Comparing Bayesian and Frequentist Models of Language Variation

There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments.

Understanding an opponent's wants is crucial for maximizing the outcomes of a multi-issue negotiation. To do this, automated systems must build an from information conveyed during a negotiation. Bayesian and frequentist models are the most commonly used. Bayesian models have a principled way to incorporate prior knowledge about an opponent's preferences. However, frequentist models have outperformed Bayesian approaches in practice, dominating the yearly agent-verses-agent negotiation competitions. With growing interest in agents that negotiate with people, this presumed dominance needs to be revisited. Human opponents convey far less information than automated agents, and people often share similar preferences (e.g., in a salary negotiation, most people care the most about salary). Thus, the theoretical advantage of Bayesian approaches may translate into practice for agent-versus-human negotiation. In this work, we compare the performance of Bayesian models against a leading frequentist approach in an agent-versus-human multi-issue salary negotiation. Although we show that frequentist opponent models outperform Bayesian models when using a uniform prior, Bayesian approaches excel when using two common priors. The best performance is achieved with an empirically-derived prior (i.e., biasing the model space using the distribution of preferences found in past human negotiators). Yet, strong performance is also observed when using a fixed-pie bias, the prior used by most human negotiators. We discuss the implication of these findings for research on human-agent negotiation.

BackgroundRandom effects modelling is routinely used in clustered data, but for prediction models, random effects are commonly substituted with the mean zero after model development. In this study, we proposed a novel approach of including prior knowledge through the random effects distribution and investigated to what extent this could improve the predictive performance.MethodsData were simulated on the basis of a random effects logistic regression model. Five prediction models were specified: a frequentist model that set the random effects to zero for all new clusters, a Bayesian model with weakly informative priors for the random effects of new clusters, Bayesian models with expert opinion incorporated into low informative, medium informative and highly informative priors for the random effects. Expert opinion at the cluster level was elicited in the form of a truncated area of the random effects distribution. The predictive performance of the five models was assessed. In addition, impact of suboptimal expert opinion that deviated from the true quantity as well as including expert opinion by means of a categorical variable in the frequentist approach were explored. The five models were further investigated in various sensitivity analyses.ResultsThe Bayesian prediction model using weakly informative priors for the random effects showed similar results to the frequentist model. Bayesian prediction models using expert opinion as informative priors showed smaller Brier scores, better overall discrimination and calibration, as well as better within cluster calibration. Results also indicated that incorporation of more precise expert opinion led to better predictions. Predictive performance from the frequentist models with expert opinion incorporated as categorical variable showed similar patterns as the Bayesian models with informative priors. When suboptimal expert opinion was used as prior information, results indicated that prediction still improved in certain settings.ConclusionsThe prediction models that incorporated cluster level information showed better performance than the models that did not. The Bayesian prediction models we proposed, with cluster specific expert opinion incorporated as priors for the random effects showed better predictive ability in new data, compared to the frequentist method that replaced random effects with zero after model development.

Bayesian methods are becoming increasingly used in applied psychological research. Previous researchers have thoroughly written about much of the details already, including the philosophy underlying Bayesian methods, computational issues associated with Bayesian model estimation, Bayesian model development and summary, and the role of Bayesian methods in the so-called replication crisis. In this paper, we seek to provide case studies comparing the use of frequentist methods to the use of Bayesian methods in applied psychological research. These case studies are intended to 'illustrate by example' the ways that Bayesian modelling differs from frequentist modelling and the differing conclusions that one may arrive at using the two methods. The intended audience is applied psychological researchers who have been trained in the traditional frequentist framework, who are familiar with mixed-effects models and who are curious about how statistical results might look in a Bayesian context. Along with our case studies, we provide general opinions and guidance on the use of Bayesian methods in applied psychological research.

