Bayesian Decision Research Articles

Incorporating costs and benefits to the evaluation of uncertain research results: Applications to cancer research funding

Abstract Correctness is a key aspiration of the scientific process, yet recent studies suggest that many high-profile findings may be difficult to replicate or require considerable evidence for verification. Proposals to fix these issues typically ask for tighter statistical controls (e.g., stricter p-value thresholds or higher statistical power). However, these approaches often overlook the importance of contemplating research outcomes’ potential costs and benefits. Here, we develop a framework grounded in Bayesian decision theory that seamlessly integrates cost-benefit analysis into evaluating research programs with potentially uncertain results. We derive minimally acceptable pre-study odds and positive predictive values for cost and benefit levels. We show that tolerance to inaccurate results changes dramatically due to uncertainties posed by research. We also show that reducing uncertainties (e.g., by recruiting more subjects) may have limited effects on the expected benefit of continuing specific research programs. We apply our framework to several types of cancer research and their funding. Our analysis shows that highly exploratory research designs are easily justifiable due to their potential benefits, even when probabilistic models suggest otherwise. We discuss how the cost and benefit of research could and should always be part of the toolkit used by scientists, institutions, or funding agencies.

Probability Updating in the Classical and the Quantum Model

Imagine a Bayesian decision agent who is keen to invest only in technologies or businesses that are conductive to achieving a sustainable economic future. Being initially keen to invest in a certain technology, subsequently two pieces of new information are received that both individually reduce the agent’s inclination to make that investment. In such a situation, it would be natural to assume that the simultaneous consideration of both pieces of information should further reduce the agent’s initial enthusiasm; after all the Bayesian method has been called “ nothing but common sense reduced to calculation.” Somewhat surprisingly, making general statements like this about the double conditional probability requires substantial additional assumptions in classical Bayesian probability theory. We investigate four schemes of assumptions that allow ‘reasonable’ conclusions about the double conditional probability. We compare this with two schemes for the quantum probability model where the double conditional results from sequential updating through projections.

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.

Bayesian Sequential Learning and Decision Making in Bike‐Sharing Systems

Bayesian Sequential Learning and Decision Making in Bike‐Sharing Systems

A UUV Cluster Route-Planning Method for Dynamic Target Search

Aiming to address the problem of regional dynamic target search under weak communication conditions, this paper proposes a UUV cluster search method based on cumulative probability optimization. First, by estimating the probability distribution of the initial target location, an initial probability map is established. Then, based on the Bayesian model and Markov decision model, the target probability distribution is periodically updated, and based on the cumulative detection probability optimal principle of the UUV cluster, the UUV cluster is guided to search the region with high detection probability preferentially. Finally, we implement the simulation experiment and compare with the random search method. The results verify that the proposed method has higher search efficiency in the cases of without prior information and with prior information.

Bayesian Decision Algorithm for Symbol Diversity in a Three-Channel Redundant System Under Harsh Electromagnetic Disturbances

Bayesian Decision Algorithm for Symbol Diversity in a Three-Channel Redundant System Under Harsh Electromagnetic Disturbances

Information-directed policy sampling for episodic Bayesian Markov decision processes

We consider finite-stage Markov Decision Processes (MDPs) under incomplete information, where the decision-maker only knows that the true transition probability and reward matrices belong to given, finite sets. The decision-maker interacts with the system over a finite number of episodes. The first episode begins with a probabilistic belief about the true probability and reward matrices. This belief is updated at the end of each episode using observed events. The goal is to maximize the expected total reward earned over all episodes. In the resulting model-based episodic Bayesian MDP, it suffices to only consider (the known) policies that are optimal to each one of the possible probability and reward matrices. Nevertheless, the decision-maker should execute policies that provide information about the true probabilities and rewards (exploration), but also exploit this knowledge to increase rewards. We propose a framework called Information-Directed Policy Sampling (IDPS). In each episode, the decision-maker balances the exploitation-exploration trade-off by executing a randomized policy that minimizes a so-called convex information ratio. We derive a regret bound that is independent of state- and action-space cardinalities when the set of matrices is exogenously determined. Numerical experiments show IDPS outperforming a state-of-the-art approach called Posterior Sampling.

