Jon Williamson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198530794
- eISBN:
- 9780191712982
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530794.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This book provides an introduction to, and analysis of, the use of Bayesian nets in causal modelling. It puts forward new conceptual foundations for causal network modelling: The book argues that ...
More
This book provides an introduction to, and analysis of, the use of Bayesian nets in causal modelling. It puts forward new conceptual foundations for causal network modelling: The book argues that probability and causality need to be interpreted as epistemic notions in order for the key assumptions behind causal models to hold. Under the epistemic view, probability and causality are understood in terms of the beliefs an agent ought to adopt. The book develops an objective Bayesian notion of probability and a corresponding epistemic theory of causality. This yields a general framework for causal modelling, which is extended to cope with recursive causal relations, logically complex beliefs and changes in an agent's language.Less
This book provides an introduction to, and analysis of, the use of Bayesian nets in causal modelling. It puts forward new conceptual foundations for causal network modelling: The book argues that probability and causality need to be interpreted as epistemic notions in order for the key assumptions behind causal models to hold. Under the epistemic view, probability and causality are understood in terms of the beliefs an agent ought to adopt. The book develops an objective Bayesian notion of probability and a corresponding epistemic theory of causality. This yields a general framework for causal modelling, which is extended to cope with recursive causal relations, logically complex beliefs and changes in an agent's language.
Jon Williamson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198530794
- eISBN:
- 9780191712982
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530794.003.0003
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter introduces Bayesian networks and probabilistic independence, and shows how Bayesian nets are used to represent probability functions. Inference in Bayesian nets is discussed and the ...
More
This chapter introduces Bayesian networks and probabilistic independence, and shows how Bayesian nets are used to represent probability functions. Inference in Bayesian nets is discussed and the problem of constructing Bayesian nets is introduced. One of the simplest methods for constructing Bayesian nets — sequentially adding arrows — is explored in some detail in order to highlight some of the key features of the construction problem.Less
This chapter introduces Bayesian networks and probabilistic independence, and shows how Bayesian nets are used to represent probability functions. Inference in Bayesian nets is discussed and the problem of constructing Bayesian nets is introduced. One of the simplest methods for constructing Bayesian nets — sequentially adding arrows — is explored in some detail in order to highlight some of the key features of the construction problem.
PHILIP DAWID, DAVID SCHUM, and AMANDA HEPLER
- Published in print:
- 2011
- Published Online:
- January 2013
- ISBN:
- 9780197264843
- eISBN:
- 9780191754050
- Item type:
- chapter
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197264843.003.0005
- Subject:
- Sociology, Methodology and Statistics
Methods for performing complex probabilistic reasoning tasks, often based on masses of different forms of evidence obtained from a variety of different sources, are being sought by, and developed ...
More
Methods for performing complex probabilistic reasoning tasks, often based on masses of different forms of evidence obtained from a variety of different sources, are being sought by, and developed for, persons in many important contexts including law, medical diagnosis, and intelligence analysis. The complexity of these tasks can often be captured and represented by graphical structures now called inference networks. These networks are directed acyclic graphs (DAGs), consisting of nodes, representing relevant hypotheses, items of evidence, and unobserved variables, and arcs (arrows) joining some of the nodes, representing dependency relations among them. This chapter describes and comments on two different approaches to inference network construction. In the first approach, a DAG network structure is explicitly constructed as a vehicle for probabilistic analyses. Since the associated computations can be regarded as generalising the use of Bayes' rule, such networks are commonly called Bayesian networks. The second approach stems from the work of the American jurist John H. Wigmore who was the very first person to attempt a systematic study of inference networks.Less
Methods for performing complex probabilistic reasoning tasks, often based on masses of different forms of evidence obtained from a variety of different sources, are being sought by, and developed for, persons in many important contexts including law, medical diagnosis, and intelligence analysis. The complexity of these tasks can often be captured and represented by graphical structures now called inference networks. These networks are directed acyclic graphs (DAGs), consisting of nodes, representing relevant hypotheses, items of evidence, and unobserved variables, and arcs (arrows) joining some of the nodes, representing dependency relations among them. This chapter describes and comments on two different approaches to inference network construction. In the first approach, a DAG network structure is explicitly constructed as a vehicle for probabilistic analyses. Since the associated computations can be regarded as generalising the use of Bayes' rule, such networks are commonly called Bayesian networks. The second approach stems from the work of the American jurist John H. Wigmore who was the very first person to attempt a systematic study of inference networks.
