of attribute weight, basic belief degree and rule weight. Afterwards, a new parameter optimization model is designed to reduce the burden of parameter optimization and maintain the interpretability of BRB, where the Adaptive Moment Estimation (Adam) algorithm is adopted to further improve the efficiency of large-scale parameter optimization. Finally, a health assessment case of an inertial navigation system (INS) verifies the proposed method.