Water Contaminant Detection and Water Purification of Household Drinking Water Using a New Stacking Ensemble Model

ABSTRACTContaminated drinking water sources pose a significant health risk worldwide. Monitoring programs for drinking water quality aims to ensure safe water supply by informing management practices. Improved online monitoring of water systems is necessary as current lab‐based methods are slow and do not offer real‐time public health protection. Rapid detection and response to potential contamination events are crucial to mitigate health risks. Mark of‐purpose water treatment strategies offer a reasonable method for upgrading drinking water quality at the family level and forestalling waterborne illnesses. This study focuses on collecting household drinking water and utilizing various sensors to measure parameters such as pH, turbidity, water level, temperature, and humidity. A consistent water quality noticing system using the stacking outfit model, which solidifies Bayesian association and decision tree techniques, is proposed in this article. Bayesian network analyzes the input data attained from sensors collecting real‐time data and concludes whether the data represents the contamination event. DTs are utilized to demonstrate the connections between multivariate water boundaries utilized in the review. Afterward, a multiobjective, such as a biobjective optimization model and a nondominated genetic algorithm (NGA) are used in this work of optimization to minimize the volume of contaminated water. After the pollution in the water is identified, water decontamination processes are done given point of purpose medicines like ceramic channels and solar water disinfection (SODIS). The method outlined is executed through Python software. The findings indicate that the estimated values for PH, temperature, and turbidity are 7.3, 31.8, and 0.77, respectively. However, the proposed method is compared with the existing C‐NSGA‐II, while compared to this method, the proposed system produces improved cost functions. Consequently, suitable water treatment and supply should be considered to reduce the effects on people's health as well as to improve living conditions, respectively.

Dynamic Valuation of Data in Bayesian Decision-Making: A Stackelberg Competition Approach

Dynamic Valuation of Data in Bayesian Decision-Making: A Stackelberg Competition Approach

Performance enhancement of classifiers through Bio inspired feature selection methods for early detection of lung cancer from microarray genes

Gene expression in the microarray is assimilated with redundant and high-dimensional information. Moreover, the information in the microarray genes mostly correlates with background noise. This paper uses dimensionality reduction and feature selection methods to employ a classification methodology for high-dimensional lung cancer microarray data. The approach is enforced in two phases; initially, the genes are dimensionally reduced through Hilbert Transform, Detrend Fluctuation Analysis and Least Square Linear Regression methods. The dimensionally reduced data is further optimized in the next phase using Elephant Herd optimization (EHO) and Cuckoo Search Feature selection methods. The classifiers used here are Bayesian Linear Discriminant, Naive Bayes, Random Forest, Decision Tree, SVM (Linear), SVM (Polynomial), and SVM (RBF). The classifier's performances are analysed with and without feature selection methods. The SVM (Linear) classifier with the DFA Dimensionality Reduction method and EHO feature selection achieved the highest accuracy of 92.26 % compared to other classifiers.

Optimizing Genomic Parental Selection for Categorical and Continuous-Categorical Multi-Trait Mixtures.

This study presents a novel approach for the optimization of genomic parental selection in breeding programs involving categorical and continuous-categorical multi-trait mixtures (CMs and CCMMs). Utilizing the Bayesian decision theory (BDT) and latent trait models within a multivariate normal distribution framework, we address the complexities of selecting new parental lines across ordinal and continuous traits for breeding. Our methodology enhances precision and flexibility in genetic selection, validated through extensive simulations. This unified approach presents significant potential for the advancement of genetic improvements in diverse breeding contexts, underscoring the importance of integrating both categorical and continuous traits in genomic selection frameworks.

