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Entropy
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Applications of Probabilistic Programming and Bayesian Statistical Modeling
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Applications of Probabilistic Programming and Bayesian Statistical Modeling

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (30 April 2021) | Viewed by 7181

Special Issue Editor

Dr. Christopher J. Fonnesbeck

E-Mail Website
Guest Editor
Department of Biostatistics, Vanderbilt University Medical Center, Nashville, TN 37203, USA
Interests: probabilistic programming; Bayesian analysis; machine learning; statistical applications; decision analysis; sports analytics

Special Issue Information

Probabilistic programming is an interdisciplinary combination of computer science, statistics and machine learning that automates the process of learning models from data. While classical machine learning methods are limited by the inability to adequately account for uncertainty, probabilistic programming is based upon Bayesian statistical procedures that allow us to infer unknown quantities using probabilistic models, and from this, make predictions and inferences that are also probabilistic. Following a period of widespread adoption over the past decade, these methods are now applied in a variety of settings, including engineering, statistics, computer science, biology, medicine, economics, and more. The availability of sophisticated, high-level software implementations for building and fitting probabilistic models continues to aid their expanded use. 

The aim of this Special Issue is to encourage researchers to present effective applications of probabilistic programming and Bayesian modeling across a range of disciplines.  In particular, we are interested in novel applications that illustrate the advantages of these methods to solve problems that might have been unassailable without them. We hope that these contributions will inspire practitioners from different fields to apply probabilistic programming in ways they might not have previously considered.

Dr. Christopher J. Fonnesbeck
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Probabilistic programming
  • Bayesian statistics
  • Statistical applications
  • Statistical computing
  • Probability models
  • Machine learning

Published Papers (3 papers)

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Research

39 pages, 10853 KiB  
Article
Graphical Models in Reconstructability Analysis and Bayesian Networks
by Marcus Harris and Martin Zwick
Entropy 2021, 23(8), 986; https://doi.org/10.3390/e23080986 - 30 Jul 2021
Cited by 1 | Viewed by 2017
Abstract
Reconstructability Analysis (RA) and Bayesian Networks (BN) are both probabilistic graphical modeling methodologies used in machine learning and artificial intelligence. There are RA models that are statistically equivalent to BN models and there are also models unique to RA and models unique to [...] Read more.
Reconstructability Analysis (RA) and Bayesian Networks (BN) are both probabilistic graphical modeling methodologies used in machine learning and artificial intelligence. There are RA models that are statistically equivalent to BN models and there are also models unique to RA and models unique to BN. The primary goal of this paper is to unify these two methodologies via a lattice of structures that offers an expanded set of models to represent complex systems more accurately or more simply. The conceptualization of this lattice also offers a framework for additional innovations beyond what is presented here. Specifically, this paper integrates RA and BN by developing and visualizing: (1) a BN neutral system lattice of general and specific graphs, (2) a joint RA-BN neutral system lattice of general and specific graphs, (3) an augmented RA directed system lattice of prediction graphs, and (4) a BN directed system lattice of prediction graphs. Additionally, it (5) extends RA notation to encompass BN graphs and (6) offers an algorithm to search the joint RA-BN neutral system lattice to find the best representation of system structure from underlying system variables. All lattices shown in this paper are for four variables, but the theory and methodology presented in this paper are general and apply to any number of variables. These methodological innovations are contributions to machine learning and artificial intelligence and more generally to complex systems analysis. The paper also reviews some relevant prior work of others so that the innovations offered here can be understood in a self-contained way within the context of this paper. Full article
(This article belongs to the Special Issue Applications of Probabilistic Programming and Bayesian Statistical Modeling)
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10 pages, 696 KiB  
Article
Principled Decision-Making Workflow with Hierarchical Bayesian Models of High-Throughput Dose-Response Measurements
by Eric J. Ma and Arkadij Kummer
Entropy 2021, 23(6), 727; https://doi.org/10.3390/e23060727 - 8 Jun 2021
Cited by 1 | Viewed by 1914
Abstract
We present a case study applying hierarchical Bayesian estimation on high-throughput protein melting-point data measured across the tree of life. We show that the model is able to impute reasonable melting temperatures even in the face of unreasonably noisy data. Additionally, we demonstrate [...] Read more.
We present a case study applying hierarchical Bayesian estimation on high-throughput protein melting-point data measured across the tree of life. We show that the model is able to impute reasonable melting temperatures even in the face of unreasonably noisy data. Additionally, we demonstrate how to use the variance in melting-temperature posterior-distribution estimates to enable principled decision-making in common high-throughput measurement tasks, and contrast the decision-making workflow against simple maximum-likelihood curve-fitting. We conclude with a discussion of the relative merits of each workflow. Full article
(This article belongs to the Special Issue Applications of Probabilistic Programming and Bayesian Statistical Modeling)
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20 pages, 3415 KiB  
Article
EcoQBNs: First Application of Ecological Modeling with Quantum Bayesian Networks
by Bruce G. Marcot
Entropy 2021, 23(4), 441; https://doi.org/10.3390/e23040441 - 9 Apr 2021
Cited by 3 | Viewed by 2522
Abstract
A recent advancement in modeling was the development of quantum Bayesian networks (QBNs). QBNs generally differ from BNs by substituting traditional Bayes calculus in probability tables with the quantum amplification wave functions. QBNs can solve a variety of problems which are unsolvable by, [...] Read more.
A recent advancement in modeling was the development of quantum Bayesian networks (QBNs). QBNs generally differ from BNs by substituting traditional Bayes calculus in probability tables with the quantum amplification wave functions. QBNs can solve a variety of problems which are unsolvable by, or are too complex for, traditional BNs. These include problems with feedback loops and temporal expansions; problems with non-commutative dependencies in which the order of the specification of priors affects the posterior outcomes; problems with intransitive dependencies constituting the circular dominance of the outcomes; problems in which the input variables can affect each other, even if they are not causally linked (entanglement); problems in which there may be >1 dominant probability outcome dependent on small variations in inputs (superpositioning); and problems in which the outcomes are nonintuitive and defy traditional probability calculus (Parrondo’s paradox and the violation of the Sure Thing Principle). I present simple examples of these situations illustrating problems in prediction and diagnosis, and I demonstrate how BN solutions are infeasible, or at best require overly-complex latent variable structures. I then argue that many problems in ecology and evolution can be better depicted with ecological QBN (EcoQBN) modeling. The situations that fit these kinds of problems include noncommutative and intransitive ecosystems responding to suites of disturbance regimes with no specific or single climax condition, or that respond differently depending on the specific sequence of the disturbances (priors). Case examples are presented on the evaluation of habitat conditions for a bat species, representing state-transition models of a boreal forest under disturbance, and the entrainment of auditory signals among organisms. I argue that many current ecological analysis structures—such as state-and-transition models, predator–prey dynamics, the evolution of symbiotic relationships, ecological disturbance models, and much more—could greatly benefit from a QBN approach. I conclude by presenting EcoQBNs as a nascent field needing the further development of the quantum mathematical structures and, eventually, adjuncts to existing BN modeling shells or entirely new software programs to facilitate model development and application. Full article
(This article belongs to the Special Issue Applications of Probabilistic Programming and Bayesian Statistical Modeling)
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