Bayesian Statistics

2021 ◽  
pp. 165-180
Author(s):  
Timothy E. Essington
Keyword(s):  
Parameter Estimation ◽  
Statistical Analysis ◽  
Model Selection ◽  
Bayesian Statistics ◽  
Bayes Theorem ◽  
Bayesian Parameter Estimation ◽  
Bayesian Approaches ◽  
Frequentist Statistics ◽  
The Difference ◽  
The Bayesian Approach

The chapter “Bayesian Statistics” gives a brief overview of the Bayesian approach to statistical analysis. It starts off by examining the difference between frequentist statistics and Bayesian statistics. Next, it introduces Bayes’ theorem and explains how the theorem is used in statistics and model selection, with the prosecutor’s fallacy given as a practice example. The chapter then goes on to discuss priors and Bayesian parameter estimation. It concludes with some final thoughts on Bayesian approaches. The chapter does not answer the question “Should ecologists become Bayesian?” However, to the extent that alternative models can be posed as alternative values of parameters, Bayesian parameter estimation can help assign probabilities to those hypotheses.

scholarly journals Simple and Two-Level Hierarchical Bayesian Approaches for Parameter Estimation with One- and Two-Layer Evapotranspiration Models of Crop Fields

Water ◽  
2021 ◽  
Vol 13 (24) ◽  
pp. 3607
Author(s):  
Shutaro Shiraki ◽  
Aung Kyaw Thu ◽  
Yutaka Matsuno ◽  
Yoshiyuki Shinogi
Keyword(s):  
Parameter Estimation ◽  
Agricultural Fields ◽  
Growth Stages ◽  
Hierarchical Bayesian ◽  
Potential Importance ◽  
Seasonal Fluctuations ◽  
Bayesian Approaches ◽  
Crop Fields ◽  
Crop Growth Stages ◽  
The Difference

The two-layer Shuttleworth–Wallace (SW) evapotranspiration (ET) model has been widely used for predicting ET with good results. Since the SW model has a large number of specific parameters, these parameters have been estimated using a simple non-hierarchical Bayesian (SB) approach. To further improve the performance of the SW model, we aimed to assess parameter estimation using a two-level hierarchical Bayesian (HB) approach that takes into account the variation in observed conditions through the comparison with a traditional one-layer Penman–Monteith (PM) model. The difference between the SB and HB approaches were evaluated using a field-based ET dataset collected from five agricultural fields over three seasons in Myanmar. For a calibration period with large variation in environmental factors, the models with parameters calibrated by the HB approach showed better fitting to observed ET than that with parameters estimated using the SB approach, indicating the potential importance of accounting for seasonal fluctuations and variation in crop growth stages. The validation of parameter estimation showed that the ET estimation of the SW model with calibrated parameters was superior to that of the PM model, and the SW model provided acceptable estimations of ET, with little difference between the SB and HB approaches.

Bayesian Basics and the Scientific Hypothesis

2019 ◽  
pp. 143-160
Author(s):  
Bradley E. Alger
Keyword(s):  
Model Selection ◽  
Hypothesis Testing ◽  
Conceptual Framework ◽  
Bayesian Statistics ◽  
Bayesian Methods ◽  
Bayes Theorem ◽  
Testing Framework ◽  
Parameter Evaluation ◽  
Bayesian Procedures ◽  
Scientific Hypothesis

This chapter covers the basics of Bayesian statistics, emphasizing the conceptual framework for Bayes’ Theorem. It works through several iterations of the theorem to demonstrate how the same equation is applied in different circumstances, from constructing and updating models to parameter evaluation, to try to establish an intuitive feel for it. The chapter also covers the philosophical underpinnings of Bayesianism and compares them with the frequentist perspective described in Chapter 5. It addresses the question of whether Bayesians are inductivists. Finally, the chapter shows how the Bayesian procedures of model selection and comparison can be pressed into service to allow Bayesian methods to be used in hypothesis testing in essentially the same way that various p-tests are used in the frequentist hypothesis testing framework.