From pre-test and post-test probabilities to medical decision making

BackgroundA central goal of modern evidence-based medicine is the development of simple and easy to use tools that help clinicians integrate quantitative information into medical decision-making. The Bayesian Pre-test/Post-test Probability (BPP) framework is arguably the most well known of such tools and provides a formal approach to quantify diagnostic uncertainty given the result of a medical test or the presence of a clinical sign. Yet, clinical decision-making goes beyond quantifying diagnostic uncertainty and requires that that uncertainty be balanced against the various costs and benefits associated with each possible decision. Despite increasing attention in recent years, simple and flexible approaches to quantitative clinical decision-making have remained elusive.MethodsWe extend the BPP framework using concepts of Bayesian Decision Theory. By integrating cost, we can expand the BPP framework to allow for clinical decision-making.ResultsWe develop a simple quantitative framework for binary clinical decisions (e.g., action/inaction, treat/no-treat, test/no-test). Let p be the pre-test or post-test probability that a patient has disease. We show that r∗=(1-p)/p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^{*}=(1-p)/p$$\\end{document} represents a critical value called a decision boundary. In terms of the relative cost of under- to over-acting, r∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^{*}$$\\end{document} represents the critical value at which action and inaction are equally optimal. We demonstrate how this decision boundary can be used at the bedside through case studies and as a research tool through a reanalysis of a recent study which found widespread misestimation of pre-test and post-test probabilities among clinicians.ConclusionsOur approach is so simple that it should be thought of as a core, yet previously overlooked, part of the BPP framework. Unlike prior approaches to quantitative clinical decision-making, our approach requires little more than a hand-held calculator, is applicable in almost any setting where the BPP framework can be used, and excels in situations where the costs and benefits associated with a particular decision are patient-specific and difficult to quantify.

A low-dimensional approximation of optimal confidence.

Human decision making is accompanied by a sense of confidence. According to Bayesian decision theory, confidence reflects the learned probability of making a correct response, given available data (e.g., accumulated stimulus evidence and response time). Although optimal, independently learning these probabilities for all possible data combinations is computationally intractable. Here, we describe a novel model of confidence implementing a low-dimensional approximation of this optimal yet intractable solution. This model allows efficient estimation of confidence, while at the same time accounting for idiosyncrasies, different kinds of biases and deviation from the optimal probability correct. Our model dissociates confidence biases resulting from the estimate of the reliability of evidence by individuals (captured by parameter α), from confidence biases resulting from general stimulus independent under and overconfidence (captured by parameter β). We provide empirical evidence that this model accurately fits both choice data (accuracy, response time) and trial-by-trial confidence ratings simultaneously. Finally, we test and empirically validate two novel predictions of the model, namely that 1) changes in confidence can be independent of performance and 2) selectively manipulating each parameter of our model leads to distinct patterns of confidence judgments. As a tractable and flexible account of the computation of confidence, our model offers a clear framework to interpret and further resolve different forms of confidence biases.

Retraction: Cost-sensitive classification algorithm combining the Bayesian algorithm and quantum decision tree

Retraction: Cost-sensitive classification algorithm combining the Bayesian algorithm and quantum decision tree

Application of Bayesian Decision Analysis to Estimate Occupational Noise Levels from Limited Exposure Data

In recent years, Bayesian statistical modeling approaches have emerged as valuable tools in Industrial Hygiene (IH), particularly in situations with limited exposure data. This paper delves into the application of Bayesian Statistical Models, specifically Bayesian Decision Analysis (BDA), to analyze occupational noise exposure data within two Similar Exposure Groups (SEGs) of groundskeeping workers, addressing the pervasive issue of high noise levels exceeding 85 dBA. The primary aim is to estimate exposure levels based on the location of the exposure profiles for the SEGs within the AIHA® Exposure Control Categories (ECCs) 0-4, later modified and expanded to AIHA-ECC 0-5. This study employs BDA to estimate noise exposures among groundskeepers, emphasizing the scarcity of literature on BDA in noise exposure rating. Groundskeepers, facing potential risk of hearing impairment due to prolonged exposure, constitute a crucial and critical demographic, with nearly one million individuals in the United States alone. Noise data from the two SEGs was analyzed by using the Exposure Assessment Strategies Committee—EASC- AIHA® IHData Analyst for BDA modeling, complemented with the AIHA IHSTAT™ for certainty rating. The resulting posterior graphs were utilized to categorize exposure profiles into respective AIHA ECCs relative to noise OEL. These findings provide valuable insights, indicating a posterior probability of approximately 43.5% and 56.5% with 95% confidence that noise exposure levels fall within AIHA ECC 3 and AIHA ECC 4, respectively. However, while the 95% percentile decision statistics suggest exposure values lower than the OEL, the Upper Tolerance Limit (UTL) significantly surpass the OEL indicating low certainty regarding these exposure values for employees. Notably, the UTLs suggest that the SEGs are experiencing noise levels above the legally required 90 dBA for more than 5% of the time, which is an unacceptable scenario. Recommendations include implementing protective strategies such as regular training, surveillance, and monitoring, alongside engineering control strategies and mandatory use of personal protective equipment. These results underscore the critical need for refining judgments about noise exposures based on variability within and between employees, suggesting the use of additional statistical tools such as ANOVA (single-multivariate), MATLAB, and Python.

