Prior Distributions for Objective Bayesian Analysis

Consonni, Guido; Fouskakis, Dimitris; Liseo, Brunero; Ntzoufras, Ioannis

doi:10.1214/18-ba1103

Cited by 132 publications

(134 citation statements)

References 144 publications

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“…As previously mentioned, for a recent and thorough review of the objective Bayesian approaches so far developed, we refer the reader to Consonni et al (2018).…”

Section: Literature Reviewmentioning

confidence: 99%

On a Class of Objective Priors from Scoring Rules (with Discussion)

2020

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Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off the chosen statistical model and in the majority of cases the resulting prior is improper, which can pose limitations to a practical implementation, even when the complexity of the model is moderate. In this paper we propose to take a novel look at the construction of objective prior distributions, where the connection with a chosen sampling distribution model is removed. We explore the notion of defining objective prior distributions which allow one to have some degree of flexibility, in particular in exhibiting some desirable features, such as being proper, or centered on specific values which would be of interest in nested model comparisons.The basic tool we use are proper scoring rules and the main result is a class of objective prior distributions that can be employed in scenarios where the usual model based priors fail, such as mixture models and model selection via Bayes factors. In addition, we show that the proposed class of priors is the result of minimising the information it contains, providing solid interpretation to the method.

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“…As previously mentioned, for a recent and thorough review of the objective Bayesian approaches so far developed, we refer the reader to Consonni et al (2018).…”

Section: Literature Reviewmentioning

confidence: 99%

On a Class of Objective Priors from Scoring Rules (with Discussion)

2020

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“…We fit further models in which we assessed the relationship between model parameters and age and EEG covariates. Following the Bayesian regression framework for cognitive models suggested by Boehm et al 2017, we used z-standardised age and EEG covariates and specified mixture of g-priors for the regression weights (Liang et al, 2008;Consonni et al, 2018). In each model we added a regression term involving a covariate or set of covariates to the fixed effects model for drift rate.…”

Section: Diffusion Modellingmentioning

confidence: 99%

Perceptual decision-making in children: Age-related differences and EEG correlates

Manning¹,

Wagenmakers²,

Norcia³

et al. 2020

Preprint

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Children make faster and more accurate decisions about perceptual information as they get older, but it is unclear how different aspects of the decision-making process change with age. Here, we used hierarchical Bayesian diffusion models to decompose performance in a perceptual task into separate processing components, testing age-related differences in model parameters and links to neural data. We collected behavioural and EEG data from 96 six- to twelve-year-olds and 20 adults completing a motion discrimination task. We used a component decomposition technique to identify two response-locked EEG components with ramping activity preceding the response in children and adults: one with activity that was maximal over centro-parietal electrodes and one that was maximal over occipital electrodes. Younger children had lower drift rates (reduced sensitivity), wider boundary separation (increased response caution) and longer non-decision times than older children and adults. Yet model comparisons suggested that the best model of children’s data included age effects only on drift rate and boundary separation (not non-decision time). Next we extracted the slope of ramping activity in our EEG components and covaried these with drift rate. The slopes of both EEG components related positively to drift rate, but the best model with EEG covariates included only the centro-parietal component. By decomposing performance into distinct components and relating them to neural markers, diffusion models have the potential to identify the reasons why children with developmental conditions perform differently to typically developing children - and to uncover processing differences inapparent in the response time and accuracy data alone.

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“…Confidence intervals (CIs) may be used, though these intervals probably should not be derived from sampling distributions, or at least probabilistic interpretations should be avoided. Instead, CIs may be calculated through bootstrapping, jackknifing, permutations (Haig, 2005;Rodgers, 1999), objective Bayesian priors (Consonni, Fouskakis, Liseo, & Ntzoufras, 2018), etc. In fact, standard hypothesis testing methods -t-tests, ANOVA, regression, etc., are fully appropriate for rough CDA, as long as they are treated as estimation methods and not as indicators of probabilistic links to some theoretical population.…”

Section: Confirmatory Data Analysismentioning

confidence: 99%

Moving Beyond the "Replication Crisis": Understanding the Exploratory/Confirmatory Data Analysis Continuum

Fife¹,

Jl²

2019

Preprint

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In light of the “replication crisis,” some (e.g., Nelson, Simmons, & Simonsohn, 2018) advocate for greater policing and transparency in research methods. Others (Baumeister, 2016; Finkel, Eastwick, & Reis, 2017; Goldin-meadow, 2016; Levenson, 2017) argue against rigid requirements that may inadvertently restrict discovery. We embrace both positions and argue that proper understanding and implementation of the well-established paradigm of Exploratory Data Analysis (EDA; Tukey, 1977) is necessary to push beyond the replication crisis. Unfortunately, many don’t realize EDA exists (Goldin-Meadow, 2016), fail to understand the philosophy and proper tools for exploration (Baumeister, 2016), or reject EDA as unscientific (Lindsay, 2015). EDA’s mistreatment is unfortunate, and is usually based on misunderstanding the nature and goal of EDA. We develop an expanded typology that situates EDA, CDA, and rough CDA in the same framework with fishing, p-hacking, and HARKing, and argue that most, if not all, questionable research practices (QRPs) would be resolved by understanding and implementing the EDA/CDA gradient. We argue most psychological research is “rough CDA,” which has often and inadvertently used the wrong tools. We conclude with guidelines about how these typologies can be integrated into a cumulative research program that is necessary to move beyond the replication crisis.

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Prior Distributions for Objective Bayesian Analysis

Cited by 132 publications

References 144 publications

On a Class of Objective Priors from Scoring Rules (with Discussion)

On a Class of Objective Priors from Scoring Rules (with Discussion)

Perceptual decision-making in children: Age-related differences and EEG correlates

Moving Beyond the "Replication Crisis": Understanding the Exploratory/Confirmatory Data Analysis Continuum

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