2021
DOI: 10.3390/math9212810
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Bayesian Inference under Small Sample Sizes Using General Noninformative Priors

Abstract: This paper proposes a Bayesian inference method for problems with small sample sizes. A general type of noninformative prior is proposed to formulate the Bayesian posterior. It is shown that this type of prior can represent a broad range of priors such as classical noninformative priors and asymptotically locally invariant priors and can be derived as the limiting states of normal-inverse-Gamma conjugate priors, allowing for analytical evaluations of Bayesian posteriors and predictors. The performance of diffe… Show more

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Cited by 9 publications
(6 citation statements)
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“…At each assessment point, the hypothesis that the interaction effect (ie, an intervention effect) was different from zero was tested using contrasts comparing each assessment point with the baseline. Moreover, no prior information was included in the analysis, resulting in flat prior distributions [ 66 ]. The probability of the collected data emerging under the null model (ie, meaning that the data were a collection of random noise) was compared with the alternative model (ie, condition [intervention vs CAU] had an effect on outcome).…”
Section: Methodsmentioning
confidence: 99%
“…At each assessment point, the hypothesis that the interaction effect (ie, an intervention effect) was different from zero was tested using contrasts comparing each assessment point with the baseline. Moreover, no prior information was included in the analysis, resulting in flat prior distributions [ 66 ]. The probability of the collected data emerging under the null model (ie, meaning that the data were a collection of random noise) was compared with the alternative model (ie, condition [intervention vs CAU] had an effect on outcome).…”
Section: Methodsmentioning
confidence: 99%
“…Here, the load effect on task performance is expected to be obvious based on data from Experiment 1 and a medium-tolarge effect size would therefore be a conservative estimate. Furthermore, the primary analysis for the choice data (i.e., Bayesian hierarchical modeling) aggregates all information across trials and participants during model fitting, and consequently reducing parameters' sensitivity to noise within each participant and to smaller sample sizes (He, Wang, Huang, Wang, & Guan, 2021;McNeish & Stapleton, 2016;Van de Schoot, Broere, Perryck, & Loey, 2015). All participants reported normal (or corrected-to-normal) vision and color vision and provided informed consent was given before the study began.…”
Section: Participantsmentioning
confidence: 99%
“…Another important parking-related feature is the density of points of interest (POI). We calculate the density of POI using a kernel function [44] presented in (10).…”
Section: Data Declarationmentioning
confidence: 99%
“…However, these smart parking services and applications are still struggling for mass deployment due to the lack of a practical approach to small-sample parking occupancy prediction (POP), i.e., a small-sample prediction problem [10]. Traditional data-hungry models are unable to predict with high accuracy and stability in a data-poor scenario, resulting in insufficient quality of service provided, which seriously undermines users' trust [11].…”
Section: Introductionmentioning
confidence: 99%