scholarly journals A very simple introduction to Bayesian statistics: From coin flips to insight

2020 ◽  
Author(s):  
Daniel Zuckerman
Keyword(s):  
Biological Sciences ◽  
Bayesian Analysis ◽  
Bayesian Statistics ◽  
Bayesian Approach ◽  
Prior Information ◽  
Model Parameters ◽  
Short Article ◽  
Absolute Minimum ◽  
Wet Lab ◽  
The Bayesian Approach

Bayesian statistical analyses are a growing part of the chemical and biological sciences for several reasons. Most importantly, the Bayesian approach of predicting underlying models based on data corresponds naturally with examination of complex systems, whether using wet-lab or computational means. The Bayesian structure also provides a systematic basis for estimating uncertainty in model parameters and permits incorporation of prior information in a quantitative and consistent way. While easy to state in words, these strengths of Bayesian analysis can be difficult to assimilate for beginners. This short article presents essential Bayesian concepts using very simple examples and the absolute minimum mathematics needed to maintain rigor.

scholarly journals Constraining absolute chronologies with the application of Bayesian analysis

ACTA IMEKO ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 14 ◽  
Author(s):  
Francesco Maspero ◽  
Emanuela Sibilia ◽  
Marco Martini
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Statistics ◽  
Case Studies ◽  
Bayesian Approach ◽  
Common Language ◽  
Multiple Data ◽  
The Common ◽  
The Bayesian Approach

<p class="Abstract"><span lang="EN-US">In this work the application of Bayesian statistics to archaeological problems will be discussed. In particular, three case studies will be analyzed, each presenting complex interpretative scenarios, and the most suitable way to solve them. It will be shown that the Bayesian approach allows to refine a dating when in presence of multiple data, even from different dating techniques. The Bayesian approach is presented as the common language between physicists, archaeologists and statisticians to perform more accurate evaluations on stratigraphies and chronologies.</span></p>

scholarly journals Bayesian probabilities for occurrence of large earthquakes in the seismogenic sources of Japan and Phillipine during the period 1998-2017

2001 ◽  
Vol 34 (4) ◽  
pp. 1619
Author(s):  
T. M. TSAPANOS ◽  
O. CH. GALANIS ◽  
S. D. MAVRIDOU ◽  
M. P. HELMl
Keyword(s):  
Seismic Hazard ◽  
Bayesian Statistics ◽  
Poisson Distribution ◽  
Bayesian Approach ◽  
Seismic Sources ◽  
Time Interval ◽  
Seismogenic Sources ◽  
The One ◽  
Large Earthquakes ◽  
The Bayesian Approach

The Bayesian statistics is adopted in 11 seismic sources of Japan and 14 of Philippine in order to estimate the probabilities of occurrence of large future earthquakes, assuming that earthquakes occurrence follows the Poisson distribution. The Bayesian approach applied represents the probability that a certain cut-off magnitude (or larger) will exceed in a given time interval of 20 years, that is 1998-2017. This cut-off magnitude is chosen the one with M=7.0 or greater. In this case we can consider these obtained probabilities as a seismic hazard presentation. More over curves are produced which present the fluctuation of the seismic hazard between these seismic sources. These graphs of varying probability are useful either for engineering or other practical purposes

scholarly journals Bayesian approach to evaluation of distance courses

2014 ◽  
Vol 55 ◽  
Author(s):  
Jonas Mockus ◽  
Irina Vinogradova
Keyword(s):  
Bayesian Approach ◽  
Prior Information ◽  
Uncertain Data ◽  
Distribution Functions ◽  
Fuzzy Sets Theory ◽  
Distance Courses ◽  
Sets Theory ◽  
Education Courses ◽  
The Bayesian Approach

Many real applications are using uncertain data This include expert decisions based on their subjective opinions, The uncertainty can be evaluated applying fuzzy sets theory or the methods of mathematical statistics. In this paper it is proposed to use the Bayesian approach by different distribution functions defining the expert opinion and some prior information. The results are illustrated evaluating the quality of distant education courses.

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.

scholarly journals Change Point Detection for Airborne Particulate Matter (PM2.5, PM10) by Using the Bayesian Approach

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 474 ◽  
Author(s):  
Muhammad Rizwan Khan ◽  
Biswajit Sarkar
Keyword(s):  
Particulate Matter ◽  
Bayesian Approach ◽  
Change Point ◽  
Airborne Particulate Matter ◽  
Change Point Detection ◽  
Model Parameters ◽  
Numerical Verification ◽  
Airborne Particulate ◽  
M 10 ◽  
The Bayesian Approach

Airborne particulate matter (PM) is a key air pollutant that affects human health adversely. Exposure to high concentrations of such particles may cause premature death, heart disease, respiratory problems, or reduced lung function. Previous work on particulate matter ( P M 2.5 and P M 10 ) was limited to specific areas. Therefore, more studies are required to investigate airborne particulate matter patterns due to their complex and varying properties, and their associated ( P M 10 and P M 2.5 ) concentrations and compositions to assess the numerical productivity of pollution control programs for air quality. Consequently, to control particulate matter pollution and to make effective plans for counter measurement, it is important to measure the efficiency and efficacy of policies applied by the Ministry of Environment. The primary purpose of this research is to construct a simulation model for the identification of a change point in particulate matter ( P M 2.5 and P M 10 ) concentration, and if it occurs in different areas of the world. The methodology is based on the Bayesian approach for the analysis of different data structures and a likelihood ratio test is used to a detect change point at unknown time (k). Real time data of particulate matter concentrations at different locations has been used for numerical verification. The model parameters before change point ( θ ) and parameters after change point ( λ ) have been critically analyzed so that the proficiency and success of environmental policies for particulate matter ( P M 2.5 and P M 10 ) concentrations can be evaluated. The main reason for using different areas is their considerably different features, i.e., environment, population densities, and transportation vehicle densities. Consequently, this study also provides insights about how well this suggested model could perform in different areas.

