Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria

Evans, Michael; Guo, Yang

doi:10.3390/e23020190

Cited by 8 publications

(9 citation statements)

References 31 publications

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“…n * evidence 10 1 -0.047 against 10 100 0.019 in favour 10 500 0.037 in favour 50 50 0.005 in favour Also, the cut-off for determining evidence for or against occurs at 0 2 = [(1 + ) log(1 + )]/ → ∞ as →∞, which implies that the associated p-value → 0. This general conclusion is not overly reliant on the particular prior chosen, see [21], and suggests that smaller p-values are necessary to determine evidence against as increases, since increases with .…”

Section: Example 2 Jeffreys-lindley Paradoxmentioning

confidence: 82%

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The Concept of Statistical Evidence

Evans¹

2021

Proceedings of the 3rd International Conference on Statistics: Theory and Applications

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The concept of statistical evidence has proven to be somewhat elusive in the development of the discipline of Statistics. Still there is a conviction that appropriately collected data contains evidence concerning the answers to questions of scientific interest. We discuss some of the attempts at making the concept of evidence precise and, in particular, present an approach based upon measuring how beliefs change from a priori to a posteriori. Of necessity this is Bayesian in nature as a proper prior is required that reflects beliefs about where the truth lies before the data is observed. Bayesian inference is often criticized for its subjective nature. It is possible, however, to deal with this subjectivity in a scientifically sound manner. In part, this is done by assessing and controlling the bias the prior and model induce into inferences and this depends intrinsically on being clear about statistical evidence. In addition, the model and the prior are falsifiable through model checking and checking for prior-data conflict. Both the assessment of bias and the falsification steps are essentially frequentist in nature so this provides a degree of unity between sometimes conflicting philosophies. This approach to statistical reasoning can be seen as dealing with the inevitable subjectivity required in the choice of ingredients to an analysis so that a statistical analysis can approach the goal of objectivity that is central to scientific work.

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Section: Example 2 Jeffreys-lindley Paradoxmentioning

confidence: 82%

“…Various optimality properties, in terms of bias, are established in [21] for this approach to characterizing/measuring statistical evidence. A satisfying overall conclusion from this is that, if bias assessments are held as being essential, then there are complementary roles for frequentism and Bayes.…”

Section: Example 2 Jeffreys-lindley Paradoxmentioning

confidence: 99%

The Concept of Statistical Evidence

Evans¹

2021

Proceedings of the 3rd International Conference on Statistics: Theory and Applications

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“…We also need to establish theoretical results for scenarios that go beyond those covered in Section 3, and more critically to cases where the likelihood itself is misspecified in consequential ways. A reviewer also reminded us to study the issue of assessing likelihood-prior combination that could lead to substantial bias, in the sense of creating regions of parameter space that are highly probable a priori; see Baskurt et al (2013); Evans and Guo (2019). Applications to high-dimensional and/or non-parametric problems are another important direction to explore, and the growing literature on the relationship between prior and posterior concentrations (see for example van der Pas et al (2014) and Strawn et al (2014) and references therein) may provide some theoretical insight on this exploration.…”

Section: Limitations and Future Workmentioning

confidence: 99%

Prior Sample Size Extensions for Assessing Prior Impact and Prior-Likelihood Discordance

Reimherr

Meng

Nicolae

2021

Journal of the Royal Statistical Society Series B: Statistical Methodology

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This paper outlines a framework for quantifying the prior's contribution to posterior inference in the presence of priorlikelihood discordance, a broader concept than the usual notion of prior-likelihood conflict. We achieve this dual purpose by extending the classic notion of prior sample size, M, in three directions: (I) estimating M beyond conjugate families; (II) formulating M as a relative notion that is as a function of the likelihood sample size k, M(k), which also leads naturally to a graphical diagnosis; and (III) permitting negative M, as a measure of prior-likelihood conflict, that is, harmful discordance. Our asymptotic regime permits the prior sample size to grow with the likelihood data size, hence making asymptotic arguments meaningful for investigating the impact of the prior relative to that of likelihood. It leads to a simple asymptotic formula for quantifying the impact of a proper prior that only involves computing a centrality and a spread measure of the prior and the posterior. We use simulated and real data to illustrate the potential of the proposed framework, including quantifying how weak is a 'weakly informative' prior adopted in a study of lupus nephritis. Whereas we take a pragmatic perspective in assessing the impact of a prior on a given inference problem under a specific evaluative metric, we also touch upon conceptual and theoretical issues such as using improper priors and permitting priors with asymptotically non-vanishing influence.

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“…There is also the issue of bias which is interpreted here as meaning that the ingredients to the analysis, namely, the data collection procedure together with the model and prior, can be chosen in such a fashion as to produce a foregone conclusion. That such bias is possible is illustrated in Evans (2015) and Evans and Guo (2021) where also a solution to this issue is developed.…”

Section: Introductionmentioning

confidence: 99%

“…As discussed in Evans and Guo (2021), the control of bias is equivalent to the a priori control of coverage probabilities. The control over the biases is effected by ensuring that an appropriate amount of data is collected as it can be shown that both biases converge to 0 as the amount of data increases.…”

Section: Introductionmentioning

confidence: 99%

On some problems of Bayesian region construction with guaranteed coverages

et al. 2023

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The general problem of constructing regions that have a guaranteed coverage probability for an arbitrary parameter of interest $$\psi \in \Psi $$ ψ ∈ Ψ is considered. The regions developed are Bayesian in nature and the coverage probabilities can be considered as Bayesian confidences with respect to the model obtained by integrating out the nuisance parameters using the conditional prior given $$\psi .$$ ψ . Both the prior coverage probability and the prior probability of covering a false value (the accuracy) can be controlled by setting the sample size. These coverage probabilities are considered as a priori figures of merit concerning the reliability of a study while the inferences quoted are Bayesian. Several problems are considered where obtaining confidence regions with desirable properties have proven difficult to obtain. For example, it is shown that the approach discussed never leads to improper regions which has proven to be an issue for some confidence regions.

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Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria

Cited by 8 publications

References 31 publications

The Concept of Statistical Evidence

The Concept of Statistical Evidence

Prior Sample Size Extensions for Assessing Prior Impact and Prior-Likelihood Discordance

On some problems of Bayesian region construction with guaranteed coverages

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