This paper studies the information interaction process in Bayesian theorem-based swarm systems. Through theoretical analysis, model construction, and simulation experiments, it explores how Bayesian decision-making utilizes information cascades to up...
In this study, the effect of day/night factor on the detection performance of the FY4A lightning mapping imager (LMI) is evaluated using the Bayesian theorem, and by comparing it to the measurements made by a ground-based low-frequency magnetic field...
To enhance frequency and active power control performance, this research proposes a decentralized robust optimal tuning approach for power grid frequency regulation support using energy storage systems (ESSs) as the primary source of grid-forming (GF...
The Gaussian mixture model (GMM) plays an important role in image segmentation, but the difficulty of GMM for modeling asymmetric, heavy-tailed, or multimodal distributions of pixel intensities significantly limits its application. One effective way...
We establish a Bernstein–von Mises (BvM) theorem for parametric competing-risks models under hybrid Type-I censoring, where observation stops at the random time
The geological and environmental conditions of the northern Shaanxi Loess Plateau are highly fragile, with frequent landslides and collapse disasters triggered by rainfall and human engineering activities. This research addresses the limitations of c...
In frequentist inference, minimizing the Hellinger distance between a kernel density estimate and a parametric family produces estimators that are both robust to outliers and statistically efficient when the parametric family contains the data-genera...
More than 8000 pedestrians were killed due to road crashes in Australia over the last 30 years. Pedestrians are assumed to be the most vulnerable users of roads. This susceptibility of pedestrians to road crashes conflicts with sustainable transporta...
Tail biting in pigs is an animal welfare problem, and tail biting should be prevented from developing into tail damage. One strategy could be to predict events of tail biting so that the farmer can make timely interventions in specific pens. In the c...
Let S be a Borel subset of a Polish space and F the set of bounded Borel functions
In the 1920s, the English philosopher W.E. Johnson introduced a characterization of the symmetric Dirichlet prior distribution in terms of its predictive distribution. This is typically referred to as Johnson’s “sufficientness” postulate, and it has...
The point estimation problems that emerge in Bayesian predictive inference are concerned with random quantities which depend on both observable and non-observable variables. Intuition suggests splitting such problems into two phases, the former relyi...
Once an emergency event (EE) happens, emergency decision-making (EDM) plays a key role in mitigating the loss. EDM is a complex problem. Compared with conventional decision-making problems, more experts participate in decision-making. It usually has...
Bayesian inference and decision analysis can be used to identify the most probable differential diagnosis and use those probabilities to identify the best choice of diagnostic or treatment among several alternatives. In this retrospective case analys...
The construction industry records higher accident rates than other industries, and thus, risk estimation is necessary to manage accident rates. Risk levels differ based on facility type and construction project size. In this sense, this study aims to...
Fuzzy Inference System behavior can be described qualitatively using a natural language, which is known as the expert-driven approach to handling non-statistical uncertainty. Generally, practical applications involve conceptualizing the problem by in...
This paper will defend a Bayesian form of argument from consciousness, which claims that central features of human consciousness provide rational support for theism when evaluated within a probabilistic framework. It focuses on rational deliberation,...
Are your perceptions, memories and observations merely a statistical fluctuation arising from of the thermal equilibrium of the universe, bearing no correlation to the actual past state of the universe? Arguments are given in the literature for and a...
The safety of offshore structures is a key topic in developing offshore oil and gas and offshore wind energy. Due to the harsh offshore environment and costly offshore field tests, offshore field trials to validate the theoretical models for offshore...
Lung cancer continues to rank as the leading cause of cancer deaths worldwide. One of the most promising techniques for early detection of cancerous cells relies on sputum cell analysis. This was the motivation behind the design and the development o...
In the cognitive and neural sciences, Bayesianism refers to a collection of concepts and methods stemming from various implementations of Bayes’ theorem, which is a formal way to calculate the conditional probability of a hypothesis being true...
The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptab...
Bayes’ Theorem is gaining acceptance in hydrology, but it is still far from standard practice to cast hydrologic analyses in a Bayesian context—especially in the realm of hydrologic practice. Three short discussions are presented to encou...
Exchangeability is a foundational concept in Bayesian statistics, crucial for ensuring the validity and generalizability of inferences from experimental data. This paper presents a theoretical and computational framework for understanding the role of...
Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction is the making of statements about past events based on current information. We present the foundations of quantum retrodicti...
This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy pr...