Katja Ickstadt, Bjöorn Bornkamp, Marco Grzegorczyk, Jakob Wieczorek, Malik R. Sheriff, Hernáan E. Grecco, and Eli Zamir
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199694587
- eISBN:
- 9780191731921
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199694587.003.0010
- Subject:
- Mathematics, Probability / Statistics
A convenient way of modelling complex interactions is by employing graphs or networks which correspond to conditional independence structures in an underlying statistical model. One main class of ...
More
A convenient way of modelling complex interactions is by employing graphs or networks which correspond to conditional independence structures in an underlying statistical model. One main class of models in this regard are Bayesian networks, which have the drawback of making parametric assumptions. Bayesian nonparametric mixture models offer a possibility to overcome this limitation, but have hardly been used in combination with networks. This manuscript bridges this gap by introducing nonparametric Bayesian network models. We review (parametric) Bayesian networks, in particular Gaussian Bayesian networks, from a Bayesian perspective as well as nonparametric Bayesian mixture models. Afterwards these two modelling approaches are combined into nonparametric Bayesian networks. The new models are compared both to Gaussian Bayesian networks and to mixture models in a simulation study, where it turns out that the nonparametric network models perform favourably in non‐Gaussian situations. The new models are also applied to an example from systems biology, namely finding modules within the MAPK cascade.Less
A convenient way of modelling complex interactions is by employing graphs or networks which correspond to conditional independence structures in an underlying statistical model. One main class of models in this regard are Bayesian networks, which have the drawback of making parametric assumptions. Bayesian nonparametric mixture models offer a possibility to overcome this limitation, but have hardly been used in combination with networks. This manuscript bridges this gap by introducing nonparametric Bayesian network models. We review (parametric) Bayesian networks, in particular Gaussian Bayesian networks, from a Bayesian perspective as well as nonparametric Bayesian mixture models. Afterwards these two modelling approaches are combined into nonparametric Bayesian networks. The new models are compared both to Gaussian Bayesian networks and to mixture models in a simulation study, where it turns out that the nonparametric network models perform favourably in non‐Gaussian situations. The new models are also applied to an example from systems biology, namely finding modules within the MAPK cascade.
N. Thompson Hobbs and Mevin B. Hooten
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691159287
- eISBN:
- 9781400866557
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159287.003.0006
- Subject:
- Biology, Ecology
This chapter seeks to explain hierarchical models and how they differ from simple Bayesian models and to illustrate building hierarchical models using mathematically correct expressions. It begins ...
More
This chapter seeks to explain hierarchical models and how they differ from simple Bayesian models and to illustrate building hierarchical models using mathematically correct expressions. It begins with the definition of hierarchical models. Next, the chapter introduces four general classes of hierarchical models that have broad application in ecology. These classes can be used individually or in combination to attack virtually any research problem. Examples are used to show how to draw Bayesian networks that portray stochastic relationships between observed and unobserved quantities. The chapter furthermore shows how to use network drawings as a guide for writing posterior and joint distributions.Less
This chapter seeks to explain hierarchical models and how they differ from simple Bayesian models and to illustrate building hierarchical models using mathematically correct expressions. It begins with the definition of hierarchical models. Next, the chapter introduces four general classes of hierarchical models that have broad application in ecology. These classes can be used individually or in combination to attack virtually any research problem. Examples are used to show how to draw Bayesian networks that portray stochastic relationships between observed and unobserved quantities. The chapter furthermore shows how to use network drawings as a guide for writing posterior and joint distributions.
Jan Lemeire, Kris Steenhaut, and Abdellah Touhafi
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199574131
- eISBN:
- 9780191728921
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199574131.003.0027
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
The principle of Kolmogorov minimal sufficient statistic (KMSS) states that the meaningful information of data is given by the regularities in the data. The KMSS is the minimal model that describes ...
