Bayesian Revision Research Articles

Revised vulnerability analysis of group buildings based on the SPO model of equivalent individual structure

Typical individual structure and group buildings with different classification features have abundant seismic damage data. To fully utilize the theoretical seismic damage data of individual structure and the statistical seismic damage data for group buildings, establish Pushover analysis model of group buildings with certain vulnerability characteristics and improve the reliability of seismic performance of corresponding classified group buildings characterized by individual structure, a method for establishing equivalent Pushover models of group buildings based on the SPO2IDA inversion algorithm is proposed, and the theoretical Pushover curve of characterized typical structure is updated through the Bayesian theory using the equivalent individual structure model established by seismic damage statistical data, and then an vulnerability analysis model that complies with seismic damage statistical laws is established. The research results show that the SPO model of equivalent individual structure of group buildings can be established based on the seismic damage statistical characteristics of buildings. The maximum accuracy and minimum accuracy of the median seismic intensity of the vulnerability model established by the Pushover model obtained after Bayesian revision can be improved by 45% and 20% respectively. This paper proposes a method to improve the accuracy of earthquake damage results of group buildings characterized by individual structure from the perspective of inherent structural attributes, which can provide more economically reasonable design solutions for buildings with specific attribute classification in relevant regions.

Refining the chronology of North America's copper using traditions: A macroscalar approach via Bayesian modeling.

North America’s ancient copper use, predicted to originate as early as 9000 cal BP, represents the earliest use of native copper for utilitarian tool production in the world. Although recent work has focused on establishing the first use of copper in the western Great Lakes region, little attention has been paid to determining the age ranges of subsequent copper using groups or to the identification of broader trends in copper use during the Archaic Period (10,000–3000 RCYBP). Here we address this issue by applying Bayesian modeling to a comprehensive suite of 76 radiocarbon dates directly associated with copper use. Our results identified two distinct peaks in copper usage, ca. 5500 cal BP and ca. 3300 cal BP. Age ranges for the three Archaic Period traditions and practices associated with copper use of the western Great Lakes are revised using modern calibration curves. Bayesian revisions of age ranges from sites where copper tools and/or production debris have been found provide insight into the historical relationships between, and cultural interactions among, these early copper using groups. This study provides an updated, refined chronology based on the most recent calibration curve (IntCal20) for the varied cultural contexts of copper use across the western Great Lakes.

Bayesian Revision of the Folsom Age Range Using IntCal20

ABSTRACT Folsom is an early Paleoindian archaeological tradition found in the North American West. Here we report new AMS radiocarbon dates for the Barger Gulch and Lindenmeier sites in Colorado along with unsuccessful dating attempts for Blackwater Draw, the Mitchell Locality, Shifting Sands, and Lipscomb on the Southern Plains. We applied Bayesian modeling using IntCal20 to our updated set of Folsom dates and estimate that the Folsom tradition lasted for a period spanning between 355–510 years at the 68 per cent credible interval or 325–650 years at the 95 per cent credible interval, starting sometime between 12,845–12,770 calendar years ago (cal yr BP) and ending sometime between 12,400–12,255 cal yr BP. Additionally, we model the spans of the start and end boundaries and find that both the adoption and abandonment of Folsom technology occurred over relatively short periods, less than 100 years and likely less than 50 years.

TWO-STAGE PRIORITIZATION PROCEDURE FOR MULTIPLICATIVE AHP-GROUP DECISION MAKING

In this paper, we propose two-stage prioritization procedure (TSPP) for multiplicative Analytic Hierarchy Process-group decision making (AHP-GDM), which involves determining the group priority vector based on the individual pair-wise comparison matrices (PCMs), simultaneously considering the consensus and consistency of the individual PCMs. The first stage of the TSPP involves checking and revising the individual PCMs for reaching the acceptable consensus and consistency. The second stage of the TSPP involves estimating the group priority vector using Bayesian approach. The main characteristics of the proposed TSPP are as follows: 1) It makes full use of the prior information as well as the sample information during the Bayesian revision of the individual PCMs and the Bayesian estimation of the group priority vector; 2) It ensures that the revised individual PCMs reach the acceptable consensus and consistency; 3) It enriches the aggregation methods for the collective preference in multiplicative AHP-GDM. Finally, two numerical examples are used to evaluate the applicability and effectiveness of the proposed TSPP by the comparisons with several other methods.

