This practical introduction is geared towards scientists who wish to employ Bayesian networks for... more This practical introduction is geared towards scientists who wish to employ Bayesian networks for applied research using the BayesiaLab software platform. Through numerous examples, this book illustrates how implementing Bayesian networks involves concepts from many disciplines, including computer science, probability theory, information theory, machine learning, and statistics. Each chapter explores a real-world problem domain, exploring aspects of Bayesian networks and simultaneously introducing functions of BayesiaLab. The book can serve as a self-study guide for learners and as a reference manual for advanced practitioners.
ABSTRACT There are a number of paradoxes and fallacies that keep recurring as popular and mind-be... more ABSTRACT There are a number of paradoxes and fallacies that keep recurring as popular and mind-bending puzzles in the media. Although there is (now) complete agreement among scientists on how to resolve them, the correct answers are often perplexing to the casual observer and still cause bewilderment. We will start off with the fallacy of the transposed conditional, which has become rather infamous and is better known as Prosecutor’s Fallacy. As the name implies, it is a problem often encountered in courts of law, and there are numerous cases of incorrect convictions as a result of this fallacy. No less serious are the potential consequences of Simpson’s Paradox, for instance, when determining the treatment effect of a new drug under study. The effect of a drug on two subgroups may appear as the complete opposite of the treatment effect on the whole group. On a much lighter note, the Monty Hall Problem has its origin in a television game show and might perhaps be the most difficult puzzle to comprehend intuitively, even when explicit proof is provided. Respected mathematicians and statisticians have struggled with this problem, and some of them have boldly proclaimed wrong solutions. The counterintuitive nature of these probabilistic problems relates to the cognitive limits of human inference. More specifically, we are dealing with the problem of updating beliefs given new evidence, i.e. carrying out inference. This cognitive challenge may seem surprising, given that humans are exceptionally gifted in discovering causal structures in their everyday environment. Discovering causality in the world is quite literally child’s play, as babies start understanding the world through a combination of observation and experimentation. Our human intuition is actually quite good when it comes to reasoning from cause to effect; our qualitative perception of such relationships (even under uncertainty) is often compatible with formal computations. However, when it comes to reasoning under uncertainty in the opposite direction, from effect to cause, i.e. diagnosis, or when combining multiple pieces of evidence, conventional wisdom frequently fails catastrophically. Even worse, the correct inference in such situations is often completely counterintuitive to people and feels utterly wrong to them. It is not an exaggeration to say that their sense of reason is violated. For more traditional computations, such as arithmetics, we have many tools that help us address our mental shortcomings. For instance, we can use paper and pencil to add 9,263,891 and 1,421,602 as most of us can’t do this in our heads. Alternatively, we can use a spreadsheet for this computation. In any case, it will not surprise us that the sum of those two numbers is a little over 10.5 million. The computed result is entirely consistent with our intuition. As this paper will show, the formally correct solutions of these probabilistic paradoxes are counterintuitive. In addition to being counterintuitive, there are few tools assisting us in solving them. There is no spreadsheet that allows us to simply plug in the numbers to calculate the result. Although we won’t be able to overcome inherent mental biases and cognitive limitations, we can now provide a very practical new tool for the correct inference in the form of Bayesian networks. Bayesian networks derive their name from Reverend Thomas Bayes, who, in the middle of the 18th century, first stated the rule for computing inverse probabilities. Bayesian networks offer a framework that allows applying Bayes’ Rule for updating beliefs in the same way spreadsheets are very convenient for applying arithmetic operations to many numbers. We will show how restating these vexing problem domains as simple Bayesian networks offers near-instant solutions. Just as spreadsheets help us perform arithmetic operations externally, i.e. outside our head, Bayesian networks offer a reliable structure to precisely perform inferential computations, which we can’t manage in our minds. The visual nature of Bayesian networks furthermore helps (at least a little) in making these paradoxes more intuitive to our own human way of thinking.