More
The principle of Kolmogorov minimal sufficient statistic (KMSS) states that the meaningful information of data is given by the regularities in the data. The KMSS is the minimal model that describes the regularities. The meaningful information given by a Bayesian network is the directed acyclic graph (DAG) which describes a decomposition of the joint probability distribution into conditional probability distributions (CPDs). If the description given by the Bayesian network is incompressible, the DAG is the KMSS and is faithful. The chapter proves that if a faithful Bayesian network exists, it is the minimal Bayesian network. Moreover, if a Bayesian network gives the KMSS, modularity of the CPDs is the most plausible hypothesis, from which the causal interpretation follows. On the other hand, if the minimal Bayesian network is compressible and is thus not the KMSS, the above implications cannot be guaranteed. When the non‐minimality of the description is due to the compressibility of an individual CPD, the true causal model is an element of the set of minimal Bayesian networks and modularity is still plausible. Faithfulness cannot be guaranteed though. When the concatenation of the descriptions of the CPDs is compressible, the true causal model is not necessarily an element of the set of minimal Bayesian networks. Also modularity may become implausible. This suggests that either there is a kind of meta‐mechanism governing some of the mechanisms or a wrong model class is considered.Less
The principle of Kolmogorov minimal sufficient statistic (KMSS) states that the meaningful information of data is given by the regularities in the data. The KMSS is the minimal model that describes the regularities. The meaningful information given by a Bayesian network is the directed acyclic graph (DAG) which describes a decomposition of the joint probability distribution into conditional probability distributions (CPDs). If the description given by the Bayesian network is incompressible, the DAG is the KMSS and is faithful. The chapter proves that if a faithful Bayesian network exists, it is the minimal Bayesian network. Moreover, if a Bayesian network gives the KMSS, modularity of the CPDs is the most plausible hypothesis, from which the causal interpretation follows. On the other hand, if the minimal Bayesian network is compressible and is thus not the KMSS, the above implications cannot be guaranteed. When the non‐minimality of the description is due to the compressibility of an individual CPD, the true causal model is an element of the set of minimal Bayesian networks and modularity is still plausible. Faithfulness cannot be guaranteed though. When the concatenation of the descriptions of the CPDs is compressible, the true causal model is not necessarily an element of the set of minimal Bayesian networks. Also modularity may become implausible. This suggests that either there is a kind of meta‐mechanism governing some of the mechanisms or a wrong model class is considered.
Dawn E. Holmes
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199574131
- eISBN:
- 9780191728921
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199574131.003.0028
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
It is well‐known that Bayesian networks are so‐called because of their use of Bayes theorem for probabilistic inference. However, since Bayesian networks commonly use frequentist probabilities ...
More
It is well‐known that Bayesian networks are so‐called because of their use of Bayes theorem for probabilistic inference. However, since Bayesian networks commonly use frequentist probabilities exclusively, is this sense they are not Bayesian. In this chapter it is argued that Bayesian networks that are objectively Bayesian, in other words those whose prior distribution is based on all and only the available information, have certain desirable properties and strengths over and above those based solely on the frequentist approach to probability. It is demonstrated, through an example, that these specially constructed graphical models may be used in otherwise intractable situations where data is unavailable or scarce and decisions need to be made.Less
It is well‐known that Bayesian networks are so‐called because of their use of Bayes theorem for probabilistic inference. However, since Bayesian networks commonly use frequentist probabilities exclusively, is this sense they are not Bayesian. In this chapter it is argued that Bayesian networks that are objectively Bayesian, in other words those whose prior distribution is based on all and only the available information, have certain desirable properties and strengths over and above those based solely on the frequentist approach to probability. It is demonstrated, through an example, that these specially constructed graphical models may be used in otherwise intractable situations where data is unavailable or scarce and decisions need to be made.
N. Thompson Hobbs and Mevin B. Hooten
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691159287
- eISBN:
- 9781400866557
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159287.003.0012
- Subject:
- Biology, Ecology
This chapter provides solutions to the problems presented in the preceding chapter. It presents the diagrams for each problem as well as some explanations on how the solutions are arrived at. As has ...
More
This chapter provides solutions to the problems presented in the preceding chapter. It presents the diagrams for each problem as well as some explanations on how the solutions are arrived at. As has been advised in the previous chapter, each solution is best referred to individually, as each problem in the preceding chapter has been solved. The problems this chapter addresses involve the mean number of ticks per sheep assuming the counts are distributed as a Poisson random variable, the portrayal of light limitation for a single tree species, the landscape occupancy of Swiss breeding birds, the allometry of savanna trees, and the movement of seals in the North Atlantic.Less
This chapter provides solutions to the problems presented in the preceding chapter. It presents the diagrams for each problem as well as some explanations on how the solutions are arrived at. As has been advised in the previous chapter, each solution is best referred to individually, as each problem in the preceding chapter has been solved. The problems this chapter addresses involve the mean number of ticks per sheep assuming the counts are distributed as a Poisson random variable, the portrayal of light limitation for a single tree species, the landscape occupancy of Swiss breeding birds, the allometry of savanna trees, and the movement of seals in the North Atlantic.