Effect of Teaching Bayesian Methods Using Learning by Concept vs Learning by Example on Medical Students’ Ability to Estimate Probability of a Diagnosis

Clinicians use probability estimates to make a diagnosis. Teaching students to make more accurate probability estimates could improve the diagnostic process and, ultimately, the quality of medical care. To test whether novice clinicians can be taught to make more accurate bayesian revisions of diagnostic probabilities using teaching methods that apply either explicit conceptual instruction or repeated examples. A randomized clinical trial of 2 methods for teaching bayesian updating and diagnostic reasoning was performed. A web-based platform was used for consent, randomization, intervention, and testing of the effect of the intervention. Participants included 61 medical students at McMaster University and Eastern Virginia Medical School recruited from May 1 to September 30, 2018. Students were randomized to (1) receive explicit conceptual instruction regarding diagnostic testing and bayesian revision (concept group), (2) exposure to repeated examples of cases with feedback regarding posttest probability (experience group), or (3) a control condition with no conceptual instruction or repeated examples. Students in all 3 groups were tested on their ability to update the probability of a diagnosis based on either negative or positive test results. Their probability revisions were compared with posttest probability revisions that were calculated using the Bayes rule and known test sensitivity and specificity. Of the 61 participants, 22 were assigned to the concept group, 20 to the experience group, and 19 to the control group. Approximate age was 25 years. Two participants were first-year; 37, second-year; 12, third-year; and 10, fourth-year students. Mean (SE) probability estimates of students in the concept group were statistically significantly closer to calculated bayesian probability than the other 2 groups (concept, 0.4%; [0.7%]; experience, 3.5% [0.7%]; control, 4.3% [0.7%]; P < .001). Although statistically significant, the differences between groups were relatively modest, and students in all groups performed better than expected, based on prior reports in the literature. The study showed a modest advantage for students who received theoretical instruction on bayesian concepts. All participants' probability estimates were, on average, close to the bayesian calculation. These findings have implications for how to teach diagnostic reasoning to novice clinicians. ClinicalTrials.gov identifier: NCT04130607.

Bayesian Revision vs. Information Distortion.

The rational status of the Bayesian calculus for revising likelihoods is compromised by the common but still unfamiliar phenomenon of information distortion. This bias is the distortion in the evaluation of a new datum toward favoring the currently preferred option in a decision or judgment. While the Bayesian calculus requires the independent combination of the prior probability and a new datum, information distortion invalidates such independence (because the prior influences the datum). Although widespread, information distortion has not generally been recognized. First, individuals are not aware when they themselves commit this bias. In addition, it is often hidden in more obvious suboptimal phenomena. Finally, the Bayesian calculus is usually explained only with undistortable data like colored balls drawn randomly. Partly because information distortion is unrecognized by the individuals exhibiting it, no way has been devised for eliminating it. Partial reduction is possible in some situations such as presenting all data simultaneously rather than sequentially with revision after each datum. The potential dangers of information distortion are illustrated for three professional revision tasks: forecasting, predicting consumer choices from internet data, and statistical inference from experimental results. The optimality of the Bayesian calculus competes with people's natural desire that their belief systems remain coherent in the face of new data. Information distortion provides this coherence by biasing those data toward greater agreement with the currently preferred position—but at the cost of Bayesian optimality.

A practical approach for applying Bayesian logic to determine the probabilities of subsurface scenarios: Example from an offshore oilfield

During appraisal of an undeveloped segment of a producing offshore oilfield, three well penetrations revealed unexpected complexity and compartmentalization. Business decisions on whether and how to develop this segment depended on understanding the possible interpretations of the subsurface. This was achieved using the following steps that incorporated a novel practical application of Bayesian logic. 1. Scenarios were identified to span the full range of possible subsurface interpretations. This was achieved through a facilitated cross-disciplinary exercise including external participants. The exercise generated 12 widely differing subsurface scenarios, which could be grouped into 4 types of mechanisms: slumping, structural, depositional, and diagenetic. 2. Prior probabilities were assigned to each scenario. These probabilities were elicited from the same subsurface team and external experts who performed step 1, using their diverse knowledge and experience. 3. The probabilities of each scenario were updated by evaluating them sequentially with 21 individual pieces of evidence, progressively down-weighting belief in scenarios that were inconsistent with the evidence. For each piece of evidence, the likelihood (chance that the scenario could produce the evidence) was estimated qualitatively by the same team using a “traffic-light” high-medium-low assessment. Offline, these were converted to numerical likelihood values. Posterior probabilities were derived by multiplying the priors by the likelihoods and renormalizing to sum to unity across all of the scenarios. 4. The most probable scenarios were selected for quantitative reservoir modeling, to evaluate the potential outcomes of business decisions, given each scenario. Of the 12 scenarios identified in step 1, most were strongly down-weighted by the sequential revisions against evidence in step 3; after this, only scenarios in the “slumping” group retained significant posterior probabilities. The data showed minimal sensitivity to the initial assumption of prior probability in step 2. This process had several benefits. First, it encouraged the subsurface team to imagine a full range of scenarios that were likely to bracket the actual subsurface “truth,” something that is critical for subsequent decision-making. Second, it allowed belief in the probability of each scenario to be updated systematically in a way that was strongly conditioned to the evidence, so that the choice of scenarios to take through to reservoir modeling was more objective and evidence-based. Third, it allowed an assessment of the usefulness of individual pieces of evidence, which could be used to guide value-of-information assessments for subsequent data acquisition. Finally, the process enabled rigorous Bayesian revision methods to be applied in a simple practical way that engaged the subsurface team without exposing them to the underlying mathematics. During field appraisal and development, when the subsurface is revealed gradually as more data are acquired and studied, the process outlined here provides a practical way of generating and modifying belief in a range of subsurface scenarios while minimizing exposure to potential biases and logical fallacies that could affect subsequent decision quality. It also helps to decide which scenarios are sufficiently probable that they need to be represented by detailed reservoir models.

