The Spirit of Cromwell’s Rule

2018 ◽  
Author(s):  
Timothy McGrew
Keyword(s):  
Bayesian Methods ◽  
Bayesian Model ◽  
Bayesian Probability ◽  
Standard Textbook ◽  
Per Se

One of the central complaints about Bayesian probability is that it places no constraints on individual subjectivity in one’s initial probability assignments. Those sympathetic to Bayesian methods have responded by adding restrictions motivated by broader epistemic concerns about the possibility of changing one’s mind. This chapter explores some cases where, intuitively, a straightforward Bayesian model yields unreasonable results. Problems arise in these cases not because there is something wrong with the Bayesian formalism per se but because standard textbook illustrations teach us to represent our inferences in simplified ways that break down in extreme cases. It also explores some interesting limitations on the extent to which successive items of evidence ought to induce us to change our minds when certain screening conditions obtain.

scholarly journals Dynamic causal modelling of COVID-19

2020 ◽  
Vol 5 ◽  
pp. 89 ◽  
Author(s):  
Karl J. Friston ◽  
Thomas Parr ◽  
Peter Zeidman ◽  
Adeel Razi ◽  
Guillaume Flandin ◽  
...  
Keyword(s):  
Bayesian Model ◽  
Causal Model ◽  
State Of The Art ◽  
Herd Immunity ◽  
Nonlinear Effects ◽  
Model Inversion ◽  
Neuronal Ensembles ◽  
Technical Report ◽  
Per Se ◽  
Dynamic Causal Model

This technical report describes a dynamic causal model of the spread of coronavirus through a population. The model is based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time. The purpose of this model is to quantify the uncertainty that attends predictions of relevant outcomes. By assuming suitable conditional dependencies, one can model the effects of interventions (e.g., social distancing) and differences among populations (e.g., herd immunity) to predict what might happen in different circumstances. Technically, this model leverages state-of-the-art variational (Bayesian) model inversion and comparison procedures, originally developed to characterise the responses of neuronal ensembles to perturbations. Here, this modelling is applied to epidemiological populations—to illustrate the kind of inferences that are supported and how the model per se can be optimised given timeseries data. Although the purpose of this paper is to describe a modelling protocol, the results illustrate some interesting perspectives on the current pandemic; for example, the nonlinear effects of herd immunity that speak to a self-organised mitigation process.

scholarly journals “Nonmonotonic” does not mean “probabilistic”

2009 ◽  
Vol 32 (1) ◽  
pp. 102-103 ◽  
Author(s):  
Keith Stenning ◽  
Michiel van Lambalgen
Keyword(s):  
Bayesian Methods ◽  
Common Sense ◽  
Bayesian Probability ◽  
Common Sense Reasoning

AbstractOaksford & Chater (O&C) advocate Bayesian probability as a way to deal formally with the pervasive nonmonotonicity of common sense reasoning. We show that some forms of nonmonotonicity cannot be treated by Bayesian methods.

scholarly journals Bayesian estimation of differential transcript usage from RNA-seq data

2017 ◽  
Vol 16 (5-6) ◽  
Author(s):  
Panagiotis Papastamoulis ◽  
Magnus Rattray
Keyword(s):  
Bayesian Methods ◽  
Bayesian Model ◽  
Bayes Factor ◽  
Null Model ◽  
Rna Seq ◽  
Mcmc Sampling ◽  
False Discovery ◽  
Fully Bayesian ◽  
Per Gene ◽  
Generation Sequencing

AbstractNext generation sequencing allows the identification of genes consisting of differentially expressed transcripts, a term which usually refers to changes in the overall expression level. A specific type of differential expression is differential transcript usage (DTU) and targets changes in the relative within gene expression of a transcript. The contribution of this paper is to: (a) extend the use of cjBitSeq to the DTU context, a previously introduced Bayesian model which is originally designed for identifying changes in overall expression levels and (b) propose a Bayesian version of DRIMSeq, a frequentist model for inferring DTU. cjBitSeq is a read based model and performs fully Bayesian inference by MCMC sampling on the space of latent state of each transcript per gene. BayesDRIMSeq is a count based model and estimates the Bayes Factor of a DTU model against a null model using Laplace’s approximation. The proposed models are benchmarked against the existing ones using a recent independent simulation study as well as a real RNA-seq dataset. Our results suggest that the Bayesian methods exhibit similar performance with DRIMSeq in terms of precision/recall but offer better calibration of False Discovery Rate.