The lives of U.S. soldiers in combat depend on complex weapon systems and advanced technologies. ... more The lives of U.S. soldiers in combat depend on complex weapon systems and advanced technologies. In combat conditions, the resources available to support the operation and maintenance of these systems are minimal. Following the failure of a critical system, technical support personnel may take days to arrive via helicopter or ground convoy—leaving soldiers and civilian experts exposed to battlefield risks. To address this problem, the U.S. Army Communications Electronics Command (CECOM) developed a suite of systems, Virtual Logistics Assistance Representative (VLAR), with a single purpose: to enable a combat soldier to maintain critical equipment. The CECOM VLAR team uses an operations research (OR) approach to codifying expert knowledge about Army equipment and applying that knowledge to troubleshooting equipment diagnostics in combat situations. VLAR infuses a classic knowledge-management spiral with OR techniques: from socializing advanced technical concepts and eliciting tacit knowledge, to integratin...
Market driver analysis and product optimization are one of the central tasks in Product Marketing... more Market driver analysis and product optimization are one of the central tasks in Product Marketing and thus relevant to virtually all types of businesses. BayesiaLab provides a uni!ed software platform, which can, based on consumer data, 1. provide deep understanding of the market preference structure 2. directly generate recommendations for prioritized product actions. The proposed approach utilizes Probabilistic Structural Equation Models (PSEM), based on machine learned Bayesian networks. PSEMs provide an ef!cient alternative to Structural Equation Models (SEM), which have been used traditionally in market research.
In this introductory paper, we present Bayesian networks (the paradigm) and BayesiaLab (the softw... more In this introductory paper, we present Bayesian networks (the paradigm) and BayesiaLab (the software tool), from the perspective of the applied researcher. In Chapter 1 we begin with the role of Bayesian networks in today’s world of analytics, juxtaposing them with traditional statistics and more recent innovations in data mining. Once we establish how Bayesian networks fit into the proverbial big picture, we present in Chapter 2 the mathematical formalism that underpins this paradigm. While employing Bayesian networks for research has become remarkably easy with BayesiaLab, we need to emphasize importance of their theory. Only a deep understanding of this theory will allow researchers to fully appreciate the wide-ranging benefits of Bayesian networks. Finally, in Chapter 3, we provide an overview of the BayesiaLab software platform, which leverages the Bayesian networks paradigm to far greater extent than any other tool that has ever been available in this field. We show how the th...
This paper’s intent is to illustrate how Bayesian networks and BayesiaLab can help overcome certa... more This paper’s intent is to illustrate how Bayesian networks and BayesiaLab can help overcome certain limitations of traditional statistical methods in high-dimensional problem domains. We consider the vehicle safety discussion in the recent Final Rule, issued by the Environmental Protection Agency (EPA) and the National Highway Traffic Safety Administration (NHTSA) on future CAFE standards, as an ideal topic for our demonstration purposes. Although this paper is meant to focus on technique as opposed to the subject matter itself, our findings will inevitably generate new insights. However, it is not our intention to challenge the judgement of the EPA/NHTSA Final Rule. Rather, we plan to take an independent look at the overall problem domain while considering the rationale presented in the Final Rule. Instead of merely replicating the existing analyses with different tools, we will draw upon a broader set of variables and use alternative methods to create a complementary view of some ...
The objective of this paper is to provide you with a practical framework for causal effect estima... more The objective of this paper is to provide you with a practical framework for causal effect estimation in the context of policy assessment and impact analysis, and in the absence of experimental data. We will present a range of methods, along with their limitations, including Directed Acyclic Graphs and Bayesian networks. These techniques are intended to help you distinguish causation from association when working with data from observational studies This paper is structured as a tutorial that revolves around a single, seemingly simple example. On the basis of this example, we will illustrate numerous techniques for causal identification and estimation.