Neil Tennant
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199655755
- eISBN:
- 9780191742125
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655755.003.0011
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology
This chapter compares and contrasts the account with three other major formal accounts of belief revision: AGM-theory; Justified Truth-Maintenance Systems; and Bayesian networks. There are both ...
More
This chapter compares and contrasts the account with three other major formal accounts of belief revision: AGM-theory; Justified Truth-Maintenance Systems; and Bayesian networks. There are both critical and constructive things to say about these competing accounts. This discussion should serve to situate our work for the reader in mathematical logic, AI and/or computing science.Less
This chapter compares and contrasts the account with three other major formal accounts of belief revision: AGM-theory; Justified Truth-Maintenance Systems; and Bayesian networks. There are both critical and constructive things to say about these competing accounts. This discussion should serve to situate our work for the reader in mathematical logic, AI and/or computing science.
Luc Bovens and Stephan Hartmann
- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199269754
- eISBN:
- 9780191601705
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199269750.003.0004
- Subject:
- Philosophy, Metaphysics/Epistemology
Introduces different interpretations of witness reliability into the models and constructs Bayesian-Network representations. Applies the models to Condorcet-style jury voting and Tversky and ...
More
Introduces different interpretations of witness reliability into the models and constructs Bayesian-Network representations. Applies the models to Condorcet-style jury voting and Tversky and Kahneman’s Linda puzzle.Less
Introduces different interpretations of witness reliability into the models and constructs Bayesian-Network representations. Applies the models to Condorcet-style jury voting and Tversky and Kahneman’s Linda puzzle.
Luc Bovens and Stephan Hartmann
- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199269754
- eISBN:
- 9780191601705
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199269750.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology
Probabilistic models have much to offer to epistemology and philosophy of science. Arguably, the coherence theory of justification claims that the more coherent a set of propositions is, the more ...
More
Probabilistic models have much to offer to epistemology and philosophy of science. Arguably, the coherence theory of justification claims that the more coherent a set of propositions is, the more confident one ought to be in its content, ceteris paribus. An impossibility result shows that there cannot exist a coherence ordering. A coherence quasi-ordering can be constructed that respects this claim and is relevant to scientific-theory choice. Bayesian-Network models of the reliability of information sources are made applicable to Condorcet-style jury voting, Tversky and Kahneman’s Linda puzzle, the variety-of-evidence thesis, the Duhem–Quine thesis, and the informational value of testimony.Less
Probabilistic models have much to offer to epistemology and philosophy of science. Arguably, the coherence theory of justification claims that the more coherent a set of propositions is, the more confident one ought to be in its content, ceteris paribus. An impossibility result shows that there cannot exist a coherence ordering. A coherence quasi-ordering can be constructed that respects this claim and is relevant to scientific-theory choice. Bayesian-Network models of the reliability of information sources are made applicable to Condorcet-style jury voting, Tversky and Kahneman’s Linda puzzle, the variety-of-evidence thesis, the Duhem–Quine thesis, and the informational value of testimony.
Christine Sinoquet
- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709022
- eISBN:
- 9780191779619
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709022.003.0002
- Subject:
- Mathematics, Probability / Statistics, Biostatistics
The aim of this chapter is to offer an advanced tutorial to scientists with no background or no deep background on probabilistic graphical models. To readers more familiar with these models, this ...