Bayesian revision of a prior given prior-data conflict, expert opinion, or a similar insight: a large-deviation approach

ABSTRACTLearning from model diagnostics that a prior distribution must be replaced by one that conflicts less with the data raises the question of which prior should instead be used for inference and decision. The same problem arises when a decision maker learns that one or more reliable experts express unexpected beliefs. In both cases, coherence of the solution would be guaranteed by applying Bayes's theorem to a distribution of prior distributions that effectively assigns the initial prior distribution a probability arbitrarily close to 1. The new distribution for inference would then be the distribution of priors conditional on the insight that the prior distribution lies in a closed convex set that does not contain the initial prior. A readily available distribution of priors needed for such conditioning is the law of the empirical distribution of sufficiently large number of independent parameter values drawn from the initial prior. According to the Gibbs conditioning principle from the theory of large deviations, the resulting new prior distribution minimizes the entropy relative to the initial prior. While minimizing relative entropy accommodates the necessity of going beyond the initial prior without departing from it any more than the insight demands, the large-deviation derivation also ensures the advantages of Bayesian coherence. This approach is generalized to uncertain insights by allowing the closed convex set of priors to be random.

A Theory of Bayesian Groups

AbstractA group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non‐public or even private information (learnt by not all or just one individual), or to non‐representable information (not representable by any event in the domain where credences are held). I propose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non‐representable information, etc. Six corresponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.'s central result (with minor corrections). Another theorem—that for public non‐representable information—fills a gap in the theory of externally Bayesian opinion pooling.

Probabilistic Inference: Task Dependency and Individual Differences of Probability Weighting Revealed by Hierarchical Bayesian Modeling.

Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.

The Statistical Distribution of Incurred Losses and Its Evolution Over Time I: Non-Parametric Models

The distribution of the total incurred losses of an accident year (or underwriting year) is considered. Before commencement of the accident year, there is a prior on this quantity. The distribution may eveolve over time according to Bayesian revision which takes account of the accumulation of data with time.The distribution in question can be made subject to various assumptions and restrictions. The different forms of these are explored in a sequence of papers that include the present one.A previoius paper examined the situation in which no restrictions were imposed. The resulting models were refered to as non-parametric.The present paper considers the case in which the posterior-to-data estimates of the subject distribution are restricted to a specific parametric family. These models are referred to as parametric. The subject distribution evolves with the evolution of its parameters under Bayesian revision. The credibility approximations to this revision are worked out in general (Section 4) and for the special case of normally distributed data (Section 5).The results are illustrated by application to a very simply example (Section 6). They are illustrated further by application to a more extensive example involving real data (Section 7). The examples use the same respective data sets as in the previous paper.All models to this point represent the loss experience of each development year in terms of a separate set of parameters applicable to just that year. Section 9 analyses the case in which all of these parameters are expressed as functions of a reduced parameter set. Again, a numerical example is given.

Updating a progic

This paper presents a progic, or probabilistic logic, in the sense of Haenni et al. [8]. The progic presented here is based on Bayesianism, as the progic discussed by Williamson [15]. However, the underlying generalised Bayesianism differs from the objective Bayesianism used by Williamson, in the calibration norm, and the liberalisation and interpretation of the reference probability in the norm of equivocation. As a consequence, the updating dynamics of both Bayesianisms differ essentially. Whereas objective Bayesianism is based on a probabilistic re-evaluation, orthodox Bayesianism is based on a probabilistic revision. I formulate a generalised and iterable orthodox Bayesian revision dynamics. This allows to define an updating procedure for the generalised Bayesian progic. The paper compares the generalised Bayesian progic and Williamson's objective Bayesian progic in strength, update dynamics and with respect to language (in)sensitivity.

