Jeffrey S. Evans, Kenneth McGarry, Peter Smith · Sunderland Repository (University of Sunderland) · 2015
In this paper, we investigate the rate of company compulsory liquidation (insolvency) (CCL) via Bayesian inference applied with the use of ‘OpenBUGS’ and ‘R’ software mediums. This study follows on from a previous ‘frequentist’ statistical based study of one of the authors and introduces the usefulness of Bayesian inference as the statistical tool. CCL occurs when a company creditor successfully petitions the courts for a winding up order. There are a finite number of variables that can affect the possibility of company creditors instigating CCL. The model in this study included those variables found to be statistically significant within the data range contained in the previous ‘frequentist’ study. We commence by presenting the model from the previous ‘frequentist’ study along with an analysis of the results of that study. We then introduce the concept of Bayesian inference to the study and apply the inference to the ‘frequentist’ model, and analyse the results of the new model. Finally, we then compare the two sets of findings and report our conclusions, and the implications for the modeling of insolvencies.
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1999
18 Blank, R.D. et al. (1988) A linkage map of mouse chromosome 12: Localization of Igh and effects of sex and interference on recombination. Genetics 120, 1073–1084 19 Churchill, G.A. et al. (1993) Pooled-sampling makes high resolution mapping practical with DNA markers. Proc. Natl.
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David R. Bickel · Statistical Papers · 2024
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David R. Bickel · HAL (Le Centre pour la Communication Scientifique Directe) · 2022
Unquantified uncertainty about probabilistic model assumptions tends to inflate claims of statistical significance, potentially leading to reported results that cannot be replicated. The same bias occurs at a higher level when Bayesian inference or frequentist inference is chosen to achieve significance in the absence of a way to propagate the uncertainty about which statistical paradigm to select.The objective of this article is to correct that bias at both levels on the basis of evidentiary first principles for statistical inference. It is found that just as Bayesian inference is warranted when a prior distribution is considered alongside the data as evidence, frequentist inference in the form of confidence intervals and their generalization to confidence distributions is warranted when a hypothesis testing procedure is considered as a piece of evidence. Hierarchical evidence in the same framework enables reporting results reflecting uncertainty about which of those pieces of evidence to admit as well as uncertainty about model assumptions. That is illustrated by a method of averaging Bayesian hypothesis testing with frequentist hypothesis testing and by a method of averaging confidence intervals and/or credible intervals.
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Jhon Jair Quiza Montealegre, Natalia Trujillo, Andrés Quintero-Zea et al. · 2024
We present a novel methodology for analyzing electroencephalographic (EEG) event-related potentials (ERP) using massive univariate statistical methods combined with Bayesian inference. This data-driven approach automatically identifies clusters of ele
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Princeton University Press eBooks · 2019
Thomas Bayes and Statistical Inference Classical Statistical Inference Bayes' Theorem Bayesian Methods for a Proportion Bayesian Methods for Other Parameters Prior Distributions Bayesian Difficulties Bayesian Strengths
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Toby St Clere Smithe · arXiv (Cornell University) · 2021
We introduce the concepts of Bayesian lens, characterizing the bidirectional structure of exact Bayesian inference, and statistical game, formalizing the optimization objectives of approximate inference problems. We prove that Bayesian inversions compose according to the compositional lens pattern, and exemplify statistical games with a number of classic statistical concepts, from maximum likelihood estimation to generalized variational Bayesian methods. This paper is the first in a series laying the foundations for a compositional account of the theory of active inference, and we therefore pay particular attention to statistical games with a free-energy objective.
