Modern Likelihood‐Frequentist Inference

Pierce, Donald A.; Bellio, Ruggero

doi:10.1111/insr.12232

Cited by 11 publications

(6 citation statements)

References 62 publications

(118 reference statements)

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“…Adjusted profile likelihood for model selection inference. Readers can see Meeker and Escobar (1995) for a brief introduction to profile likelihood in the context of confidence interval construction and Pierce and Bellio (2017) for a substantial review of practical likelihood adjustments. A gentle introduction to model selection through information criteria can be found in Anderson (2008), with more technically robust discussions in Burnham and Anderson (2002) or Konishi and Kitagawa (2008).…”

Section: Competing Models With Unknown Parameter Valuesmentioning

confidence: 99%

Assessing the Global and Local Uncertainty of Scientific Evidence in the Presence of Model Misspecification

et al. 2021

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Scientists need to compare the support for models based on observed phenomena. The main goal of the evidential paradigm is to quantify the strength of evidence in the data for a reference model relative to an alternative model. This is done via an evidence function, such as ΔSIC, an estimator of the sample size scaled difference of divergences between the generating mechanism and the competing models. To use evidence, either for decision making or as a guide to the accumulation of knowledge, an understanding of the uncertainty in the evidence is needed. This uncertainty is well characterized by the standard statistical theory of estimation. Unfortunately, the standard theory breaks down if the models are misspecified, as is commonly the case in scientific studies. We develop non-parametric bootstrap methodologies for estimating the sampling distribution of the evidence estimator under model misspecification. This sampling distribution allows us to determine how secure we are in our evidential statement. We characterize this uncertainty in the strength of evidence with two different types of confidence intervals, which we term “global” and “local.” We discuss how evidence uncertainty can be used to improve scientific inference and illustrate this with a reanalysis of the model identification problem in a prominent landscape ecology study using structural equations.

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Section: Competing Models With Unknown Parameter Valuesmentioning

confidence: 99%

Assessing the Global and Local Uncertainty of Scientific Evidence in the Presence of Model Misspecification

et al. 2021

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“…Therefore, the inferential conclusions based on these CDs match the conclusions based on the likelihood or profile likelihood functions. Higher order asymptotic developments relating likelihood inference to CDs include, for instance, Hall (1992); Reid and Fraser (2010); Pierce and Bellio (2017), among others.…”

Section: If [R2] Holds Asymptotically (Or Approximately) Then H(•) Is...mentioning

confidence: 99%

Bridging Bayesian, frequentist and fiducial (BFF) inferences using confidence distribution

Thornton

Xie

2020

Preprint

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Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community (cf., Reid and Cox 2015;Kass 2011;Efron 1998). Most practitioners are probably more familiar with the two dominant statistical inferential paradigms, Bayesian inference and frequentist inference. The third, lesser known fiducial inference paradigm was pioneered by R.A. Fisher in an attempt to define an inversion procedure for inference as an alternative to Bayes' theorem. Although each paradigm has its own strengths and limitations subject to their different philosophical underpinnings, this article intends to bridge these different inferential methodologies through the lenses of confidence distribution theory and Monte-Carlo simulation procedures. This article attempts to understand how these three distinct paradigms, Bayesian, frequentist, and fiducial inference, can be unified and compared on a foundational level, thereby increasing the range of possible techniques available to both statistical theorists and practitioners across all fields.

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“…Barndorff-Nielsen (1986) developed a modified signed likelihood root R * (ψ) which is standard normal with error of order O(n −3/2 ). Following this seminal work, there have been various alternative versions of R * (ψ) (see Pierce and Bellio, 2017, for an accessible overview).…”

Section: Likelihood Inferencementioning

confidence: 99%

Parametric bootstrap inference for stratified models with high-dimensional nuisance specifications

Bellio¹,

Kosmidis²,

Salvan³

et al. 2020

Preprint

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Inference about a scalar parameter of interest typically relies on the asymptotic normality of common likelihood pivots, such as the signed likelihood root, the score and Wald statistics. Nevertheless, the resulting inferential procedures have been known to perform poorly when the dimension of the nuisance parameter is large relative to the sample size and when the information about the parameters is limited. In such cases, the use of asymptotic normality of analytical modifications of the signed likelihood root is known to recover inferential performance. It is proved here that parametric bootstrap of standard likelihood pivots results in as accurate inferences as analytical modifications of the signed likelihood root do in stratified models with stratum specific nuisance parameters. We focus on the challenging case where the number of strata increases as fast or faster than the stratum samples size. It is also shown that this equivalence holds regardless of whether constrained or unconstrained bootstrap is used. This is in contrast to when the dimension of the parameter space is fixed relative to the sample size, where constrained bootstrap is known to correct inference to higher-order than unconstrained bootstrap does. Large scale simulation experiments support the theoretical findings and demonstrate the excellent performance of bootstrap in some extreme modelling scenarios.

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Modern Likelihood‐Frequentist Inference

Cited by 11 publications

References 62 publications

Assessing the Global and Local Uncertainty of Scientific Evidence in the Presence of Model Misspecification

Assessing the Global and Local Uncertainty of Scientific Evidence in the Presence of Model Misspecification

Bridging Bayesian, frequentist and fiducial (BFF) inferences using confidence distribution

Parametric bootstrap inference for stratified models with high-dimensional nuisance specifications

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