More
The aim of this chapter is to offer an advanced tutorial to scientists with no background or no deep background on probabilistic graphical models. To readers more familiar with these models, this chapter is to be used as a compendium of definitions and general methods, to browse through at will. Intentionally self-contained, this chapter first begins with reminders of essential definitions such as the distinction between marginal independence and conditional independence. Then the chapter briefly surveys the most popular classes of probabilistic graphical models: Markov chains, Bayesian networks, and Markov random fields. Next probabilistic inference is explained and illustrated in the Bayesian network context. Finally parameter and structure learning are presented.Less
The aim of this chapter is to offer an advanced tutorial to scientists with no background or no deep background on probabilistic graphical models. To readers more familiar with these models, this chapter is to be used as a compendium of definitions and general methods, to browse through at will. Intentionally self-contained, this chapter first begins with reminders of essential definitions such as the distinction between marginal independence and conditional independence. Then the chapter briefly surveys the most popular classes of probabilistic graphical models: Markov chains, Bayesian networks, and Markov random fields. Next probabilistic inference is explained and illustrated in the Bayesian network context. Finally parameter and structure learning are presented.
Steven Sloman
- Published in print:
- 2005
- Published Online:
- January 2007
- ISBN:
- 9780195183115
- eISBN:
- 9780199870950
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195183115.001.0001
- Subject:
- Philosophy, Philosophy of Mind
Human beings are active agents who can think. To understand how thought serves action requires understanding how people conceive of the relation between cause and effect, between action and outcome. ...
More
Human beings are active agents who can think. To understand how thought serves action requires understanding how people conceive of the relation between cause and effect, between action and outcome. This book presents the question, in cognitive terms: how do people construct and reason with the causal models we use to represent our world? A revolution is occurring in how statisticians, philosophers, and computer scientists answer this question. Those fields have ushered in new insights about causal models by thinking about how to represent causal structure mathematically, in a framework that uses graphs and probability theory to develop what are called causal Bayesian networks. The framework starts with the idea that the purpose of causal structure is to understand and predict the effects of intervention. How does intervening on one thing affect other things? This is not a question merely about probability (or logic), but about action. The framework offers a new understanding of mind: thought is about the effects of intervention and cognition is thus intimately tied to actions that take place either in the actual physical world or in imagination, in counterfactual worlds. This book offers a conceptual introduction to the key mathematical ideas, presenting them in a non-technical way, focusing on the intuitions rather than the theorems. It tries to show why the ideas are important to understanding how people explain things and why thinking not only about the world as it is but the world as it could be is so central to human action. The book reviews the role of causality, causal models, and intervention in the basic human cognitive functions: decision making, reasoning, judgment, categorization, inductive inference, language, and learning. In short, the book offers a discussion about how people think, talk, learn, and explain things in causal terms, in terms of action and manipulation.Less
Human beings are active agents who can think. To understand how thought serves action requires understanding how people conceive of the relation between cause and effect, between action and outcome. This book presents the question, in cognitive terms: how do people construct and reason with the causal models we use to represent our world? A revolution is occurring in how statisticians, philosophers, and computer scientists answer this question. Those fields have ushered in new insights about causal models by thinking about how to represent causal structure mathematically, in a framework that uses graphs and probability theory to develop what are called causal Bayesian networks. The framework starts with the idea that the purpose of causal structure is to understand and predict the effects of intervention. How does intervening on one thing affect other things? This is not a question merely about probability (or logic), but about action. The framework offers a new understanding of mind: thought is about the effects of intervention and cognition is thus intimately tied to actions that take place either in the actual physical world or in imagination, in counterfactual worlds. This book offers a conceptual introduction to the key mathematical ideas, presenting them in a non-technical way, focusing on the intuitions rather than the theorems. It tries to show why the ideas are important to understanding how people explain things and why thinking not only about the world as it is but the world as it could be is so central to human action. The book reviews the role of causality, causal models, and intervention in the basic human cognitive functions: decision making, reasoning, judgment, categorization, inductive inference, language, and learning. In short, the book offers a discussion about how people think, talk, learn, and explain things in causal terms, in terms of action and manipulation.
Jee Young Moon, Elias Chaibub Neto, Xinwei Deng, and Brian S. Yandell
- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709022
- eISBN:
- 9780191779619
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709022.003.0007
- Subject:
- Mathematics, Probability / Statistics, Biostatistics
In a segregating population, quantitative trait loci (QTL) mapping can identify QTLs with a causal effect on a phenotype. A common feature of these methods is that QTL mapping and phenotype network ...
