A Passive Source Location Method in a Shallow Water Waveguide with a Single Sensor Based on Bayesian Theory by Xiaoman Li, Shengchun Piao, Minghui Zhang, Yan Liu

“…In this paper, the source location was transformed to the inversion of the source location and environmental parameters, which can be estimated accurately based on the multi-dimensional posterior probability density (PPD). This method is less limited by environmental factors, and the accuracy of inversion results can be analyzed according to the PPD of inversion parameters, which has higher reliability and a wider application scope. …”
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A Bayesian approach to the tomographic problem with constraints from geodynamic modeling: Application to a synthetic subduction zone by John Keith Magali, Thomas Bodin

“…The final output is an ensemble of models of L, R, θ, Tc and E cast in terms of a posterior probability distribution and their uncertainty limits. …”
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pplacer: linear time maximum-likelihood and Bayesian phylogenetic placement of sequences onto a fixed reference tree by Kodner Robin B, Matsen Frederick A, Armbrust E Virginia

“…<monospace>Pplacer</monospace> features calculation of the posterior probability of a placement on an edge, which is a statistically rigorous way of quantifying uncertainty on an edge-by-edge basis. …”
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Conditional Entropy and Location Error in Indoor Localization Using Probabilistic Wi-Fi Fingerprinting by Rafael Berkvens, Herbert Peremans, Maarten Weyn

“…In contrast, we propose the use of the conditional entropy of a posterior probability distribution as a complementary measure of uncertainty. …”
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Constructing training set using distance between learnt graphical models of time series data on patient physiology, to predict disease scores. by Dalia Chakrabarty, Kangrui Wang, Gargi Roy, Akash Bhojgaria, Chuqiao Zhang, Jiri Pavlu, Joydeep Chakrabartty

“…In our work, the VOD-score of each patient in a retrospective cohort, is defined as the distance between the (posterior) probability of a random graph variable-given the inter-variable partial correlation matrix of the time series data on variables that represent different aspects of patient physiology-and that given such time series data of an arbitrarily-selected reference patient. …”
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Bland–Altman Limits of Agreement from a Bayesian and Frequentist Perspective by Oke Gerke, Sören Möller

“…While a frequentist confidence interval represents a range of nonrejectable values for null hypothesis significance testing of H₀: θ₁ ≤ −δ or θ₂ ≥ δ against H₁: θ₁ > −δ and θ₂ < δ, with a predefined benchmark value δ, Bayesian analysis allows for direct interpretation of both the posterior probability of the alternative hypothesis and the likelihood of parameter values. …”
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Information-Theoretic Models for Physical Observables by D. Bernal-Casas, J. M. Oller

“…In parallel, we find that the global probability density function of the collective mode of a set of quantum harmonic oscillators at the lowest energy level equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. …”
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Probabilistic calibration of a Greenland Ice Sheet model using spatially resolved synthetic observations: toward projections of ice mass loss with uncertainties by W. Chang, P. J. Applegate, M. Haran, K. Keller

“…Specifically, we estimate the joint posterior probability density function of model parameters using Gaussian process-based emulation and calibration. …”
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Building Extraction from High Spatial Resolution Remote Sensing Images via Multiscale-Aware and Segmentation-Prior Conditional Random Fields by Qiqi Zhu, Zhen Li, Yanan Zhang, Qingfeng Guan

“…The conditional random field (CRF) is directly modelled by the maximum posterior probability, which can make full use of the spatial neighbourhood information of both labelled and observed images. …”
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Continuous measures of confidence in direction of environmental trends at site and other spatial scales by T, H Snelder, C Fraser, A.L. Whitehead

“…As an alternative to NHST, we propose a continuous measure of confidence in the direction of an individual site trend based on the posterior probability distribution. Confidence that the trend direction is correctly inferred (i.e., that the assessed trend direction has the same sign as the population value) is expressed as a probability. …”
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Complete mitochondrial genome of Amorophaga japonica Robinson, 1986 (Lepidoptera: Tineidae) by Jong Seok Kim, Min Jee Kim, Sung Soo Kim, Iksoo Kim

“…Phylogenetic analyses with concatenated sequences of the 13 PCGs and two rRNA genes using the Bayesian inference method placed A. japonica in Tineidae as a sister to the cofamilial species, Tineola bisselliella, with high nodal support (Bayesian posterior probability [BPP] = 0.99), presenting the superfamily Tineoidea in a monophyletic group with a BPP of 0.99. …”
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Energy-Efficient Time Synchronization Based on Nonlinear Clock Skew Tracking for Underwater Acoustic Networks by Di Liu, Min Zhu, Dong Li, Xiaofang Fang, Yanbo Wu

“…To combat the nonlinear and non-Gaussian problem, the particle filter (PF)-based algorithm is used to track the time-varying clock state and an accurate posterior probability density function under the GMM error model is also given in PF. …”
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Overview of Research on Bayesian Inference and Parallel Tempering by ZHAN Jin, WANG Xuefei, CHENG Yurong, YUAN Ye