Bayesian revision of the individual pair-wise comparison matrices under consensus in AHP–GDM

Analytic hierarchy process (AHP) has been widely used in group decision making (GDM). There are two traditional aggregation methods for the synthesis of group priorities in AHP–GDM: aggregation of the individual judgments (AIJ) and aggregation of the individual priorities (AIP). However, AIJ and AIP may be less reliable because of inconsistency of the individual pair-wise comparison matrices (PCMs) and deviation among decision makers. Based on multiplicative AHP model with lognormal errors, we propose a Bayesian revision method for improving the individual PCMs under the assumption that the consensus exists among decision makers, which is considered an aid to AIJ and AIP. In order to effectively deal with decision making involving multiple actors when using AHP as the methodological support, we revise the individual PCMs using the Bayesian revision method before using AIJ and AIP for the synthesis of group priorities. The Bayesian revision method not only makes full use of the prior distribution for parameters and sample information while complying with the Pareto principal of social choice theory, but also provides the reliable individual Bayesian PCMs for AIJ and AIP. Finally two numerical examples are examined to illustrate the applications and advantages of the Bayesian revision method.

Uncertainty estimates by Bayesian method with likelihood of AR (1) plus Normal model and AR (1) plus Multi-Normal model in different time-scales hydrological models

Bayesian revision is widely used in hydrological model uncertainty assessment. With respect to model calibration, parameter estimation and analysis of uncertainty sources, various regression and probabilistic approaches have been used in different models calibrated for either daily or monthly time step. None of these applications however includes a comparison of uncertainty analysis in hydrological models with respect to the time periods, at which the models are operated. This study pursues a comprehensive inter-comparison and evaluation of uncertainty assessments by Bayesian revision using the Metropolis Hasting (MH) algorithm with the hydrological model WASMOD with daily and monthly time step. In the daily step model three likelihood functions are used in combination with Bayesian revision: (i) the AR (1) plus Normal time period independent model (Model 1), (ii) the AR (1) plus Multi-Normal model (Model 2), and (iii) the AR (1) plus Normal time period dependent model (Model 3). In addition an index called the percentage of observations bracketed by the Unit Confidence Interval (PUCI) was used for uncertainty evaluation. The results reveal that it is more important to consider the autocorrelation in daily WASMOD rather than monthly WASMOD. Firstly, the resulting goodness of fit of the daily model vs. observations as measured by the Nash-Sutcliffe efficiency value is comparable with that calculated by the optimization algorithm in monthly WASMOD. Secondly, the AR (1) model is not sufficiently adequate to estimate the distribution of residuals in daily WASMOD since PUCI shows that Model 2 outperforms Model 1. Furthermore, the maximum Nash-Sutcliffe efficiency value of Model 2 is the largest. Thirdly, Model 3 performs best over the entire flow range, while Model 2 outperforms Model 3 for high flows. This shows that additional statistical parameters reflect the statistical characters of the residuals more efficiently and accurately. Fourthly, by considering the difference in terms of application and computational efficiency it becomes evident that Model 3 performs best for daily WASMOD. Model 2 on the other hand is superior for daily time step WASMOD if the auto-correlation of parameters is considered. (C) 2011 Elsevier B.V. All rights reserved.

Dynamic portfolio choice under ambiguity and regime switching mean returns

I examine a continuous-time intertemporal consumption and portfolio choice problem under ambiguity, where expected returns of a risky asset follow a hidden Markov chain. Investors with Chen and Epstein's (2002) recursive multiple priors utility possess a set of priors for unobservable investment opportunities. The optimal consumption and portfolio policies are explicitly characterized in terms of the Malliavin derivatives and stochastic integrals. When the model is calibrated to U.S. stock market data, I find that continuous Bayesian revisions under incomplete information generate ambiguity-driven hedging demands that mitigate intertemporal hedging demands. In addition, ambiguity aversion magnifies the importance of hedging demands in the optimal portfolio policies. Out-of-sample experiments demonstrate the economic importance of accounting for ambiguity.