Joint modeling of choices and reaction times based on Bayesian contextual behavioral control.

In cognitive neuroscience and psychology, reaction times are an important behavioral measure. However, in instrumental learning and goal-directed decision making experiments, findings often rely only on choice probabilities from a value-based model, instead of reaction times. Recent advancements have shown that it is possible to connect value-based decision models with reaction time models. However, typically these models do not provide an integrated account of both value-based choices and reaction times, but simply link two types of models. Here, we propose a novel integrative joint model of both choices and reaction times by combining a computational account of Bayesian sequential decision making with a sampling procedure. This allows us to describe how internal uncertainty in the planning process shapes reaction time distributions. Specifically, we use a recent context-specific Bayesian forward planning model which we extend by a Markov chain Monte Carlo (MCMC) sampler to obtain both choices and reaction times. As we will show this makes the sampler an integral part of the decision making process and enables us to reproduce, using simulations, well-known experimental findings in value based-decision making as well as classical inhibition and switching tasks. Specifically, we use the proposed model to explain both choice behavior and reaction times in instrumental learning and automatized behavior, in the Eriksen flanker task and in task switching. These findings show that the proposed joint behavioral model may describe common underlying processes in these different decision making paradigms.

Planning cost-effective operational forest inventories.

We address a Bayesian two-stage decision problem in operational forestry where the inner stage considers scheduling the harvesting to fulfill demand targets and the outer stage considers selecting the accuracy of pre-harvest inventories that are used to estimate the timber volumes of the forest tracts. The higher accuracy of the inventory enables better scheduling decisions but also implies higher costs. We focus on the outer stage, which we formulate as a maximization of the posterior value of the inventory decision under a budget constraint. The posterior value depends on the solution to the inner stage problem and its computation is analytically intractable, featuring an NP-hard binary optimization problem within a high-dimensional integral. In particular, the binary optimization problem is a special case of a generalized quadratic assignment problem. We present a practical method that solves the outer stage problem with an approximation which combines Monte Carlo sampling with a greedy, randomized method for the binary optimization problem. We derive inventory decisions for a dataset of 100 Swedish forest tracts across a range of inventory budgets and estimate the value of the information to be obtained.