Distinguishing Normative Processes From Noise

2016 ◽  
Vol 79 (4) ◽  
pp. 311-332 ◽  
Author(s):  
Jonathan H. Morgan ◽  
Kimberly B. Rogers ◽  
Mao Hu
Keyword(s):  
Bayesian Methods ◽  
Bayesian Model ◽  
Stepwise Regression ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Ground Truth ◽  
Model Specification ◽  
Affect Control Theory ◽  
False Discovery ◽  
Social Events

This research evaluates the relative merits of two established and two newly proposed methods for modeling impressions of social events: stepwise regression, ANOVA, Bayesian model averaging, and Bayesian model sampling. Models generated with each method are compared against a ground truth model to assess performance at variable selection and coefficient estimation. We also assess the theoretical impacts of different modeling choices. Results show that the ANOVA procedure has a significantly lower false discovery rate than stepwise regression, whereas Bayesian methods exhibit higher true positive rates and comparable false discovery rates to ANOVA. Bayesian methods also generate coefficient estimates with less bias and variance than either stepwise regression or ANOVA. We recommend the use of Bayesian methods for model specification in affect control theory.

scholarly journals Detecting planetary signals with Bayesian methods

2009 ◽  
Vol 5 (H15) ◽  
pp. 693-693
Author(s):  
Samuli Kotiranta ◽  
Mikko Tuomi
Keyword(s):  
Radial Velocity ◽  
Bayesian Methods ◽  
Bayesian Model ◽  
Model Comparison ◽  
Planetary System ◽  
Velocity Measurements ◽  
Bayesian Model Comparison

AbstractIn this paper we present an application of Bayesian model comparison to the radial velocity measurements of suspected extra-solar planetary system host star.

Sequential multilocation auditing and the New York food stamps program

2018 ◽  
Author(s):  
Karl W. Heiner ◽  
Marc Kennedy ◽  
Anthony O'Hagan
Keyword(s):  
New York ◽  
Hierarchical Model ◽  
Bayesian Methods ◽  
Bayesian Model ◽  
Error Rates ◽  
Food Stamps ◽  
Estimation Of Error ◽  
One Year ◽  
Over Time

This article discusses the use of Bayesian methods in analysing data that evolve over time in sequential multilocation auditing. Using the New York food stamps program as a case study, it proposes a model that incorporates a nonparametric component for the error magnitudes (taints), a hierarchical model for overall error rates across counties and parameters controlling the variation of rates from one year to the next, including an overall trend in error rates. The article first provides an overview of the New York food stamps program, along with the auditing concepts and terminology, before introducing the Bayesian model. This model is used to examine a sample of individual awards of food stamps to see if the value awarded is correct according to the rules of the scheme. The model makes it possible to smooth estimation of error rates and error classes in small counties across counties and through time.

scholarly journals Comparing Bayesian and non-Bayesian accounts of human confidence reports

2016 ◽  
Author(s):  
William T. Adler ◽  
Wei Ji Ma
Keyword(s):  
Bayesian Model ◽  
Model Comparison ◽  
Bayesian Probability ◽  
Perceptual Categorization ◽  
Brain Areas ◽  
Low Level ◽  
Response Modality ◽  
Manipulation Task ◽  
Cognitive Decision ◽  
Sensory Uncertainty

Humans can meaningfully report their confidence in a perceptual or cognitive decision. It is widely believed that these reports reflect the Bayesian probability that the decision is correct, but this hypothesis has not been rigorously tested against non-Bayesian alternatives. We use two perceptual categorization tasks in which Bayesian confidence reporting requires subjects to take sensory uncertainty into account in a specific way. We find that subjects do take sensory uncertainty into account when reporting confidence, suggesting that brain areas involved in reporting confidence can access low-level representations of sensory uncertainty. However, behavior is not fully consistent with the Bayesian hypothesis and is better described by simple heuristic models. Both conclusions are robust to changes in the uncertainty manipulation, task, response modality, model comparison metric, and additional flexibility in the Bayesian model. Our results suggest that adhering to a rational account of confidence behavior may require incorporating implementational constraints.

scholarly journals “I tawt I taw a puddy tat!": Extinction and uncertain sightings of the Barbary lion

2015 ◽  
Author(s):  
Tamsin E Lee ◽  
Simon A Black ◽  
Amina Fellous ◽  
Nobuyuki Yamaguchi ◽  
Francesco Angelici ◽  
...  
Keyword(s):  
Bayesian Methods ◽  
Bayesian Model ◽  
As Species ◽  
Barbary Lion