ABSTRACT There are a number of paradoxes and fallacies that keep recurring as popular and mind-be... more ABSTRACT There are a number of paradoxes and fallacies that keep recurring as popular and mind-bending puzzles in the media. Although there is (now) complete agreement among scientists on how to resolve them, the correct answers are often perplexing to the casual observer and still cause bewilderment. We will start off with the fallacy of the transposed conditional, which has become rather infamous and is better known as Prosecutor’s Fallacy. As the name implies, it is a problem often encountered in courts of law, and there are numerous cases of incorrect convictions as a result of this fallacy. No less serious are the potential consequences of Simpson’s Paradox, for instance, when determining the treatment effect of a new drug under study. The effect of a drug on two subgroups may appear as the complete opposite of the treatment effect on the whole group. On a much lighter note, the Monty Hall Problem has its origin in a television game show and might perhaps be the most difficult puzzle to comprehend intuitively, even when explicit proof is provided. Respected mathematicians and statisticians have struggled with this problem, and some of them have boldly proclaimed wrong solutions. The counterintuitive nature of these probabilistic problems relates to the cognitive limits of human inference. More specifically, we are dealing with the problem of updating beliefs given new evidence, i.e. carrying out inference. This cognitive challenge may seem surprising, given that humans are exceptionally gifted in discovering causal structures in their everyday environment. Discovering causality in the world is quite literally child’s play, as babies start understanding the world through a combination of observation and experimentation. Our human intuition is actually quite good when it comes to reasoning from cause to effect; our qualitative perception of such relationships (even under uncertainty) is often compatible with formal computations. However, when it comes to reasoning under uncertainty in the opposite direction, from effect to cause, i.e. diagnosis, or when combining multiple pieces of evidence, conventional wisdom frequently fails catastrophically. Even worse, the correct inference in such situations is often completely counterintuitive to people and feels utterly wrong to them. It is not an exaggeration to say that their sense of reason is violated. For more traditional computations, such as arithmetics, we have many tools that help us address our mental shortcomings. For instance, we can use paper and pencil to add 9,263,891 and 1,421,602 as most of us can’t do this in our heads. Alternatively, we can use a spreadsheet for this computation. In any case, it will not surprise us that the sum of those two numbers is a little over 10.5 million. The computed result is entirely consistent with our intuition. As this paper will show, the formally correct solutions of these probabilistic paradoxes are counterintuitive. In addition to being counterintuitive, there are few tools assisting us in solving them. There is no spreadsheet that allows us to simply plug in the numbers to calculate the result. Although we won’t be able to overcome inherent mental biases and cognitive limitations, we can now provide a very practical new tool for the correct inference in the form of Bayesian networks. Bayesian networks derive their name from Reverend Thomas Bayes, who, in the middle of the 18th century, first stated the rule for computing inverse probabilities. Bayesian networks offer a framework that allows applying Bayes’ Rule for updating beliefs in the same way spreadsheets are very convenient for applying arithmetic operations to many numbers. We will show how restating these vexing problem domains as simple Bayesian networks offers near-instant solutions. Just as spreadsheets help us perform arithmetic operations externally, i.e. outside our head, Bayesian networks offer a reliable structure to precisely perform inferential computations, which we can’t manage in our minds. The visual nature of Bayesian networks furthermore helps (at least a little) in making these paradoxes more intuitive to our own human way of thinking.
Market driver analysis and product optimization are one of the central tasks in Product Marketing... more Market driver analysis and product optimization are one of the central tasks in Product Marketing and thus relevant to virtually all types of businesses. BayesiaLab provides a uni!ed software platform, which can, based on consumer data, 1. provide deep understanding of the market preference structure 2. directly generate recommendations for prioritized product actions. The proposed approach utilizes Probabilistic Structural Equation Models (PSEM), based on machine learned Bayesian networks. PSEMs provide an ef!cient alternative to Structural Equation Models (SEM), which have been used traditionally in market research.