More
In a segregating population, quantitative trait loci (QTL) mapping can identify QTLs with a causal effect on a phenotype. A common feature of these methods is that QTL mapping and phenotype network reconstruction are conducted separately. As both tasks have to benefit from each other, this chapter presents an approach which jointly infers a causal phenotype network and causal QTLs. The joint network of causal phenotype relationships and causal QTLs is modeled as a Bayesian network. In addition, a prior distribution on phenotype network structures is adjusted by biological knowledge, thus extending the former framework, QTLnet, into QTLnet-prior. This integrative approach can incorporate several sources of biological knowledge such as protein-protein interactions, gene ontology annotations, and transcription factor and DNA binding information. A Metropolis-Hastings scheme is described that iterates between accepting a network structure and accepting k weights corresponding to the k types of biological knowledge.Less
In a segregating population, quantitative trait loci (QTL) mapping can identify QTLs with a causal effect on a phenotype. A common feature of these methods is that QTL mapping and phenotype network reconstruction are conducted separately. As both tasks have to benefit from each other, this chapter presents an approach which jointly infers a causal phenotype network and causal QTLs. The joint network of causal phenotype relationships and causal QTLs is modeled as a Bayesian network. In addition, a prior distribution on phenotype network structures is adjusted by biological knowledge, thus extending the former framework, QTLnet, into QTLnet-prior. This integrative approach can incorporate several sources of biological knowledge such as protein-protein interactions, gene ontology annotations, and transcription factor and DNA binding information. A Metropolis-Hastings scheme is described that iterates between accepting a network structure and accepting k weights corresponding to the k types of biological knowledge.
Kevin B. Korb, Erik P. Nyberg, and Lucas Hope
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199574131
- eISBN:
- 9780191728921
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199574131.003.0030
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
The causal power of C over E is (roughly) the degree to which changes in C cause changes in E. A formal measure of causal power would be very useful, as an aid to understanding and modelling complex ...
More
The causal power of C over E is (roughly) the degree to which changes in C cause changes in E. A formal measure of causal power would be very useful, as an aid to understanding and modelling complex stochastic systems. Previous attempts to measure causal power, such as those of Good (1961), Cheng (1997), and Glymour (2001), while useful, suffer from one fundamental flaw: they only give sensible results when applied to very restricted types of causal system, all of which exhibit causal transitivity. Causal Bayesian networks, however, are not in general transitive. The chapter develops an information‐theoretic alternative, causal information, which applies to any kind of causal Bayesian network. Causal information is based upon three ideas. First, the chapter assumes that the system can be represented causally as a Bayesian network. Second, the chapter uses hypothetical interventions to select the causal from the non‐causal paths connecting C to E. Third, we use a variation on the information‐theoretic measure mutual information to summarize the total causal influence of C on E. The chapter's measure gives sensible results for a much wider variety of complex stochastic systems than previous attempts and promises to simplify the interpretation and application of Bayesian networks.Less
The causal power of C over E is (roughly) the degree to which changes in C cause changes in E. A formal measure of causal power would be very useful, as an aid to understanding and modelling complex stochastic systems. Previous attempts to measure causal power, such as those of Good (1961), Cheng (1997), and Glymour (2001), while useful, suffer from one fundamental flaw: they only give sensible results when applied to very restricted types of causal system, all of which exhibit causal transitivity. Causal Bayesian networks, however, are not in general transitive. The chapter develops an information‐theoretic alternative, causal information, which applies to any kind of causal Bayesian network. Causal information is based upon three ideas. First, the chapter assumes that the system can be represented causally as a Bayesian network. Second, the chapter uses hypothetical interventions to select the causal from the non‐causal paths connecting C to E. Third, we use a variation on the information‐theoretic measure mutual information to summarize the total causal influence of C on E. The chapter's measure gives sensible results for a much wider variety of complex stochastic systems than previous attempts and promises to simplify the interpretation and application of Bayesian networks.
N. Thompson Hobbs and Mevin B. Hooten
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691159287
- eISBN:
- 9781400866557
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159287.003.0011
- Subject:
- Biology, Ecology
This chapter provides a set of structured problems to hone the reader's skills in model building. Each problem requires the reader to draw a Bayesian network and write the posterior and joint ...