As species become rare and approach extinction, purported sightings can be controversial, especially when scarce management resources are at stake. We report a Bayesian model where we consider the probability that each individual sighting is valid. Obtaining these probabilities clearly requires a strict framework to ensure that they are as representative as possible. We used a process, which has proven to provide accurate estimates from a group of experts, to obtain probabilities for the validation of 35 sightings of the Barbary lion. We considered the scenario where experts are simply asked whether a sighting was valid, as well as when we asked them to score the sighting based on distinguishablity, observer competence, and verifiability. We find that asking experts to provide scores for these three aspects resulted in each sighting being considered more individually. Additionally, since the heavy reliance on the choice of prior can often be the downfall of Bayesian methods, we use an informed prior which changes with time.

scholarly journals Comparison of Two Bayesian Methods in Evaluation of the Absence of the Gold Standard Diagnostic Tests

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Taishun Li ◽  
Pei Liu
Keyword(s):  
Bayesian Methods ◽  
Gold Standard ◽  
Diagnostic Tests ◽  
Prior Distribution ◽  
Bayesian Model ◽  
Conditional Independence ◽  
Probabilistic Constraint ◽  
Conditional Covariance ◽  
Prior Constraint ◽  
Constraint Model

Objective. The Bayesian model plays an important role in diagnostic test evaluation in the absence of the gold standard, which used the external prior distribution of a parameter combined with sample data to yield the posterior distribution of the test characteristics. However, the correlation between diagnostic tests has always been a problem that cannot be ignored in the Bayesian model evaluation. This study will discuss how different Bayesian model, correlation scenarios, and prior distribution affect the outcome. Methods. The data analyzed in this study was gathered during studies of patients presenting to the Nanjing Chest Hospital with suspected tuberculosis. The diagnostic character of T-SPOT.Tb and KD38 tuberculosis antibody test were evaluated in different Bayesian model, and discharge diagnosis as a gold standard was used to verify the model results in the end. Result. The comparison of four models under the conditional independence situation found that Bayesian probabilistic constraint model was consistent with the Conditional Covariance Bayesian model. The results were mainly affected by prior information. The sensitivity and specificity of the two tests in Conditional Covariance Bayesian model in prior constraint situation were considerably higher than the Bayesian probabilistic constraint model in prior constraint situation. The results of the four models under the conditional dependence situation were similar to the conditional independence situation; pD was also negative with no prior constraint situation in both model Bayesian probabilistic constraint model and Conditional Covariance Bayesian model. The Deviance Information Criterion of Bayesian probabilistic constraint model was close to model Conditional Covariance Bayesian model, but pD of Conditional Covariance Bayesian model in Prior constraint situation (pD=2.40) was higher than the Bayesian probabilistic constraint model in Prior constraint situation (pD=1.66). Conclusion. The result of Conditional Covariance Bayesian model in prior constraint with conditional independence situation was closest to the result of gold standard evaluation in our data. Both of the two Bayesian methods are the feasible way for the evaluation of diagnostic test in the absence of the gold standard diagnostic. Prior source, priority number, and conditional dependencies should be considered in the method selection, the accuracy of posterior estimation mainly depending on the prior distribution.

scholarly journals “I tawt I taw a puddy tat!": Extinction and uncertain sightings of the Barbary lion

2015 ◽  
Author(s):  
Tamsin E Lee ◽  
Simon A Black ◽  
Amina Fellous ◽  
Nobuyuki Yamaguchi ◽  
Francesco Angelici ◽  
...  
Keyword(s):  
Bayesian Methods ◽  
Bayesian Model ◽  
As Species ◽  
Barbary Lion

As species become rare and approach extinction, purported sightings can be controversial, especially when scarce management resources are at stake. We report a Bayesian model where we consider the probability that each individual sighting is valid. Obtaining these probabilities clearly requires a strict framework to ensure that they are as representative as possible. We used a process, which has proven to provide accurate estimates from a group of experts, to obtain probabilities for the validation of 35 sightings of the Barbary lion. We considered the scenario where experts are simply asked whether a sighting was valid, as well as when we asked them to score the sighting based on distinguishablity, observer competence, and verifiability. We find that asking experts to provide scores for these three aspects resulted in each sighting being considered more individually. Additionally, since the heavy reliance on the choice of prior can often be the downfall of Bayesian methods, we use an informed prior which changes with time.

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