While many studies have previously conducted direct comparisons between results obtained from frequentist and Bayesian models, our research introduces a novel perspective by examining these models in the context of a small dataset comprising phonetic data. Specifically, we employed mixed-effects models and Bayesian regression models to explore differences between monolingual and bilingual populations in the acoustic values of produced vowels. The former models are widely utilized in linguistic and phonetic research, whereas the latter offer promising approaches for achieving greater precision in data analysis. Our findings revealed that Bayesian hypothesis testing identified more differences compared to the post hoc test. Specifically, the post hoc test identified differences solely in the F1 of the vowel /a/, whereas the evidence ratios provided strong evidence of differences across multiple vowels and all measured parameters, including F1, F2, F3, and duration. These results may call into question the findings of a large number of studies incorporating frequentist models. In conclusion, our study supports the assertion that different statistical frameworks can lead to divergent interpretations, especially in cases with small sample sizes and complex data structures like those commonly found in phonetics. This can open a discussion about the need for careful methodological considerations and the potential benefits of Bayesian approaches in such situations.

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates were significant in some frequentist models, but in the Bayesian model their credible intervals contained zero; such discrepancies were observed in multiple datasets. Variance components from the Bayesian model reflected substantial autocorrelation, consistent with the frequentist models, except for the auto-regressive moving average model. Plots of means from the Bayesian model showed good fit to the observed data. The proposed Bayesian model provides an approach for modeling non-stationary autocorrelation in a hierarchical modeling framework to estimate task means, standard deviations, quantiles, and parameter estimates for covariates that are less biased and have better performance characteristics than some of the contemporary methods.

Associations between illness burden and care experiences among Medicare beneficiaries before or after a cancer diagnosis

Combining the advantages of local mean decomposition and variational Bayesian hidden Markov model, a blind source separation method for mechanical faults based on local mean decomposition and variational Bayesian hidden Markov model is proposed. In the proposed method, the non-stationary signals are decomposed into a series of production functions by the local mean decomposition, then the obtained production functions and the original observed signals are used to construct new observation signals, therefore the underdetermined blind source separation problem is transformed into the overdetermined blind source separation problem. Finally, the source signals are estimated by the variational Bayesian hidden Markov model method. The proposed method has been successfully applied to the blind separation of bearing faults, and the experiment results verify the effectiveness of the proposed method. The obtained outcome in this paper provides an effective separation method for mechanical fault diagnosis.

Knowledge-informed Variational Bayesian Gaussian mixture regression model for predicting mixed oil length

PurposeThe COVID-19 pandemic has harmed the socioeconomic well-being of millions of low-income people across the globe. The study is to examine the financial strategies adopted by Char dwellers in Bangladesh to deal with the global pandemic’s shock.Design/methodology/approachA quantitative survey was conducted for data collection, and respondents were chosen through a multistage sampling technique. Binary logistic model, probit model and multinomial logit models and Bayesian multinomial logistic models have been conducted to achieve the objectives. The objective of incorporating Bayesian models is to evaluate the probabilistic certainty and robustness of estimates in the presence of uncertainty and sparse data.FindingsFindings from the binary logit model, probit model, Bayesian logit model and Bayesian probit model show that income, income instability, number of dependents in a family, shrinking work opportunities, financial contributions to family, savings and a comparison of household expenses to pre-pandemic expenses influence the households’ daily financial management strategies. The multinomial logit model and Bayesian multinomial logit model results, on the other hand, show that education, savings, employment status and major sources of expenditure influenced the choice of financial strategies mostly.Practical implicationsThis research offers policy recommendations that might alleviate the financial challenges of extremely poor people posed by global crises such as the COVID-19 pandemic. Policymakers can use the results of this study to improve social safety nets, diversify livelihoods and provide char dwellers with banking services. Community leaders and organizations can learn from char dwellers’ coping strategies to improve financial hardship. By sharing lessons learned and best practices during the COVID-19 epidemic, stakeholders may better help vulnerable communities like char dwellers.Originality/valueTo the best of the authors’ knowledge, this is the first study, in Bangladesh to investigate how financially disadvantaged people living in the char region have dealt with the COVID-19 pandemic and thus this paper presents new background information on strategies adopted by poor to cope up with COVID-19 pandemic using both frequentist and Bayesian modeling approaches. A methodological breakthrough, the incorporation of Bayesian analysis strengthens and probabilistically illuminates studies of socio-economic crises. This research clarified about vulnerable groups’ crisis response, financial situations and adaptive behaviors.