More
This chapter provides a set of structured problems to hone the reader's skills in model building. Each problem requires the reader to draw a Bayesian network and write the posterior and joint distributions. Computational syntax is de-emphasized because there are many sources that teach the details of writing code for MCMC software using ecological examples and a few that show how to construct one's own MCMC algorithms. The examples offered in this chapter are drawn from several ecological sub-disciplines, though the intent of these problems is to be instructive regardless of the reader's focus of research. The chapter also offers some pointers for approaching these problems and how to apply their lessons to one's own research.Less
This chapter provides a set of structured problems to hone the reader's skills in model building. Each problem requires the reader to draw a Bayesian network and write the posterior and joint distributions. Computational syntax is de-emphasized because there are many sources that teach the details of writing code for MCMC software using ecological examples and a few that show how to construct one's own MCMC algorithms. The examples offered in this chapter are drawn from several ecological sub-disciplines, though the intent of these problems is to be instructive regardless of the reader's focus of research. The chapter also offers some pointers for approaching these problems and how to apply their lessons to one's own research.
Sandra L. Rodriguez–Zas and Bruce R. Southey
- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709022
- eISBN:
- 9780191779619
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709022.003.0004
- Subject:
- Mathematics, Probability / Statistics, Biostatistics
Most Bayesian network applications to gene network reconstruction assume a single distributional model across all the samples and treatments analyzed. This assumption is likely to be unrealistic ...
More
Most Bayesian network applications to gene network reconstruction assume a single distributional model across all the samples and treatments analyzed. This assumption is likely to be unrealistic especially when describing the relationship between genes across a range of treatments with potentially different impacts on the networks. To address this limitation, a mixture Bayesian network approach has been developed. Besides, the equivalence between Bayesian networks and regression approaches has been demonstrated. Here, two strategies are compared: the mixture Bayesian network approach and the mixture regression approach, when used for the purpose of gene network inference. The finite mixture model that is integrated into both strategies allows the characterization of gene relationships unique to particular conditions as well as the identification of interactions shared across conditions. The chapter reviews performances on real data describing a pathway analyzed under up to nine different experimental conditions, and highlights the strengths of the approaches evaluated.Less
Most Bayesian network applications to gene network reconstruction assume a single distributional model across all the samples and treatments analyzed. This assumption is likely to be unrealistic especially when describing the relationship between genes across a range of treatments with potentially different impacts on the networks. To address this limitation, a mixture Bayesian network approach has been developed. Besides, the equivalence between Bayesian networks and regression approaches has been demonstrated. Here, two strategies are compared: the mixture Bayesian network approach and the mixture regression approach, when used for the purpose of gene network inference. The finite mixture model that is integrated into both strategies allows the characterization of gene relationships unique to particular conditions as well as the identification of interactions shared across conditions. The chapter reviews performances on real data describing a pathway analyzed under up to nine different experimental conditions, and highlights the strengths of the approaches evaluated.
Péter Antal, András Millinghoffer, Gábor Hullám, Gergely Hajós, Péter Sárközy, András Gézsi, Csaba Szalai, and András Falus
- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709022
- eISBN:
- 9780191779619
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709022.003.0013
- Subject:
- Mathematics, Probability / Statistics, Biostatistics
The relative scarcity of the results reported by genetic association studies (GAS) prompted many research directions. Despite the centrality of the concept of association in GASs, refined concepts of ...
More
The relative scarcity of the results reported by genetic association studies (GAS) prompted many research directions. Despite the centrality of the concept of association in GASs, refined concepts of association are missing; meanwhile, various feature subset selection methods became de facto standards for defining multivariate relevance. On the other hand, probabilistic graphical models, including Bayesian networks (BNs) are more and more popular, as they can learn nontransitive, multivariate, nonlinear relations between complex phenotypic descriptors and heterogeneous explanatory variables. To integrate the advantages of Bayesian statistics and BNs, the Bayesian network based Bayesian multilevel analysis of relevance (BN-BMLA) was proposed. This approach allows the processing of multiple target variables, while ensuring scalability and providing a multilevel view of the results of multivariate analysis. This chapter discusses the use of Bayesian BN-based analysis of relevance in exploratory data analysis, optimal decision and study design, and knowledge fusion, in the context of GASs.Less
The relative scarcity of the results reported by genetic association studies (GAS) prompted many research directions. Despite the centrality of the concept of association in GASs, refined concepts of association are missing; meanwhile, various feature subset selection methods became de facto standards for defining multivariate relevance. On the other hand, probabilistic graphical models, including Bayesian networks (BNs) are more and more popular, as they can learn nontransitive, multivariate, nonlinear relations between complex phenotypic descriptors and heterogeneous explanatory variables. To integrate the advantages of Bayesian statistics and BNs, the Bayesian network based Bayesian multilevel analysis of relevance (BN-BMLA) was proposed. This approach allows the processing of multiple target variables, while ensuring scalability and providing a multilevel view of the results of multivariate analysis. This chapter discusses the use of Bayesian BN-based analysis of relevance in exploratory data analysis, optimal decision and study design, and knowledge fusion, in the context of GASs.
