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After rejecting the null hypothesis in the analysis of variance, the next step is to make the pairwise comparisons to find out differences in means. The purpose of this paper is threefold. The foremost aim is to suggest expression for…
Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and…
Machine learning models are being used extensively in many important areas, but there is no guarantee a model will always perform well or as its developers intended. Understanding the correctness of a model is crucial to prevent potential…
Bayesian Belief Networks (BBNs) are a powerful formalism for reasoning under uncertainty but bear some severe limitations: they require a large amount of information before any reasoning process can start, they have limited contradiction…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
A {\it pure significance test} (PST) tests a simple null hypothesis $H_f:Y\sim f$ {\it without specifying an alternative hypothesis} by rejecting $H_f$ for {\it small} values of $f(Y)$. When the sample space supports a proper uniform pmf…
The so-called 'energy test' is a frequentist technique used in experimental particle physics to decide whether two samples are drawn from the same distribution. Its usage requires a good understanding of the distribution of the test…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
As a convention, p-value is often computed in frequentist hypothesis testing and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. The smaller the p-value, the more significant…
Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…
In this work, we address the question of how to enhance signal-agnostic searches by leveraging multiple testing strategies. Specifically, we consider hypothesis tests relying on machine learning, where model selection can introduce a bias…
Continuous time Bayesian networks are investigated with a special focus on their ability to express causality. A framework is presented for doing inference in these networks. The central contributions are a representation of the intensity…
Despite remarkable progress made in natural language processing, even the state-of-the-art models often make incorrect predictions. Such predictions hamper the reliability of systems and limit their widespread adoption in real-world…
Bayesian statistics plays a pivotal role in advancing medical science by enabling healthcare companies, regulators, and stakeholders to assess the safety and efficacy of new treatments, interventions, and medical procedures. The Bayesian…
While sample efficiency is the main motive for use of Bayesian optimisation when black-box functions are expensive to evaluate, the standard approach based on type II maximum likelihood (ML-II) may fail and result in disappointing…
We recapitulate the Bayesian formulation of neural network based classifiers and show that, while sampling from the posterior does indeed lead to better generalisation than is obtained by standard optimisation of the cost function, even…
This paper seeks to provide a thorough account of the ubiquitous nature of the Bayesian paradigm in modern statistics, data science and artificial intelligence. Once maligned, on the one hand by those who philosophically hated the very idea…
In cell biology, statistical analysis means testing the hypothesis that there was no effect. This weak form of hypothesis testing neglects effect size, is universally misinterpreted, and is disastrously prone to error when combined with…
Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the prior/no-prior classification isn't exhaustive, and most…
Despite much research targeted at enabling conventional machine learning models to continually learn tasks and data distributions sequentially without forgetting the knowledge acquired, little effort has been devoted to account for more…