“…Bayesian inference is one of the main problems in statistics.It aims to update the prior knowledge of the probability distribution model based on the observation data.For the posterior probability that cannot be observed or is difficult to directly calculate,which is often encountered in real situations,Bayesian inference can obtain a good approximation.It is a kind of important method based on Bayesian theorem.Many machine learning problems involve the process of simulating and approximating the target distribution of various types of feature data,such as classification models,topic modeling,and data mining.Therefore,Bayesian inference has shown important and unique research value in the field of machine learning.With the beginning of the big data era,the experimental data collected by researchers through actual information is very large,resulting in the complex distribution of targets to be simulated and calculated.How to perform accurate and time-efficient approximation inferences on target distributions under complex data has become a major and difficult point in Bayesian inference problems today.Aiming at the infe-rence problem under this complex distribution model,this paper systematically introduces and summarizes the two main methods for solving Bayesian inference problems in recent years,which are variational inference and sampling methods.Firsly,this paper gives the problem definition and theoretical knowledge of variational inference,introduces in detail the variational inference algorithm based on coordinate ascent,and gives the existing applications and future prospects of this method.Next,it reviews the research results of existing sampling methods at home and abroad,gives the specific algorithm procedure of various main sampling methods,as well as summarizes and compares the characteristics,advantages and disadvantages of these methods.Finally,this paper introduces parallel tempering technique,outlines its basic theories and methods,discusses the combination and application of parallel tempering and sampling methods,and explores new research directions for the future development of Bayesian inference problems.…”
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A Variational Bayesian-Based Simultaneous Localization and Mapping Method for Autonomous Underwater Vehicle Navigation by Pengcheng Mu, Xin Zhang, Ping Qin, Bo He

“…Firstly, the VB method is used to estimate the joint posterior probability of the AUV path and observation noise. …”
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Evaluating the effectiveness of a brief digital procrastination intervention targeting university students in Sweden: study protocol for the Focus randomised controlled trial by Marcus Bendtsen, Katarina Åsberg

“…Monte Carlo simulations (assuming a standardised effect of 0.35 Cohen’s d of the intervention on the primary outcome, to at least 80% of the time estimate a posterior probability of effect of at least 95%) indicated that data from 1000 participants are required for analysis, meaning that 2000 participants are required to be randomised when assuming a 50% attrition rate. …”
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The diagnostic utility of endocytoscopy for the detection of esophageal lesions: A systematic review and meta-analysis by Lu Wang, Bofu Tang, Feifei Liu, Zhenyu Jiang, Xianmei Meng

“…Meta-analysis results showed that the combined sensitivity (SE), specificity (SP), positive likelihood ratio (PLR), negative likelihood ratio (NLR), diagnostic odds ratio (DOR) and positive posterior probability (PPP) of ECS screening for early EC were 0.95 [95%CI: 0.84, 0.98], 0.92 [95%CI: 0.83, 0.96], 11.8 [95%CI: 5.3, 26.1], 0.06 [95%CI: 0.02, 0.18], 203 [95%CI: 50, 816], and 75%, respectively. …”
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The joint application of a metaheuristic algorithm and a Bayesian statistics approach for uncertainty and stability assessment of nonlinear magnetotelluric data by Mukesh, K. Sarkar, U. K. Singh

“…As a result, we used a Bayesian statistical technique to construct and assess the posterior probability density function (PDF) rather than picking the global model based on the lowest misfit error. …”
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Association of hypernatremia with mortality in patients with COVID‐19: A systematic review and meta‐analysis by Yongzhi Ma, Panjuan Zhang, Ming Hou

“…Meta‐analysis showed that hypernatremia was associated with mortality in patients with COVID‐19 [OR = 4.15, 95% CI (2.95–5.84), p = .002, I² = 66.7%] with a sensitivity of 0.36 [0.26, 0.48] and a specificity of 0.88 [0.83, 0.91]. The posterior probability of mortality was 42% in patients with COVID‐19 hypernatremia and 15% in patients who did not have COVID‐19 hypernatremia. …”
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Validation of a Novel ELISA for the Diagnosis of Hemorrhagic Septicemia in Dairy Cattle from Thailand Using a Bayesian Approach by Tawatchai Singhla, Pallop Tankaew, Nattawooti Sthitmatee

“…Estimated sensitivity and estimated specificity of the ELISA test were 90.5% (95% posterior probability interval (PPI) = 83.2–95.4%) and 70.8% (95% PPI = 60.8–79.8%), respectively. …”
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Ecological and morphological differentiation among COI haplotype groups in the plant parasitic nematode species Mesocriconema xenoplax by Matczyszyn Julianne N., Harris Timothy, Powers Kirsten, Everhart Sydney E., Powers Thomas O.

“…Maximum-likelihood and Bayesian phylogenies recognized seven COI HG (≥99/0.99 posterior probability/bootstrap value). Species delimitation metrics largely supported the genetic integrity of the HG. …”
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