David Danks
- Published in print:
- 2007
- Published Online:
- April 2010
- ISBN:
- 9780195176803
- eISBN:
- 9780199958511
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195176803.003.0012
- Subject:
- Psychology, Developmental Psychology
Many different, seemingly mutually exclusive, theories of categorization have been proposed in recent years. The most notable theories have been those based on prototypes, exemplars, and causal ...
More
Many different, seemingly mutually exclusive, theories of categorization have been proposed in recent years. The most notable theories have been those based on prototypes, exemplars, and causal models. This chapter provides “representation theorems” for each of these theories in the framework of probabilistic graphical models. More specifically, it shows for each of these psychological theories that the categorization judgments predicted and explained by the theory can be wholly captured using probabilistic graphical models. In other words, probabilistic graphical models provide a lingua franca for these disparate categorization theories, and so we can quite directly compare the different types of theories. These formal results are used to explain a variety of surprising empirical results, and to propose several novel theories of categorization.Less
Many different, seemingly mutually exclusive, theories of categorization have been proposed in recent years. The most notable theories have been those based on prototypes, exemplars, and causal models. This chapter provides “representation theorems” for each of these theories in the framework of probabilistic graphical models. More specifically, it shows for each of these psychological theories that the categorization judgments predicted and explained by the theory can be wholly captured using probabilistic graphical models. In other words, probabilistic graphical models provide a lingua franca for these disparate categorization theories, and so we can quite directly compare the different types of theories. These formal results are used to explain a variety of surprising empirical results, and to propose several novel theories of categorization.
Raphaël Mourad (ed.)
- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709022
- eISBN:
- 9780191779619
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709022.001.0001
- Subject:
- Mathematics, Probability / Statistics, Biostatistics
At the crossroads between statistics and machine learning, probabilistic graphical models provide a powerful formal framework to model complex data. Probabilistic graphical models are probabilistic ...
More
At the crossroads between statistics and machine learning, probabilistic graphical models provide a powerful formal framework to model complex data. Probabilistic graphical models are probabilistic models whose graphical components denote conditional independence structures between random variables. The probabilistic framework makes it possible to deal with data uncertainty while the conditional independence assumption helps process high dimensional and complex data. Examples of probabilistic graphical models are Bayesian networks and Markov random fields, which represent two of the most popular classes of such models. With the rapid advancements of high-throughput technologies and the ever decreasing costs of these next generation technologies, a fast-growing volume of biological data of various types—the so-called omics—is in need of accurate and efficient methods for modeling, prior to further downstream analysis. Network reconstruction from gene expression data represents perhaps the most emblematic area of research where probabilistic graphical models have been successfully applied. However these models have also created renew interest in genetics, in particular: association genetics, causality discovery, prediction of outcomes, detection of copy number variations, epigenetics, etc.. For all these reasons, it is foreseeable that such models will have a prominent role to play in advances in genome-wide analyses.Less
At the crossroads between statistics and machine learning, probabilistic graphical models provide a powerful formal framework to model complex data. Probabilistic graphical models are probabilistic models whose graphical components denote conditional independence structures between random variables. The probabilistic framework makes it possible to deal with data uncertainty while the conditional independence assumption helps process high dimensional and complex data. Examples of probabilistic graphical models are Bayesian networks and Markov random fields, which represent two of the most popular classes of such models. With the rapid advancements of high-throughput technologies and the ever decreasing costs of these next generation technologies, a fast-growing volume of biological data of various types—the so-called omics—is in need of accurate and efficient methods for modeling, prior to further downstream analysis. Network reconstruction from gene expression data represents perhaps the most emblematic area of research where probabilistic graphical models have been successfully applied. However these models have also created renew interest in genetics, in particular: association genetics, causality discovery, prediction of outcomes, detection of copy number variations, epigenetics, etc.. For all these reasons, it is foreseeable that such models will have a prominent role to play in advances in genome-wide analyses.