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Murali Krishna Pasupuleti · International Journal of Academic and Industrial Research Innovations(IJAIRI) · 2025
Abstract: Small sample sizes and high-dimensional data present fundamental obstacles for statistical modeling, inference, and decision-making across a wide range of scientific and engineering disciplines. Traditional statistical techniques often break down under these regimes, yielding unstable or biased estimates. Adaptive Bayesian methods, with their intrinsic ability to incorporate prior information, update beliefs sequentially, and flexibly model complex structures, offer a powerful alternative. This paper synthesizes insights from cutting-edge studies on scalable inference, sequential Bayesian experimental design, and robust prior modeling for small-sample and high-dimensional settings. We provide critical evaluations of existing techniques, propose new adaptive frameworks for improved inference stability, and explore strategies to enhance both computational scalability and statistical robustness. Our findings underscore the pivotal role of adaptive Bayesian methods in navigating the challenges of complex, modern data environments. Keywords: Adaptive Bayesian Inference, Small Sample Challenges, High-Dimensional Data, Scalable Bayesian Methods, Sequential Design, Robust Priors, Hybrid Sampling, Bayesian Nonparametrics, Posterior Approximation, Experimental Design under Uncertainty
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Rebai Rim, Ali Ben Mrad, Maalej Mohamed Amin · Procedia Computer Science · 2025
The application of Bayesian statistical approaches has grown in the last few years in a variety of scientific domains, including computing. Bayesian inference integrates experimental data with prior knowledge to perform analysis. Unlike classical methods, Bayesian approaches offer fundamentally different perspectives on statistical inference. In this paper, we adopt Bayesian inference as a thorough and reliable formalism to handle uncertain data in user modeling. Inference methods are driven by evidence. Hard evidence and probabilistic evidence are the two main categories of evidence that are the subject of this essay. Specifically, we emphasize updating the evidence represented in a Bayesian model. The paper illustrates the use of fixed probabilistic evidence, or soft evidence, in an adaptive user interface.
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B. Abraham, J. Ledolter, Statistical John Wiley et al. · 1985
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Martin, Andrew D. · Deep Blue (University of Michigan) · 2015
This article surveys modern Bayesian methods of estimating statistical models.It first provides an introduction to the Bayesian approach for statistical inference, contrasting it with more conventional approaches.It then explains the Monte Carlo principle and reviews commonly used Markov Chain Monte Carlo (MCMC) methods.This is followed by a practical justification for the use of Bayesian methods in the social sciences, and a number of examples from the literature where Bayesian methods have proven useful are shown.The article finally provides a review of modern software for Bayesian inference, and a discussion of the future of Bayesian methods in political science.One area ripe for research is the use of prior information in statistical analyses.Mixture models and those with discrete parameters (such as change point models in the time-series context) are completely underutilized in political science.
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Andrew D. Martin · Oxford University Press eBooks · 2009
Abstract This article surveys modern Bayesian methods of estimating statistical models. It first provides an introduction to the Bayesian approach for statistical inference, contrasting it with more conventional approaches. It then explains the Monte Carlo principle and reviews commonly used Markov Chain Monte Carlo (MCMC) methods. This is followed by a practical justification for the use of Bayesian methods in the social sciences, and a number of examples from the literature where Bayesian methods have proven useful are shown. The article finally provides a review of modern software for Bayesian inference, and a discussion of the future of Bayesian methods in political science. One area ripe for research is the use of prior information in statistical analyses. Mixture models and those with discrete parameters (such as change point models in the time-series context) are completely underutilized in political science.
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Jim Albert · 1995
Teaching classical statistical inference at an elementary level can be hard, due to the difficulty in teaching sampling distributions and the correct interpretation of statistical confidence. Bayesian methods have the attractive feature that statistical conclusions can be stated using the language of subjective probability. Simple methods of teaching Bayes rule are described and these methods are illustrated for inference and prediction problems for one and two proportions. We discuss the advantages and disadvantages of this approach and give texts that provide examples and software for implementing Bayesian methods in an elementary class. 1 Introduction 1.1 Teaching statistical inference Consider the traditional approach to teaching statistical inference at an elementary level. First some basic concepts of probability theory are introduced. This discussion includes the relative frequency interpretation of probability which is essential for understanding the interpretation of confide...
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Richard Barker, Matthew Schofield · International Journal of Sports Physiology and Performance · 2008
In a recent commentary on statistical inference, Batterham and Hopkins advocated an approach to statistical inference centered on expressions of uncertainty in parameters. After criticizing an approach to statistical inference driven by null hypothesis testing, they proposed a method of "magnitude-based" inference and then claimed that this approach is essentially Bayesian but with no prior assumption about the true value of the parameter. In this commentary, after we address the issues raised by Batterham and Hopkins, we show that their method is "approximately" Bayesian and rather than assuming no prior information their approach has a very specific, but hidden, joint prior on parameters. To correctly adopt the type of inference advocated by Batterham and Hopkins, sport scientists need to use fully Bayesian methods of analysis.