Income inequality, which refers to the uneven distribution of income in a population, has been linked to many societal problems, including crime. Although environmental criminology theories, such as rational choice theory, suggest a positive association between income inequality and crime, previous empirical studies have reported divergent results based on different crime types, statistical models, and spatial units of analysis. This study employs non-spatial and spatial regression models using frequentist and Bayesian modelling frameworks to explore the impacts of within-area and across-area income inequality on five types of major crimes in the City of Toronto at the census tract and dissemination area scales. The use of spatial regression models improves the model fit in both frequentist and Bayesian frameworks. The Bayesian shared component model, which accounts for the interactions between different types of crimes, further enhances model performance. Results obtained from the best-fitting frequentist and Bayesian models are inconsistent but do not conflict in terms of the relationship between crime and income inequality, where within-area income inequality generally increases major crime rates, while across-area income inequality has varying effects dependent on crime type and spatial scale. The discrepancies between spatial scales are a manifestation of the modifiable areal unit problem (MAUP).

Wireless signals are commonly subject to diverse and complex noise interference. The typical assumption of Gaussian white noise often oversimplifies the noise, resulting in reduced accuracy in estimating the direction of arrival (DOA), especially in complex scenarios. To tackle this issue, this paper introduces a new Bayesian model for off‐grid DOA estimation. This model utilizes Gaussian mixture model (GMM)‐based Dirichlet processes (DP) to characterize noise, allowing adaptive adjustments in the number of Gaussian mixture models. Leveraging the factor graph representation of the Bayesian model, a low‐complexity mixed messaging passing algorithm, employing generalized approximate message passing (GAMP) and mean field (MF), is proposed. Simulation results validate the efficacy of the proposed algorithm.

The rapid depletion of fossil-based energy supplies, along with the growing reliance on renewable resources, has placed supreme importance on the predictability of renewables. Research focusing on wind park power modelling has mainly been concerned with point estimators, while most probabilistic studies have been reserved for forecasting. In this paper, a few different approaches to estimate probability distributions for individual turbine powers in a real off-shore wind farm were studied. Two variational Bayesian inference models were used, one employing a multilayered perceptron and another a graph neural network (GNN) architecture. Furthermore, generative adversarial networks (GAN) have recently been proposed as Bayesian models and was here investigated as a novel area of research. The results showed that the two Bayesian models outperformed the GAN model with regards to mean absolute errors (MAE), with the GNN architecture yielding the best results. The GAN on the other hand, seemed potentially better at generating diverse distributions. Standard deviations of the predicted distributions were found to have a positive correlation with MAEs, indicating that the models could correctly provide estimates on the confidence associated with particular predictions.

Recent advances in sediment fingerprinting research have seen Bayesian mixing models being increasingly employed as an effective method to coherently translate component uncertainties into source apportionment results. Here, we advance earlier work by presenting an extended Bayesian mixing model capable of providing a full Bayes treatment of geochemical uncertainties. The performance of the extended full Bayes model was assessed against the equivalent empirical Bayes model and traditional frequentist optimisation. The performance of models coded in different Bayesian software (JAGS and Stan) was also evaluated, alongside an assessment of model sensitivity to reduced source representativeness and nonconservative fingerprint behaviour. Results revealed comparable accuracy and precision for the full and empirical Bayes models across both synthetic and real sediment geochemistry datasets, demonstrating that the empirical treatment of source data here represents a close approximation of the full Bayes treatment. Contrasts in the performance of models coded in JAGS and Stan revealed that the choice of software employed can impact significantly upon source apportionment results. Bayesian models coded in Stan were the least sensitive to both reduced source representativeness and nonconservative fingerprint behaviour, indicating Stan as the preferred software for future Bayesian sediment fingerprinting studies. Whilst the frequentist optimisation generally yielded comparable accuracy to the Bayesian models, uncertainties around apportionment estimates were substantially greater and the frequentist model was less effective at dealing with nonconservative behaviour. Overall, the effective performance of the extended full Bayes mixing model coded in Stan represents a notable advancement in source apportionment modelling relative to previous approaches. Both the mixing model and the software comparisons presented here should provide useful guidelines for future sediment fingerprinting studies.

Network meta-analysis (NMA) is an increasingly popular statistical method of synthesising evidence to assess the comparative benefits and harms of multiple treatments in a single analysis. Several automated software packages...