scholarly journals Being Bayesian: Discussions from the Perspectives of Stakeholders and Hydrologists

Water ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 461
Author(s):  
Ty P.A. Ferre
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Approach ◽  
Bayes Theorem ◽  
Standard Practice ◽  
Natural Approach ◽  
The Third ◽  
Optimal Observation ◽  
Bayes Theory ◽  
Hydrologic Analysis ◽  
Natural Choice

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 encourage more complete adoption of a Bayesian approach. The first, aimed at a stakeholder audience, seeks to explain that an informal Bayesian analysis is the default approach that we all take to any decision made under uncertainty. The second, aimed at a general hydrologist audience, seeks to establish multi-model approaches as the natural choice for Bayesian hydrologic analysis. The goal of this discussion is to provide a bridge from the stakeholder’s natural approach to a more formal, quantitative Bayesian analysis. The third discussion is targeted to a more advanced hydrologist audience, suggesting that some elements of hydrologic practice do not yet reflect a Bayesian philosophy. In particular, an example is given that puts Bayes Theory to work to identify optimal observation sets before data are collected.

scholarly journals Bayesian analysis of data from segmented super-resolution images for quantifying protein clustering

2020 ◽  
Vol 22 (3) ◽  
pp. 1107-1114
Author(s):  
Tina Košuta ◽  
Marta Cullell-Dalmau ◽  
Francesca Cella Zanacchi ◽  
Carlo Manzo
Keyword(s):  
Bayesian Analysis ◽  
Relative Abundance ◽  
Bayesian Approach ◽  
Super Resolution ◽  
Molecular Aggregates ◽  
Protein Clustering ◽  
Precise Quantification

A Bayesian approach enables the precise quantification of the relative abundance of molecular aggregates of different stoichiometry from segmented super-resolution images.

A Survey of Bayesian Data Mining

Data Mining ◽  
2011 ◽  
pp. 1-26 ◽  
Author(s):  
Stefan Arnborg
Keyword(s):  
Data Mining ◽  
Bayesian Analysis ◽  
Graphical Models ◽  
Bayesian Approach ◽  
Data Sets ◽  
Media Distribution ◽  
Dirichlet Prior ◽  
Approach Problem ◽  
The Bayesian Approach ◽  
Selection Of

This chapter reviews the fundamentals of inference, and gives a motivation for Bayesian analysis. The method is illustrated with dependency tests in data sets with categorical data variables, and the Dirichlet prior distributions. Principles and problems for deriving causality conclusions are reviewed, and illustrated with Simpson’s paradox. The selection of decomposable and directed graphical models illustrates the Bayesian approach. Bayesian and EM classification is shortly described. The material is illustrated on two cases, one in personalization of media distribution, one in schizophrenia research. These cases are illustrations of how to approach problem types that exist in many other application areas.

A Bayesian Approach to the Stereo Correspondence Problem

2002 ◽  
Vol 14 (6) ◽  
pp. 1371-1392 ◽  
Author(s):  
Jenny C. A. Read
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Approach ◽  
Probabilistic Approach ◽  
Correspondence Problem ◽  
Stereo Correspondence ◽  
Retinal Position ◽  
Single Solution ◽  
Ill Posed ◽  
The Right ◽  
Limiting Case

I present a probabilistic approach to the stereo correspondence problem. Rather than trying to find a single solution in which each point in the left retina is assigned a partner in the right retina, all possible matches are considered simultaneously and assigned a probability of being correct. This approach is particularly suitable for stimuli where it is inappropriate to seek a unique partner for each retinal position—for instance, where objects occlude each other, as in Panum's limiting case. The probability assigned to each match is based on a Bayesian analysis previously developed to explain psychophysical data (Read, 2002). This provides a convenient way to incorporate constraints that enable the ill-posed correspondence problem to be solved. The resulting model behaves plausibly for a variety of different stimuli.

LOSS OF QUANTUM COHERENCE DUE TO TOPOLOGICAL CHANGES: A TOY MODEL

1988 ◽  
Vol 03 (13) ◽  
pp. 1231-1242 ◽  
Author(s):  
G.V. LAVRELASHVILI ◽  
V.A. RUBAKOV ◽  
P.G. TINYAKOV
Keyword(s):  
State Vector ◽  
Arbitrary Number ◽  
Quantum Coherence ◽  
The Third ◽  
Natural Choice ◽  
Topological Changes

We present a toy model for the third quantization theory of topological changes. We find that the natural choice of the “Heisenberg” state vector of the system with one large universe and an arbitrary number of small universes gives rise to the loss of quantum coherence.

Bayesian Analysis of the Brown–Proschan Model

2015 ◽  
Vol 30 (1) ◽  
Author(s):  
Dinh Tuan Nguyen ◽  
Yann Dijoux ◽  
Mitra Fouladirad
Keyword(s):  
Weibull Distribution ◽  
Bayesian Analysis ◽  
Failure Rate ◽  
Bayesian Approach ◽  
Real Data ◽  
Posterior Distributions ◽  
Imperfect Maintenance ◽  
Maintenance Model ◽  
Informative Prior Distributions

AbstractThe paper presents a Bayesian approach of the Brown–Proschan imperfect maintenance model. The initial failure rate is assumed to follow a Weibull distribution. A discussion of the choice of informative and non-informative prior distributions is provided. The implementation of the posterior distributions requires the Metropolis-within-Gibbs algorithm. A study on the quality of the estimators of the model obtained from Bayesian and frequentist inference is proposed. An application to real data is finally developed.