Bayesian Statistics in Sociology: Past, Present, and Future

2019 ◽  
Vol 45 (1) ◽  
pp. 47-68 ◽  
Author(s):  
Scott M. Lynch ◽  
Bryce Bartlett
Keyword(s):  
Social Science ◽  
Bayesian Statistics ◽  
Bayesian Approach ◽  
Bayesian Methods ◽  
Bayes Theorem ◽  
Widespread Application ◽  
Software Packages ◽  
The Future ◽  
Direct Use ◽  
The Bayesian Approach

Although Bayes’ theorem has been around for more than 250 years, widespread application of the Bayesian approach only began in statistics in 1990. By 2000, Bayesian statistics had made considerable headway into social science, but even now its direct use is rare in articles in top sociology journals, perhaps because of a lack of knowledge about the topic. In this review, we provide an overview of the key ideas and terminology of Bayesian statistics, and we discuss articles in the top journals that have used or developed Bayesian methods over the last decade. In this process, we elucidate some of the advantages of the Bayesian approach. We highlight that many sociologists are, in fact, using Bayesian methods, even if they do not realize it, because techniques deployed by popular software packages often involve Bayesian logic and/or computation. Finally, we conclude by briefly discussing the future of Bayesian statistics in sociology.

scholarly journals Inference of experimental radial impurity transport on Alcator C-Mod: Bayesian parameter estimation and model selection

2020 ◽  
Vol 60 (12) ◽  
pp. 126014
Author(s):  
F. Sciortino ◽  
N.T. Howard ◽  
E.S. Marmar ◽  
T. Odstrcil ◽  
N.M. Cao ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Model Selection ◽  
Bayesian Parameter Estimation ◽  
Impurity Transport

scholarly journals What is a Bayes Factor?

2020 ◽  
Author(s):  
Xenia Schmalz ◽  
José Biurrun Manresa ◽  
Lei Zhang
Keyword(s):  
Bayesian Statistics ◽  
Bayes Factor ◽  
Bayes Factors ◽  
Prior Beliefs ◽  
Software Packages ◽  
Alternative Approach ◽  
General Logic ◽  
Frequentist Statistics ◽  
Current Article ◽  
The Bayesian Approach

The use of Bayes Factors is becoming increasingly common in psychological sciences. Thus, it is important that researchers understand the logic behind the Bayes Factor in order to correctly interpret it, and the strengths of weaknesses of the Bayesian approach. As education for psychological scientists focuses on Frequentist statistics, resources are needed for researchers and students who want to learn more about this alternative approach. The aim of the current article is to provide such an overview to a psychological researcher. We cover the general logic behind Bayesian statistics, explain how the Bayes Factor is calculated, how to set the priors in popular software packages, to reflect the prior beliefs of the researcher, and finally provide a set of recommendations and caveats for interpreting Bayes Factors.

scholarly journals Investigative advising: a job for Bayes

2021 ◽  
Author(s):  
Jared C. Allen
Keyword(s):  
Decision Support ◽  
Bayes Theorem ◽  
The Other ◽  
Bayesian Approaches ◽  
Bayesian Paradigm ◽  
Rate Information ◽  
Statistical Approaches ◽  
To Come ◽  
The Bayesian Approach ◽  
Investigative Advising

Background: Bayesian approaches to police decision support offer an improvement upon more commonly used statistical approaches. Common approaches to case decision support often involve using frequencies from cases similar to the case under consideration to come to an isolated likelihood that a given suspect either a) committed the crime or b) has a given characteristic or set of characteristics. The Bayesian approach, in contrast, offers formally contextualized estimates and utilizes the formal logic desired by investigators. Findings: Bayes’ theorem incorporates the isolated likelihood as one element of a three-part equation, the other parts being 1) what was known generally about the variables in the case prior to the case occurring (the scientific-theoretical priors) and 2) the relevant base rate information that contextualizes the evidence obtained (the event context). These elements are precisely the domain of decision support specialists (investigative advisers), and the Bayesian paradigm is uniquely apt for combining them into contextualized estimates for decision support. Conclusions: By formally combining the relevant knowledge, context, and likelihood, Bayes’ theorem can improve the logic, accuracy, and relevance of decision support statements.

Sign in / Sign up

Export Citation Format

Share Document