Bayesian Ideas Research Articles

Metacognition in the listening brain.

How do you know you have heard right? Metacognition, the ability to assess and monitor one's own cognitive state, is key to understanding human communication in complex environments. However, the foundational role of metacognition in hearing and communication is only beginning to be explored, and the neuroscience behind it is an emerging field: how does confidence express in neural dynamics of the listening brain? What is known about auditory metaperceptual alterations as a hallmark phenomenon in psychosis, dementia, or hearing loss? Building on Bayesian ideas of auditory perception and auditory neuroscience, 'meta-listening' offers a framework for more comprehensive research into how metacognition in humans and non-humans shapes the listening brain.

Bayesian encoding and decoding as distinct perspectives on neural coding.

The Bayesian brain hypothesis is one of the most influential ideas in neuroscience. However, unstated differences in how Bayesian ideas are operationalized make it difficult to draw general conclusions about how Bayesian computations map onto neural circuits. Here, we identify one such unstated difference: some theories ask how neural circuits could recover information about the world from sensory neural activity (Bayesian decoding), whereas others ask how neural circuits could implement inference in an internal model (Bayesian encoding). These two approaches require profoundly different assumptions and lead to different interpretations of empirical data. We contrast them in terms of motivations, empirical support and relationship to neural data. We also use a simple model to argue that encoding and decoding models are complementary rather than competing. Appreciating the distinction between Bayesian encoding and Bayesian decoding will help to organize future work and enable stronger empirical tests about the nature of inference in the brain.

Short-term interval prediction of PV power based on quantile regression-stacking model and tree-structured parzen estimator optimization algorithm

In recent years, the photovoltaic (PV) industry has grown rapidly and the scale of grid-connected PV continues to increase. The random and fluctuating nature of PV power output is beginning to threaten the safe and stable operation of the power system. PV power interval forecasting can provide more comprehensive information to power system decision makers and help to achieve risk control and risk decision. PV power interval forecasting is of great importance to power systems. Therefore, in this study, a Quantile Regression-Stacking (QR-Stacking) model is proposed to implement PV power interval prediction. This integrated model uses three models, extreme gradient boosting (Xgboost), light gradient boosting machine (LightGBM) and categorical boosting (CatBoost), as the base learners and Quantile Regression-Long and Short Term Memory (QR-LSTM) model as the meta-learner. It is worth noting that in order to determine the hyperparameters of the three base learners and one meta-learner, the optimal hyperparameters of the model are searched using a Tree-structured Parzen Estimator (TPE) optimization algorithm based on Bayesian ideas. Meanwhile, the correlation coefficient is applied to determine the input characteristics of the model. Finally, the validity of the proposed model is verified using the actual data of a PV plant in China.

Bayesian Ideas in Survey Sampling: The Legacy of Basu

Survey sampling and, more generally, Official Statistics are experiencing an important renovation time. On one hand, there is the need to exploit the huge information potentiality that the digital revolution made available in terms of data. On the other hand, this process occurred simultaneously with a progressive deterioration of the quality of classical sample surveys, due to a decreasing willingness to participate and an increasing rate of missing responses. The switch from survey-based inference to a hybrid system involving register-based information has made more stringent the debate and the possible resolution of the design-based versus model-based approaches controversy. In this new framework, the use of statistical models seems unavoidable and it is today a relevant part of the official statistician toolkit. Models are important in several different contexts, from Small area estimation to non sampling error adjustment, but they are also crucial for correcting bias due to over and undercoverage of administrative data, in order to prevent potential selection bias, and to deal with different definitions and/or errors in the measurement process of the administrative sources. The progressive shift from a design-based to a model-based approach in terms of super-population is a matter of fact in the practice of the National Statistical Institutes. However, the introduction of Bayesian ideas in official statistics still encounters difficulties and resistance. In this work, we attempt a non-systematic review of the Bayesian development in this area and try to highlight the extra benefit that a Bayesian approach might provide. Our general conclusion is that, while the general picture is today clear and most of the basic topics of survey sampling can be easily rephrased and tackled from a Bayesian perspective, much work is still necessary for the availability of a ready-to-use platform of Bayesian survey sampling in the presence of complex sampling design, non-ignorable missing data patterns, and large datasets.

A Massage Area Positioning Algorithm for Intelligent Massage System.