In deciding whether to accept or reject one theory rather than another, scientists often look at the evidence that agrees or disagrees with each theory. We formalize this method of comparison in terms of a 2-by-2 matrix where rows are the theories be...
The entropic dynamics (ED) approach to quantum mechanics is ideally suited to address the problem of measurement because it is based on entropic and Bayesian methods of inference that have been designed to process information and data. The approach s...
Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities; they should be calibrated to our evidence of physical probabilities; and they should otherwise equivocate sufficiently between the basic propos...
Bayes’ Theorem represents a mathematical formalization of the common sense. What we know about the world today is what we knew yesterday plus what the data told us. The lack of understanding of this concept is the source of many errors and wrong judg...
Studying cloud-to-ground lightning strokes and ground-strike points provides an alternative method of lightning mapping for lightning risk assessment. Various k-means algorithms have been used to verify the ground-strike points from lightning locatin...
Bayesian Network is one of the famous network models, and the loop cutset is one of the crucial structures for Bayesian Inference. In the Bayesian Network and its inference, how to measure the relationship between nodes is very important, because the...
We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Eq...
The Gibbs distribution of statistical physics is an exponential family of probability distributions, which has a mathematical basis of duality in the form of the Legendre transformation. Recent studies of complex systems have found lots of distributi...
The elucidation of protein dynamics, especially in the context of intrinsically disordered proteins, is challenging and requires cooperation between experimental studies and computational analysis. Molecular dynamics simulations are an essential inve...
A scientific method that proposes a value Y to estimate a target value
Bayesian networks (BNs) are probabilistic graphical models that leverage Bayes’ theorem to portray dependencies and cause-and-effect relationships between variables. These networks have gained prominence in the field of health sciences, particu...
A newborn girl had, from two weeks on, small bruises on varying body locations, but not on her chest. Her Armenian grandmother easily bruised, too. Her mother was diagnosed with hypermobility-type Ehlers-Danlos-Syndrome (hEDS), an autosomal dominant...
In science and technology, the application of mathematics and mathematical modelling is crucial. A more conceptual and axiomatic approach has been taken in developing the narrative from geometry in the enormous history of mathematics. Mathematics is...
For a one-dimensional time-fractional diffusion-wave equation, we investigate joint recovery of its fractional order and the initial velocity from measurements taken at one interior point. Uniqueness is proved through analytic continuation, Laplace t...
There are several mystifications and a couple of mysteries pertinent to MaxEnt. The mystifications, pitfalls and traps are set up mainly by an unfortunate formulation of Jaynes' die problem, the cause célèbre of MaxEnt. After discussing the mystifica...
We focus on a Bayesian inference framework for finite element (FE) model updating of a long-span cable-stayed bridge using long-term monitoring data collected from a wireless sensor network (WSN). A robust Bayesian inference method is proposed which...
The forecasting demand for new technology for which few historical data observations are available is difficult but essential to sustainable development. The current study suggests an alternative forecasting methodology based on a hazard rate model u...
We present a new word embedding technique in a (non-linear) metric space based on the shared membership of terms in a corpus of textual documents, where the metric is naturally defined by the Boolean algebra of all subsets of the corpus and a measure...
The entropy production in stochastic dynamical systems is linked to the structure of their causal representation in terms of Bayesian networks. Such a connection was formalized for bipartite (or multipartite) systems with an integral fluctuation theo...
In order to build a local electricity market (LEM), community members can trade electricity peer-to-peer (P2P) with their neighbors. This paper proposes a Hierarchical Bidding and Transaction Structure based on blockchain (HBTS). First, combined with...
Since the seminal work of Kolmogorov, probability theory has been based on measure theory, where the central components are so-called probability measures, defined as measures with total mass equal to 1. In Kolmogorov’s theory, a probability me...
We numerically study the evolution of the extrinsic energy density in the context of an inflationary regime at the background level in a five-dimensional model using a Bayesian analysis from a dynamic nested sampler (DYNESTY) code. By means of the Na...
A hydrometeor classification algorithm is developed by applying Bayes’ theorem to C-band polarimetric weather radar measurements. The Bayesian hydrometeor classification algorithm (BHCA) includes eight hydrometeor types: hail, rain, graupel, dr...
This paper reconsiders a powerful man-in-the-middle attack against Random-HB# and HB# authentication protocols, two prominent representatives of the HB family of protocols, which are built based on the Learning Parity in Noise (LPN) problem. A recent...
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