Bayesian Statistics and Political Recruitment: A Comment

1976 ◽  
Vol 6 (1) ◽  
pp. 124-125
Author(s):  
Paul Whiteley
Keyword(s):  
Bayesian Statistics ◽  
Bayesian Approach ◽  
Subjective Probability ◽  
Analytical Techniques ◽  
Political Activism ◽  
Background Characteristics ◽  
Political Recruitment ◽  
Political Activist ◽  
The Individual ◽  
The Bayesian Approach

In an important contribution to the improvement of data analytical techniques in political science, Budge and Farlie examine the predictive success of various background characteristics in determining political activism [Ian Budge and Dennis Farlie, ‘Political Recruitment and Dropout’, this Journal, v (1975), 33–68]. The authors use the framework of Bayesian statistics, in which the subjective probability that a given individual will be a political activist is revised in the light of sample information about the background characteristics of activists to give a posterior (i.e. after the information or event) probability that the individual is an activist. Unfortunately, as the authors admit, they do not utilize fully all the components of the Bayesian approach.

scholarly journals A Bayesian Approach to Estimating Reciprocal Effects with the Bivariate STARTS Model using Markov Chain Monte Carlo

2021 ◽  
Author(s):  
Oliver Lüdtke ◽  
Alexander Robitzsch ◽  
Esther Ulitzsch
Keyword(s):  
Bayesian Approach ◽  
Prior Distribution ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Reciprocal Effects ◽  
Ml Estimation ◽  
Model Parameterization ◽  
Lagged Effects ◽  
The Bayesian Approach ◽  
Over Time

The bivariate Stable Trait, AutoRegressive Trait, and State (STARTS) model provides a general approach for estimating reciprocal effects between constructs over time. However, previous research has shown that this model is difficult to estimate using the maximum likelihood (ML) method (e.g., nonconvergence). In this article, we introduce a Bayesian approach for estimating the bivariate STARTS model and implement it in the software Stan. We discuss issues of model parameterization and show how appropriate prior distributions for model parameters can be selected. Specifically, we propose the four-parameter beta distribution as a flexible prior distribution for the autoregressive and cross-lagged effects. Using a simulation study, we show that the proposed Bayesian approach provides more accurate estimates than ML estimation in challenging data constellations. An example is presented to illustrate how the Bayesian approach can be used to stabilize the parameter estimates of the bivariate STARTS model.

scholarly journals Principles of Statistical Inference: Likelihood and the Bayesian Paradigm

2010 ◽  
Vol 16 ◽  
pp. 1-18 ◽  
Author(s):  
Steve C. Wang
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Bayesian Approach ◽  
Subjective Probability ◽  
Prior Information ◽  
Maximum Likelihood Estimators ◽  
Likelihood Ratio Tests ◽  
Bayesian Paradigm ◽  
Point Estimators ◽  
The Bayesian Approach

We review two foundations of statistical inference, the theory of likelihood and the Bayesian paradigm. We begin by applying principles of likelihood to generate point estimators (maximum likelihood estimators) and hypothesis tests (likelihood ratio tests). We then describe the Bayesian approach, focusing on two controversial aspects: the use of prior information and subjective probability. We illustrate these analyses using simple examples.

Use of Measured Vibration of In-Situ Sleeper for Detecting Underlying Railway Ballast Damage

2015 ◽  
Vol 15 (08) ◽  
pp. 1540026 ◽  
Author(s):  
Q. Hu ◽  
H. F. Lam ◽  
S. A. Alabi
Keyword(s):  
Damage Detection ◽  
Bayesian Approach ◽  
Model Updating ◽  
Probabilistic Approach ◽  
Modeling Method ◽  
Detection Methods ◽  
Model Parameters ◽  
Railway Ballast ◽  
Continuous Modeling ◽  
The Bayesian Approach

The identification of railway ballast damage under a concrete sleeper is investigated by following the Bayesian approach. The use of a discrete modeling method to capture the distribution of ballast stiffness under the sleeper introduces artificial stiffness discontinuities between different ballast regions. This increases the effects of modeling errors and reduces the accuracy of the ballast damage detection results. In this paper, a continuous modeling method was developed to overcome this difficulty. The uncertainties induced by modeling error and measurement noise are the major difficulties of vibration-based damage detection methods. In the proposed methodology, Bayesian probabilistic approach is adopted to explicitly address the uncertainties associated with the identified model parameters. In the model updating process, the stiffness of the ballast foundation is assumed to be continuous along the sleeper by using a polynomial of order N. One of the contributions of this paper is to calculate the order N conditional on a given set of measurement utilizing the Bayesian model class selection method. The proposed ballast damage detection methodology was verified with vibration data obtained from a segment of full-scale ballasted track under laboratory conditions, and the experimental verification results are very encouraging showing that it is possible to use the Bayesian approach along with the newly developed continuous modeling method for the purpose of ballast damage detection.

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