A growing number of studies have been conducted over the past few years on the positioning of daily massage robots. However, most methods used for research have low interactivity, and a systematic method should be designed for accurate and intelligent positioning, thus compromising usability and user experience. In this study, a massage positioning algorithm with online learning capabilities is presented. The algorithm has the following main innovations: (1) autonomous massage localization can be achieved by gaining insights into natural human-machine interaction behavior and (2) online learning of user massage habits can be achieved by integrating recursive Bayesian ideas. As revealed by the experimental results, combining natural human-computer interaction and online learning with massage positioning is capable of helping people get rid of positioning aids, reducing their psychological and cognitive load, and achieving a more desirable positioning effect. Furthermore, the results of the analysis of user evaluations further verify the effectiveness of the algorithm.

Sampling properties of the Bayesian posterior mean with an application to WALS estimation

Many statistical and econometric learning methods rely on Bayesian ideas. When applied in a frequentist setting, their precision is often assessed using the posterior variance. This is permissible asymptotically, but not necessarily in finite samples. We explore this issue focusing on weighted-average least squares (WALS), a Bayesian-frequentist ‘fusion’. Exploiting the sampling properties of the posterior mean in the normal location model, we derive estimators of the finite-sample bias and variance of WALS. We study the performance of the proposed estimators in an empirical application and a closely related Monte Carlo experiment which analyze the impact of legalized abortion on crime.

Why Bayesian Ideas Should Be Introduced in the Statistics Curricula and How to Do So

While computing has become an important part of the statistics field, course offerings are still influenced by a legacy of mathematically centric thinking. Due to this legacy, Bayesian ideas are not required for undergraduate degrees and have largely been taught at the graduate level; however, with recent advances in software and emphasis on computational thinking, Bayesian ideas are more accessible. Statistics curricula need to continue to evolve and students at all levels should be taught Bayesian thinking. This article advocates for adding Bayesian ideas for three groups of students: intro-statistics students, undergraduate statistics majors, and graduate student scientists; and furthermore, provides guidance and materials for creating Bayesian-themed courses for these audiences. Supplementary files for this article are available on line.

Sampling Properties of the Bayesian Posterior Mean With an Application to WALS Estimation

Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this paper we explore this issue by first considering the frequentist properties (bias and variance) of the posterior mean in the important case of the normal location model, which consists of a single observation on a univariate Gaussian distribution with unknown mean and known variance. Based on these results, we derive new estimators of the frequentist bias and variance of the WALS estimator in finite samples. We then study the finite-sample performance of the proposed estimators by a Monte Carlo experiment with design derived from a real data application about the effect of abortion on crime rates.

A method for robotic grasping based on improved Gaussian mixture model.

The present research envisages a method for the robotic grasping based on the improved Gaussian mixture model. The improved Gaussian mixture model is a method proposed by incorporating Bayesian ideas into the Gaussian model. It will use the Gaussian model to perform grasping training in a certain area which we called trained area. The improved Gaussian models utilized the trained Gaussian models as prior models. The proposed method improved the cumulative updates and the evaluation results of the improved models to make robots more adaptable to grasp in the untrained areas. The self-taught learning ability of the robot about grasping was semi-supervised. Firstly, the observable variables of objects were determined by a camera. Then, we dragged the robot to grasp object. The relationship between the variables and robot's joint angles were mapped. We obtained new samples in the close untrained area to improve the Gaussian model. With these new observable variables, the robot grasped it successfully. Finally, the effectiveness of the method was verified by experiments and comparative tests on grasping of real objects and grasping simulation of the improved Gaussian models through the virtual robot experimentation platform.

Bayesian Two-Stage Adaptive Design in Bioequivalence.

Bioequivalence (BE) studies are an integral component of new drug development process, and play an important role in approval and marketing of generic drug products. However, existing design and evaluation methods are basically under the framework of frequentist theory, while few implements Bayesian ideas. Based on the bioequivalence predictive probability model and sample re-estimation strategy, we propose a new Bayesian two-stage adaptive design and explore its application in bioequivalence testing. The new design differs from existing two-stage design (such as Potvin's method B, C) in the following aspects. First, it not only incorporates historical information and expert information, but further combines experimental data flexibly to aid decision-making. Secondly, its sample re-estimation strategy is based on the ratio of the information in interim analysis to total information, which is simpler in calculation than the Potvin's method. Simulation results manifested that the two-stage design can be combined with various stop boundary functions, and the results are different. Moreover, the proposed method saves sample size compared to the Potvin's method under the conditions that type I error rate is below 0.05 and statistical power reaches 80 %.

Rejoinder: Probabilistic Integration: A Role in Statistical Computation?

