Bayesian Inference

2021 ◽  
pp. 17-19
Author(s):  
Arnaud Dufays
Keyword(s):  
Bayesian Inference ◽  
Bayesian Statistics ◽  
Statistical Method ◽  
Bayesian Approach ◽  
Posterior Probability ◽  
Complex Problem ◽  
Sampling Techniques ◽  
Computational Power ◽  
Analytical Computation ◽  
The Bayesian Approach

This chapter evaluates Bayesian inference, which refers to the Bayesian statistical method for estimating the parameters of a model and for testing a hypothesis. It relies on subjective statistics and extensively uses Bayes’s theorem. In the early 1990s, Bayesian statistics boomed with the emergence of sampling techniques. These new tools rely on the computational power to sample from (rather than evaluate) the posterior probability. However, the main drawback of the Bayesian approach lies in the computation of the posterior probability. The analytical computation of the posterior probability is a complex problem for any application, and this has limited Bayesian statistics for years.

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

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 Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate from Microwave Observations

2006 ◽  
Vol 45 (8) ◽  
pp. 1073-1095 ◽  
Author(s):  
J. Christine Chiu ◽  
Grant W. Petty
Keyword(s):  
Probability Distribution ◽  
Bayesian Approach ◽  
Posterior Probability ◽  
Rain Rate ◽  
Sensitivity Analyses ◽  
Bayesian Algorithm ◽  
Additional Advantage ◽  
Posterior Probability Distribution ◽  
Surface Rain Rate ◽  
The Bayesian Approach

Abstract A new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) over the ocean is presented, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain-rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes’s theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance the understanding of theoretical benefits of the Bayesian approach, sensitivity analyses have been conducted based on two synthetic datasets for which the “true” conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism, but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak owing to saturation effects. It is also suggested that both the choice of the estimators and the prior information are crucial to the retrieval. In addition, the performance of the Bayesian algorithm herein is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

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.

Bayesian statistics

2010 ◽  
pp. 477-497
Author(s):  
Janet L. Peacock ◽  
Philip J. Peacock
Keyword(s):  
Bayesian Statistics ◽  
Bayesian Approach ◽  
Bayesian Methods ◽  
Posterior Distributions ◽  
Bayesian Analyses ◽  
Prior Distributions ◽  
Unknown Quantity ◽  
Frequentist Approach ◽  
Pros And Cons ◽  
The Bayesian Approach

Bayesian statistics 478 How Bayesian methods work 480 Prior distributions 482 Likelihood; posterior distributions 484 Summarizing and presenting results 486 Using Bayesian analyses in medicine 488 Software for Bayesian statistics 492 Reading Bayesian analyses in papers 494 Bayesian methods: a summary 496 In this chapter we describe the Bayesian approach to statistical analysis in contrast to the frequentist approach. We describe how Bayesian methods work including a description of prior and posterior distributions. We outline the role and choice of prior distributions and how they are combined with the data collected to provide an updated estimate of the unknown quantity being studied. We include examples of the use of Bayesian methods in medicine, and discuss the pros and cons of the Bayesian approach compared with the frequentist approach Finally, we give guidance on how to read and interpret Bayesian analyses in the medical literature....

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 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 The Bayesian Approach and the Results of the ISAR-REACT 5 Trial

2021 ◽  
Vol 14 (2) ◽  
pp. 231-232
Author(s):  
Adnan Kastrati ◽  
Alexander Hapfelmeier
Keyword(s):  
Bayesian Approach ◽  
The Bayesian Approach

scholarly journals PathFinder: Bayesian inference of clone migration histories in cancer

2020 ◽  
Vol 36 (Supplement_2) ◽  
pp. i675-i683
Author(s):  
Sudhir Kumar ◽  
Antonia Chroni ◽  
Koichiro Tamura ◽  
Maxwell Sanderford ◽  
Olumide Oladeinde ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Cancer Cells ◽  
Bayesian Approach ◽  
Genetic Variants ◽  
Cancer Development ◽  
Posterior Probabilities ◽  
Migration Routes ◽  
Primary Tumors ◽  
History Of ◽  
The Web

Abstract Summary Metastases cause a vast majority of cancer morbidity and mortality. Metastatic clones are formed by dispersal of cancer cells to secondary tissues, and are not medically detected or visible until later stages of cancer development. Clone phylogenies within patients provide a means of tracing the otherwise inaccessible dynamic history of migrations of cancer cells. Here, we present a new Bayesian approach, PathFinder, for reconstructing the routes of cancer cell migrations. PathFinder uses the clone phylogeny, the number of mutational differences among clones, and the information on the presence and absence of observed clones in primary and metastatic tumors. By analyzing simulated datasets, we found that PathFinder performes well in reconstructing clone migrations from the primary tumor to new metastases as well as between metastases. It was more challenging to trace migrations from metastases back to primary tumors. We found that a vast majority of errors can be corrected by sampling more clones per tumor, and by increasing the number of genetic variants assayed per clone. We also identified situations in which phylogenetic approaches alone are not sufficient to reconstruct migration routes. In conclusion, we anticipate that the use of PathFinder will enable a more reliable inference of migration histories and their posterior probabilities, which is required to assess the relative preponderance of seeding of new metastasis by clones from primary tumors and/or existing metastases. Availability and implementation PathFinder is available on the web at https://github.com/SayakaMiura/PathFinder.

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