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Erik Otárola‐Castillo, Melissa G. Torquato · Annual Review of Anthropology · 2018
Null hypothesis significance testing (NHST) is the most common statistical framework used by scientists, including archaeologists. Owing to increasing dissatisfaction, however, Bayesian inference has become an alternative to these methods. In this article, we review the application of Bayesian statistics to archaeology. We begin with a simple example to demonstrate the differences in applying NHST and Bayesian inference to an archaeological problem. Next, we formally define NHST and Bayesian inference, provide a brief historical overview of their development, and discuss the advantages and limitations of each method. A review of Bayesian inference and archaeology follows, highlighting the applications of Bayesian methods to chronological, bioarchaeological, zooarchaeological, ceramic, lithic, and spatial analyses. We close by considering the future applications of Bayesian statistics to archaeological research.
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El Mahdi Khribch, Pierre Alquier · arXiv (Cornell University) · 2024
Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for statistical models. The derived bound has wide-ranging applications in statistical inference. It yields improved contraction rates for fractional posteriors in Bayesian nonparametrics. It can also be used to study a wide range of estimation methods, such as variational inference or Maximum Likelihood Estimation (MLE). By bridging these diverse areas, this work advances our understanding of the fundamental limits of statistical inference and the role of information in learning from data. We hope that these results will not only clarify connections between statistical inference and information theory but also help to develop a new toolbox to study a wide range of estimators.
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Borek Puza · ANU eView eBooks · 2015
Bayesian methods for statistical analysis is a book on statistical methods for analysing a wide variety of data. The book consists of 12 chapters, starting with basic concepts and covering numerous topics, including Bayesian estimation, decision theory, prediction, hypothesis testing, hierarchical models, Markov chain Monte Carlo methods, finite population inference, biased
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Yijie Zhang · arXiv (Cornell University) · 2024
Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are treated as random variables with prior distributions, allowing for a probabilistic interpretation and quantification of predictive uncertainty. However, Bayesian methods lack theoretical generalization guarantees for unseen data. PAC-Bayesian analysis addresses this limitation by offering a frequentist framework to derive generalization bounds for randomized predictors, thereby certifying the reliability of Bayesian methods in machine learning. Temperature $T$, or inverse-temperature $λ= \frac{1}{T}$, originally from statistical mechanics in physics, naturally arises in various areas of statistical inference, including Bayesian inference and PAC-Bayesian analysis. In Bayesian inference, when $T < 1$ (``cold'' posteriors), the likelihood is up-weighted, resulting in a sharper posterior distribution. Conversely, when $T > 1$ (``warm'' posteriors), the likelihood is down-weighted, leading to a more diffuse posterior distribution. By balancing the influence of observed data and prior regularization, temperature adjustments can address issues of underfitting or overfitting in Bayesian models, bringing improved predictive performance.
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Santos, Quinton Marco Dos, Maina, John Ndegwa, Avenant-Oldewage, Annemariè · Zenodo (CERN European Organization for Nuclear Research) · 2019
Figure 4. Evolutionary history of Gyrodactylus magadiensis n. sp. based on Bayesian Inference approaches using ITS sequences for selected gyrodactylids. Statistical support for Bayesian inference (BI) and maximum likelihood (ML) methods indicated at branch nodes with posterior probabilities and bootstrap support indicated, respectively (ML/BI).
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José M. Bernardo · 2009
Scientific Reporting. Mathematical statistics uses two major paradigms, conventional (or frequentist), and Bayesian. Bayesian methods provide a complete paradigm for both statistical inference and decision making under uncertainty. Bayesian methods may be derived from an axiomatic system, and hence provide a general, coherent methodology. Bayesian methods contain as particular cases many of the more often used frequentist procedures, solve many of the difficulties faced by conventional statistical methods, and extend the applicability of statistical methods. In particular, Bayesian methods make it possible to incorporate scientific hypothesis in the analysis (by means of the prior distribution) and may be applied to problems whose structure is too complex for conventional methods to be able to handle. The Bayesian paradigm is based on an interpretation of probability as a rational, conditional measure of uncertainty, which closely matches the sense of the word ‘probability ’ in ordinary language. Statistical inference about a quantity of interest is described as the modification of the uncertainty about its value in the light of evidence, and Bayes ’ theorem precisely specifies how this modification should be made. The special situation, often met in scientific reporting and public decision making, where the only acceptable information is that which may be deduced from available documented data, is addressed by objective Bayesian methods, as a particular case. 1.
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