FaBSR: a method for cluster failure prediction based on Bayesian serial revision and an application to LANL cluster

Accurate failure number prediction of Repairable Large-scale Long-running Computing (RLLC) cluster systems is a challenge because of the reparability and large scale of the system. Furthermore, the variational failure rate derived from system maintenance yields a small sample problem, that is, the failure numbers observed from different time phases do not belong to the same population. To address the challenge, a general Bayesian serial revision prediction method (FaBSR) is proposed on the basis of the Time Series and Bootstrap approaches, and it can determine the distribution of failure number, analyze the variation trend of failure rate and accurately predict the failure number. To demonstrate the performance gains of the method, the data of Los Alamos National Laboratory (LANL) cluster system are used as a typical RLLC system to do extensive experiments. And experimental results show that the prediction accuracy of FaBSR is 80.4%, improved by more than 4% compared with other existing methods. Copyright © 2010 John Wiley & Sons, Ltd.

‘Preferring that which you desire less’: A Condillacian approach to choice under uncertainty

In his Dissertation sur la liberté (1754b), Condillac propounds a theory of choice that is intrinsically probabilistic. Reflecting on the cases which we would qualify as ‘paradoxes in expected utility’ he puts these down to common faults, explicable by ‘delusions’ and ‘dominant desires’. This article concerns the revelation of this original procedure of a philosopher who had little interest in mathematics who constructed a clearly probabilistic procedure of choice. By a Bayesian revision of our probabilistic belief and our ‘delusions’, we sometimes ‘prefer that which we desire less’ and this way of thinking explain our endogenous changes of preferences.

Dynamic Portfolio Choice under Ambiguity and Regime Switching Mean Returns

I examine a continuous-time intertemporal consumption and portfolio choice problem under ambiguity, where expected returns of a risky asset follow a hidden Markov chain. Investors with Chen and Epstein''s (2002) recursive multiple priors utility possess a set of priors for unobservable investment opportunities. We explicitly characterize optimal consumption and portfolio policies in terms of the Malliavin derivatives and stochastic integrals. When the model is calibrated to U.S. stock market data, I find that continuous Bayesian revisions under incomplete information generate ambiguity-driven hedging demands that mitigate intertemporal hedging demands. In addition, ambiguity aversion magnifies the importance of hedging demands in the optimal portfolio policies. Out-of-sample experiments demonstrate the economic importance of accounting for ambiguity.

Uncertainty assessment via Bayesian revision of ensemble streamflow predictions in the operational river Rhine forecasting system

Ensemble streamflow forecasts obtained by using hydrological models with ensemble weather products are becoming more frequent in operational flow forecasting. The uncertainty of the ensemble forecast needs to be assessed for these products to become useful in forecasting operations. A comprehensive framework for Bayesian revision has been recently developed and applied to operational flood forecasting with deterministic weather forecasts. The Bayesian revision yields a posterior density, conditional on all information available to the forecaster at the onset of a forecast run. This conditional density objectively quantifies the uncertainty. Here the Bayesian approach is generalized for use with ensemble weather predictions. An end‐to‐end application of a Bayesian postprocessor for ensemble streamflow forecasts in the river Rhine forecasting system is presented. A verification of the postprocessor shows good performance when compared in terms of the ranked probability skill score to non‐Bayesian uncertainty assessment, such as ranking threshold exceedance probabilities for members of a streamflow ensemble prediction. In this context it is also addressed how the proposed Bayesian processor can serve in supporting rational decision making for flood warning under conditions of uncertainty.

Second-order Bayesian revision of a generalised linear model

It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general multivariate EDF. This paper derives a second-order approximation to the posterior likelihood of a naturally conjugated generalised linear model (GLM), i.e., multivariate EDF subject to a link function (Section 5.5). It is not the same as a normal approximation. It does, however, lead to second-order Bayes estimators of parameters of the posterior. The family of second-order approximations is found to be closed under Bayesian revision. This generates a recursion for repeated Bayesian revision of the GLM with the acquisition of additional data. The recursion simplifies greatly for a canonical link. The resulting structure is easily extended to a filter for estimation of the parameters of a dynamic generalised linear model (DGLM) (Section 6.2). The Kalman filter emerges as a special case. A second type of link function, related to the canonical link, and with similar properties, is identified. This is called here the companion canonical link. For a given GLM with canonical link, the companion to that link generates a companion GLM (Section 4). The recursive form of the Bayesian revision of this GLM is also obtained (Section 5.5.3). There is a perfect parallel between the development of the GLM recursion and its companion. A dictionary for translation between the two is given so that one is readily derived from the other (Table 5.1). The companion canonical link also generates a companion DGLM. A filter for this is obtained (Section 6.3). Section 1.2 provides an indication of how the theory developed here might be applied to loss reserving. A sequel paper, providing numerical illustrations of this, is planned.