This article is the rejoinder for the paper “Probabilistic Integration: A Role in Statistical Computation?” (Statist. Sci. 34 (2019) 1–22). We would first like to thank the reviewers and many of our colleagues who helped shape this paper, the Editor for selecting our paper for discussion, and of course all of the discussants for their thoughtful, insightful and constructive comments. In this rejoinder, we respond to some of the points raised by the discussants and comment further on the fundamental questions underlying the paper: (i) Should Bayesian ideas be used in numerical analysis? and (ii) If so, what role should such approaches have in statistical computation?

Comparison and Assessment of Epidemic Models

Model criticism is a growing focus of research in stochastic epidemic modelling, following the successful addressing of model fitting and parameter estimation via powerful computationally intensive statistical methods in recent decades. In this paper, we consider a variety of stochastic representations of epidemic outbreaks, with emphasis on individual-based continuous-time models, and review the range of model comparison and assessment approaches currently applied. We highlight some of the factors that can serve to impede checking and criticism of epidemic models such as lack of replication, partial observation of processes, lack of prior knowledge on parameters in competing models, the nonnested nature of models to be compared, and computational challenges. Based on a wide selection of approaches as reported in the literature, we argue that assessment and comparison of stochastic epidemic models is complex and often, by necessity, idiosyncratic to specific applications. We particularly advocate following the advice of Box [J. Amer. Statist. Assoc. 71 (1976) 791–799] to be selective regarding the model inadequacies for which one tests and, moreover, to be open to the blending of classical and Bayesian ideas in epidemic model criticism, rather than adhering to a single philosophy.

Near-Optimal Regret Bounds for Thompson Sampling

Thompson Sampling (TS) is one of the oldest heuristics for multiarmed bandit problems. It is a randomized algorithm based on Bayesian ideas and has recently generated significant interest after several studies demonstrated that it has favorable empirical performance compared to the state-of-the-art methods. In this article, a novel and almost tight martingale-based regret analysis for Thompson Sampling is presented. Our technique simultaneously yields both problem-dependent and problem-independent bounds: (1) the first near-optimal problem-independent bound of O (√ NT ln T ) on the expected regret and (2) the optimal problem-dependent bound of (1 + ϵ)Σ i ln T / d (μ i ,μ 1 ) + O ( N /ϵ 2 ) on the expected regret (this bound was first proven by Kaufmann et al. (2012b)). Our technique is conceptually simple and easily extends to distributions other than the Beta distribution used in the original TS algorithm. For the version of TS that uses Gaussian priors, we prove a problem-independent bound of O (√ NT ln N ) on the expected regret and show the optimality of this bound by providing a matching lower bound. This is the first lower bound on the performance of a natural version of Thompson Sampling that is away from the general lower bound of Ω (√ NT ) for the multiarmed bandit problem.

Bayesian data analysis for newcomers.

This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.

Bayesian Information for Sensors

An engineering company manufacturing high‐precision sensors had accumulated huge historical databases of information on a type of sensors, which had been tested. The aim of the company was not to use this historical data to improve estimation of future individual sensor parameters, but rather to use it to reduce the number of measurements needed per sensor, guaranteeing a required level of accuracy. In the paper, we show how this can be performed, using Bayesian ideas, and introduce the novel theory for linear regression models, which determines how the reduction in individual sensor measurements can be achieved.Specifically, for estimating parameters of closely related sensors, an estimate can be thought of as comprising a global component, that is, the mean of all the sensors, and a local component, which is a shift from the mean. The historical data can, in a Bayesian framework, provide the global component and hence all that is needed from an individual sensor is the local component. In non‐Bayesian estimation methods, both components are required, and hence, many measurements are needed. On the other hand, with Bayesian methods, only the local fit is needed, and hence, fewer measurements per sensor are required. We provide the supporting theory and demonstrate on a real‐life application with real data. Copyright © 2014 John Wiley & Sons, Ltd.

Protocol for evaluation of the cost-effectiveness of ePrescribing systems and candidate prototype for other related health information technologies.

