Search results for "Bayes factor"

Decomposing encoding and decisional components in visual-word recognition: a diffusion model analysis.

2014

In a diffusion model, performance as measured by latency and accuracy in two-choice tasks is decomposed into different parameters that can be linked to underlying cognitive processes. Although the diffusion model has been utilized to account for lexical decision data, the effects of stimulus manipulations in previous experiments originated from just one parameter: the quality of the evidence. Here we examined whether the diffusion model can be used to effectively decompose the underlying processes during visual-word recognition. We explore this issue in an experiment that features a lexical manipulation (word frequency) that we expected to affect mostly the quality of the evidence (the dri…

P-Value, Confidence Intervals, and Statistical Inference: A New Dataset of Misinterpretation

2017

Statistical inference is essential for science since the twentieth century (Salsburg, 2001). Since it's introduction into science, the null hypothesis significance testing (NHST), in which the P-value serves as the index of “statistically significant,” is the most widely used statistical method in psychology (Sterling et al., 1995; Cumming et al., 2007), as well as other fields (Wasserstein and Lazar, 2016). However, surveys consistently showed that researchers in psychology may not able to interpret P-value and related statistical procedures correctly (Oakes, 1986; Haller and Krauss, 2002; Hoekstra et al., 2014; Badenes-Ribera et al., 2016). Even worse, these misinterpretations of P-value …

Bayesian analysis and design for comparison of effect-sizes

2002

Comparison of effect-sizes, or more generally, of non-centrality parameters of non-central t distributions, is a common problem, especially in meta-analysis. The usual simplifying assumptions of either identical or non-related effect-sizes are often too restrictive to be appropriate. In this paper, the effect-sizes are modeled as random effects with t distributions. Bayesian hierarchical models are used both to design and analyze experiments. The main goal is to compare effect-sizes. Sample sizes are chosen so as to make accurate inferences about the difference of effect-sizes and also to convincingly solve the testing of equality of effect-sizes if such is the goal.

A Bayesian analysis of classical hypothesis testing

1980

The procedure of maximizing the missing information is applied to derive reference posterior probabilities for null hypotheses. The results shed further light on Lindley’s paradox and suggest that a Bayesian interpretation of classical hypothesis testing is possible by providing a one-to-one approximate relationship between significance levels and posterior probabilities.

Extending conventional priors for testing general hypotheses in linear models

2007

We consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters. We approach this problem from an objective Bayesian, model-selection perspective. Crucial ingredients for this approach are 'proper objective priors' to be used for deriving the Bayes factors. Jeffreys-Zellner-Siow priors have good properties for testing null hypotheses defined by specific values of the parameters in full-rank linear models. We extend these priors to deal with general hypotheses in general linear models, not necessarily of full rank. The resulting priors, which we call 'conventional priors', are expressed as a generalizat…

Generalization of Jeffreys Divergence-Based Priors for Bayesian Hypothesis Testing

2008

Summary We introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence-based (DB) priors. DB priors have simple forms and desirable properties like information (finite sample) consistency and are often similar to other existing proposals like intrinsic priors. Moreover, in normal linear model scenarios, they reproduce the Jeffreys–Zellner–Siow priors exactly. Most importantly, in challenging scenarios such as irregular models and mixture models, DB priors are well defined and very reasonable, whereas alternative proposals are not. We derive approximations to the DB priors as w…

Prior-based Bayesian information criterion

2019

We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood function, and then a suitable prior distribution is chosen to allow exact computation of the (approximate) marginal likelihood arising from the Laplace approximation and the prior. The result is a closed-form expression similar to BIC, but now involves a term arising from the prior distribution (which BIC ignores) and also incorporates the idea that different parameters can have different effective sample sizes (whereas BIC only allows one ov…

PValues for Composite Null Models

2000

Abstract The problem of investigating compatibility of an assumed model with the data is investigated in the situation when the assumed model has unknown parameters. The most frequently used measures of compatibility are p values, based on statistics T for which large values are deemed to indicate incompatibility of the data and the model. When the null model has unknown parameters, p values are not uniquely defined. The proposals for computing a p value in such a situation include the plug-in and similar p values on the frequentist side, and the predictive and posterior predictive p values on the Bayesian side. We propose two alternatives, the conditional predictive p value and the partial…

Statistical relationship between hardness of drinking water and cerebrovascular mortality in Valencia: a comparison of spatiotemporal models

2003

The statistical detection of environmental risk factors in public health studies is usually difficult due to the weakness of their effects and their confounding with other covariates. Small area geographical data bring the opportunity of observing health response in a wide variety of exposure values. Temporal sequences of these geographical datasets are crucial to gaining statistical power in detecting factors. The spatiotemporal models required to perform the statistical analysis have to allow for spatial and temporal correlations, which are more easily modelled via hierarchical structures of hidden random factors. These models have produced important research activity during the last deca…

Reference Posterior Distributions for Bayesian Inference

1979