Convolutional Neural Network‐Based CT Image Segmentation of Kidney Tumours

ABSTRACTKidney tumours are one of the most common tumours in humans and the main current treatment is surgical removal. The CT images are usually manually segmented by a specialist for pre‐operative planning, but this can be influenced by the surgeon's experience and skill and can be time‐consuming. Due to the complex lesions and different morphologies of kidney tumours that make segmentation difficult, this article proposes a convolutional neural network‐based automatic segmentation method for CT images of kidney tumours to address the most common problems of boundary blurring and false positives in tumour segmentation images. The method is highly accurate and reliable, and is used to assist doctors in surgical planning as well as diagnostic treatment, relieving medical pressure to a certain extent. The EfficientNetV2‐UNet segmentation model proposed in this article includes three main parts: feature extractor, reconstruction network and Bayesian decision algorithm. Firstly, for the phenomenon of tumour false positives, the EfficientNetV2 feature extractor, which has high training accuracy and efficiency, is selected as the backbone network, which extracts shallow features such as tumour location, morphology and texture in the CT image by downsampling. Secondly, on the basis of the backbone network, the reconstruction network is designed, which mainly consists of conversion block, deconvolution block, convolution block and output block. Then, the up‐sampling architecture is constructed to gradually recover the spatial resolution of the feature map, fully identify the contextual information and form a complete encoding–decoding structure. Multi‐scale feature fusion is achieved by superimposing all levels of feature map channels on the left and right sides of the network, preventing the loss of details and performing accurate tumour segmentation. Finally, a Bayesian decision algorithm is designed for the edge blurring phenomenon of segmented tumours and cascaded over the output of the reconstruction network, combining the edge features of the original CT image and the segmented image for probability estimation, which is used to improve the accuracy of the model edge segmentation. Medical images in NII special format were converted to Numpy matrix format using python, and then more than 2000 CT images containing only kidney tumours were selected from the KiTS19 dataset as the dataset for the model, and the dimensions were standardised to 128 × 128, and the experimental results show that the model outperforms many other advanced models with good segmentation performance.

Framework for rational decision-making in bridge maintenance

Bridges are deteriorating, and their safety must be continuously assessed. Efficient management of bridges is essentially about making decisions on maintenance activities in line with the decision maker’s preferences. In other words, structural safety should be ensured while optimally allocating resources. In theory, methods are available for solving this complex task; however, they have not yet been implemented by bridge owners. In this study, the implementation into practice is facilitated by presenting a consistent framework for rational decision-making. It is argued that structural assessment is a decision problem that infrastructure owners are obliged to take responsibility for. Bayesian decision theory is presented as the theoretically ideal decision-making framework. The main components of the framework—representations of structural reliability and failure consequences—are discussed in detail, and human safety constraints are integrated. For demonstration purposes, the decision-making framework is applied to two case studies. In addition, it is parameterised by the relative cost of the intervention to failure and the current failure probability to be applicable for any assessment situation. In that way, this study contributes to more efficient maintenance of single bridges and the development of generally applicable structural codes for assessing existing structures.

Confinement energy landscape classification reveals membrane receptor nano-organization mechanisms

The cell membrane organization has an essential functional role through the control of membrane receptor confinement in micro- or nanodomains. Several mechanisms have been proposed to account for these properties, although some features have remained controversial, notably the nature, size, and stability of cholesterol- and sphingolipid-rich domains or lipid rafts. Here, we probed the effective energy landscape acting on single-nanoparticle-labeled membrane receptors confined in raft nanodomains— epidermal growth factor receptor (EGFR), Clostridium perfringens ε-toxin receptor (CPεTR), and Clostridium septicum α-toxin receptor (CSαTR)—and compared it with hop-diffusing transferrin receptors. By establishing a new analysis pipeline combining Bayesian inference, decision trees, and clustering approaches, we systematically classified single-protein trajectories according to the type of effective confining energy landscape. This revealed the existence of only two distinct organization modalities: confinement in a quadratic energy landscape for EGFR, CPεTR, and CSαTR (A), and free diffusion in confinement domains resulting from the steric hindrance due to F-actin barriers for transferrin receptor (B).The further characterization of effective confinement energy landscapes by Bayesian inference revealed the role of interactions with the domain environment in cholesterol- and sphingolipid-rich domains with (EGFR) or without (CPεTR and CSαTR) interactions with F-actin to regulate the confinement energy depth. These two distinct mechanisms result in the same organization type (A). We revealed that the apparent domain sizes for these receptor trajectories resulted from Brownian exploration of the energy landscape in a steady-state-like regime at a common effective temperature, independently of the underlying molecular mechanisms. These results highlight that confinement domains may be adequately described as interaction hotspots rather than rafts with abrupt domain boundaries. Altogether, these results support a new model for functional receptor confinement in membrane nanodomains and pave the way to the constitution of an atlas of membrane protein organization.