BackgroundThis protocol concerns the assessment of cost-effectiveness of hospital health information technology (HIT) in four hospitals. Two of these hospitals are acquiring ePrescribing systems incorporating extensive decision support, while the other two will implement systems incorporating more basic clinical algorithms. Implementation of an ePrescribing system will have diffuse effects over myriad clinical processes, so the protocol has to deal with a large amount of information collected at various ‘levels’ across the system.Methods/DesignThe method we propose is use of Bayesian ideas as a philosophical guide.Assessment of cost-effectiveness requires a number of parameters in order to measure incremental cost utility or benefit – the effectiveness of the intervention in reducing frequency of preventable adverse events; utilities for these adverse events; costs of HIT systems; and cost consequences of adverse events averted. There is no single end-point that adequately and unproblematically captures the effectiveness of the intervention; we therefore plan to observe changes in error rates and adverse events in four error categories (death, permanent disability, moderate disability, minimal effect). For each category we will elicit and pool subjective probability densities from experts for reductions in adverse events, resulting from deployment of the intervention in a hospital with extensive decision support. The experts will have been briefed with quantitative and qualitative data from the study and external data sources prior to elicitation. Following this, there will be a process of deliberative dialogues so that experts can “re-calibrate” their subjective probability estimates. The consolidated densities assembled from the repeat elicitation exercise will then be used to populate a health economic model, along with salient utilities. The credible limits from these densities can define thresholds for sensitivity analyses.DiscussionThe protocol we present here was designed for evaluation of ePrescribing systems. However, the methodology we propose could be used whenever research cannot provide a direct and unbiased measure of comparative effectiveness.

New tools for evaluating LQAS survey designs

Lot Quality Assurance Sampling (LQAS) surveys have become increasingly popular in global health care applications. Incorporating Bayesian ideas into LQAS survey design, such as using reasonable prior beliefs about the distribution of an indicator, can improve the selection of design parameters and decision rules. In this paper, a joint frequentist and Bayesian framework is proposed for evaluating LQAS classification accuracy and informing survey design parameters. Simple software tools are provided for calculating the positive and negative predictive value of a design with respect to an underlying coverage distribution and the selected design parameters. These tools are illustrated using a data example from two consecutive LQAS surveys measuring Oral Rehydration Solution (ORS) preparation. Using the survey tools, the dependence of classification accuracy on benchmark selection and the width of the ‘grey region’ are clarified in the context of ORS preparation across seven supervision areas. Following the completion of an LQAS survey, estimation of the distribution of coverage across areas facilitates quantifying classification accuracy and can help guide intervention decisions.

A study of TODIM in a intuitionistic fuzzy and random environment

Nowadays the process of decision making may be very complex. Many methods to support Multi-Criteria Decision Making (MCDM) have been proposed. Recently, the TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) method, which is based on the prospect theory, has received more attention. In this paper we generalize the Fuzzy-TODIM method to deal with intuitionistic fuzzy information and to be capable to consider underlying random vectors that affects the performance of the alternatives. The method makes use of some Bayesian ideas to provide an overall ranking of the alternatives. This work considers information represented by intuitionistic fuzzy number and intuitionistic fuzzy sets (IFS). Also, a new formula of distance between IFS and a new score function to compare IFS are introduced. Examples are discussed and compared with other works, showing the feasibility of the proposed method.

Bayesian Methods for Evidence Evaluation

“First they ignore you, then they laugh at you, then they fight you, then you win,” a saying reportedly misattributed to Mahatma Ghandi,1 might apply to the use of Bayesian statistics in medical research. The idea that Bayesian approaches might be used to “affirm” findings derived from conventional methods, and thereby be regarded as more authoritative, is a dramatic turnabout from an era not very long ago when those embracing Bayesian ideas were considered barbarians at the gate. I remember my own initiation into the Bayesian fold, reading with a mixture of astonishment and subversive pleasure one of George Diamond’s early pieces taking aim at conventional interpretations of large cardiovascular trials of the early 1980s.2 It is gratifying to see that the Bayesian approach, which saw negligible application in biomedical research in the 1980s and began to get traction in the 1990s, is now not just a respectable alternative to standard methods, but sometimes might be regarded as preferable. That said, it is premature to declare a win, and the statistical lingua franca of biomedical research is still firmly frequentist, with P -values, confidence intervals, and type I and II errors dominating the journal landscape. It is helpful to use the thoughtful and thorough Bayesian exercise of Bittl et al3 to reflect on what Bayesian approaches give us, and what they do not. Many introductions to this approach can be found in the literature, and those basics will not be repeated here.4–6 But it is useful to examine the philosophical foundations of Bayesianism, which have their roots not so much in the Bayes theorem, from which the approach gets its name, but in its definition of probability, which Bittl et al allude to. Uncertainty can be roughly divided into 2 types: stochastic and epistemic. …

Comment: Bayesian Ideas Reemerged in the 1950s

Gelman and Robert (2013) in their fascinating article looked backward with modern eyes to a brief passage in William Feller's classic book on probability (Feller 1950) and used it as a launching pa...