scholarly journals Forecasting undetected COVID-19 cases in Small Island Developing States using Bayesian approach

2020 ◽  
Author(s):  
Andrio Adwibowo
Keyword(s):  
Health Systems ◽  
Bayesian Approach ◽  
Bayes Theorem ◽  
Fundamental Question ◽  
Small Island ◽  
Robust Estimator ◽  
Small Island Developing States ◽  
Modeling Tool ◽  
Current Health

In dealing with the COVID-19, the fundamental question is how many actually undetected cases are going around regarding the capabilities of current health systems to contain the virus?. Due to a large number of asymptomatic cases, most COVID-19 cases are possibly undetected. For that reason, this study aims to provide an efficient, versatile, easy to compute, and robust estimator for the number of undetected cases using Bayes theorem based on the actual COVID-19 cases. This theorem is applied to 25 Small Island Developing States (SIDS) due to SIDS vulnerability. The results in this study forecast that possibly undetected COVID-19 cases are approximately 4 times larger than the numbers of actual COVID-19 cases as observed. This finding highlights the importance of using modeling tool to get the better and comprehensive of current COVID-19 cases and to take immediately precaution approaches to mitigate the growing numbers of COVID-19 cases as well.

scholarly journals Introdução à estatística bayesiana aplicada à linguística

2021 ◽  
Author(s):  
Guilherme D. Garcia ◽  
Ronaldo Mangueira Lima Jr
Keyword(s):  
Data Analysis ◽  
Simple Model ◽  
Bayesian Analysis ◽  
Regression Model ◽  
Bayesian Approach ◽  
Linguistic Data ◽  
Bayesian Data Analysis ◽  
Frequentist Statistics

Neste artigo, apresentamos os conceitos básicos de uma análise estatística bayesiana e demonstramos como rodar um modelo de regressão utilizando a linguagem R. Ao longo do artigo, comparamos estatística bayesiana e estatística frequentista, destacamos as diferentes vantagens apresentadas por uma abordagem bayesiana, e demonstramos como rodar um modelo simples e visualizar efeitos de interesse. Por fim, sugerimos leituras adicionais aos interessados neste tipo de análise.In this paper, we introduce the basics of Bayesian data analysis and demonstrate how to run a regression model in R using linguistic data. Throughout the paper, we compare Bayesian and Frequentist statistics, highlighting the different advantages of a Bayesian approach. We also show how to run a simple model and how to visualize effects of interest. Finally, we suggest additional readings to those interested in Bayesian analysis more generally.

Yielding stability of early maturing potato varieties: Bayesian analysis

2020 ◽  
pp. 1-10
Author(s):  
M. Przystalski ◽  
T. Lenartowicz
Keyword(s):  
Expected Utility ◽  
Bayesian Approach ◽  
Decision Process ◽  
Field Trials ◽  
The Third ◽  
Stable Variety ◽  
Early Maturing ◽  
Theoretic Problem ◽  
The Bayesian Approach ◽  
Variety Testing

Abstract Field trials conducted in multiple years across several locations play an essential role in plant breeding and variety testing. Usually, the analysis of the series of field trials is performed using a two-stage approach, where each combination of year and site is treated as environment. In variety testing based on the results from the analysis, the best varieties are recommended for cultivation. Under a Bayesian approach, the variety recommendation process can be treated as a formal decision theoretic problem. In the present study, we describe Bayesian counterparts of two stability measures and compare the varieties in terms of the posterior expected utility. Using the described methodology, we identify the most stable and highest tuber yielding varieties in the Polish potato series of field trials conducted from 2016 to 2018. It is shown that variety Arielle was the highest yielding, the third most stable variety and was the second best variety in terms of the posterior expected utility. In the present work, application of the Bayesian approach allowed us to incorporate the prior knowledge about the tested varieties and offered a possibility of treating the variety recommendation process as a formal decision process.

scholarly journals Bayesian Inference in Auditing With Partial Prior Information Using Maximum Entropy Priors

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 919
Author(s):  
María Martel-Escobar ◽  
Francisco-José Vázquez-Polo ◽  
Agustín Hernández-Bastida 
Keyword(s):  
Bayesian Inference ◽  
Bayesian Analysis ◽  
Maximum Entropy ◽  
Prior Information ◽  
Likelihood Function ◽  
Bayes Theorem ◽  
Main Interest ◽  
Book Value ◽  
Numerical Examples ◽  
Modified Likelihood

Problems in statistical auditing are usually one–sided. In fact, the main interest for auditors is to determine the quantiles of the total amount of error, and then to compare these quantiles with a given materiality fixed by the auditor, so that the accounting statement can be accepted or rejected. Dollar unit sampling (DUS) is a useful procedure to collect sample information, whereby items are chosen with a probability proportional to book amounts and in which the relevant error amount distribution is the distribution of the taints weighted by the book value. The likelihood induced by DUS refers to a 201–variate parameter p but the prior information is in a subparameter θ linear function of p , representing the total amount of error. This means that partial prior information must be processed. In this paper, two main proposals are made: (1) to modify the likelihood, to make it compatible with prior information and thus obtain a Bayesian analysis for hypotheses to be tested; (2) to use a maximum entropy prior to incorporate limited auditor information. To achieve these goals, we obtain a modified likelihood function inspired by the induced likelihood described by Zehna (1966) and then adapt the Bayes’ theorem to this likelihood in order to derive a posterior distribution for θ . This approach shows that the DUS methodology can be justified as a natural method of processing partial prior information in auditing and that a Bayesian analysis can be performed even when prior information is only available for a subparameter of the model. Finally, some numerical examples are presented.

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