The objective of this paper is to provide you with a practical framework for causal effect estima... more The objective of this paper is to provide you with a practical framework for causal effect estimation in the context of policy assessment and impact analysis, and in the absence of experimental data. We will present a range of methods, along with their limitations, including Directed Acyclic Graphs and Bayesian networks. These techniques are intended to help you distinguish causation from association when working with data from observational studies This paper is structured as a tutorial that revolves around a single, seemingly simple example. On the basis of this example, we will illustrate numerous techniques for causal identification and estimation.
In this introductory paper, we present Bayesian networks (the paradigm) and BayesiaLab (the softw... more In this introductory paper, we present Bayesian networks (the paradigm) and BayesiaLab (the software tool), from the perspective of the applied researcher. In Chapter 1 we begin with the role of Bayesian networks in today’s world of analytics, juxtaposing them with traditional statistics and more recent innovations in data mining. Once we establish how Bayesian networks fit into the proverbial big picture, we present in Chapter 2 the mathematical formalism that underpins this paradigm. While employing Bayesian networks for research has become remarkably easy with BayesiaLab, we need to emphasize importance of their theory. Only a deep understanding of this theory will allow researchers to fully appreciate the wide-ranging benefits of Bayesian networks. Finally, in Chapter 3, we provide an overview of the BayesiaLab software platform, which leverages the Bayesian networks paradigm to far greater extent than any other tool that has ever been available in this field. We show how the th...
This practical introduction is geared towards scientists who wish to employ Bayesian networks for... more This practical introduction is geared towards scientists who wish to employ Bayesian networks for applied research using the BayesiaLab software platform. Through numerous examples, this book illustrates how implementing Bayesian networks involves concepts from many disciplines, including computer science, probability theory, information theory, machine learning, and statistics. Each chapter explores a real-world problem domain, exploring aspects of Bayesian networks and simultaneously introducing functions of BayesiaLab. The book can serve as a self-study guide for learners and as a reference manual for advanced practitioners.
ABSTRACT There are a number of paradoxes and fallacies that keep recurring as popular and mind-be... more ABSTRACT There are a number of paradoxes and fallacies that keep recurring as popular and mind-bending puzzles in the media. Although there is (now) complete agreement among scientists on how to resolve them, the correct answers are often perplexing to the casual observer and still cause bewilderment. We will start off with the fallacy of the transposed conditional, which has become rather infamous and is better known as Prosecutor’s Fallacy. As the name implies, it is a problem often encountered in courts of law, and there are numerous cases of incorrect convictions as a result of this fallacy. No less serious are the potential consequences of Simpson’s Paradox, for instance, when determining the treatment effect of a new drug under study. The effect of a drug on two subgroups may appear as the complete opposite of the treatment effect on the whole group. On a much lighter note, the Monty Hall Problem has its origin in a television game show and might perhaps be the most difficult puzzle to comprehend intuitively, even when explicit proof is provided. Respected mathematicians and statisticians have struggled with this problem, and some of them have boldly proclaimed wrong solutions. The counterintuitive nature of these probabilistic problems relates to the cognitive limits of human inference. More specifically, we are dealing with the problem of updating beliefs given new evidence, i.e. carrying out inference. This cognitive challenge may seem surprising, given that humans are exceptionally gifted in discovering causal structures in their everyday environment. Discovering causality in the world is quite literally child’s play, as babies start understanding the world through a combination of observation and experimentation. Our human intuition is actually quite good when it comes to reasoning from cause to effect; our qualitative perception of such relationships (even under uncertainty) is often compatible with formal computations. However, when it comes to reasoning under uncertainty in the opposite direction, from effect to cause, i.e. diagnosis, or when combining multiple pieces of evidence, conventional wisdom frequently fails catastrophically. Even worse, the correct inference in such situations is often completely counterintuitive to people and feels utterly wrong to them. It is not an exaggeration to say that their sense of reason is violated. For more traditional computations, such as arithmetics, we have many tools that help us address our mental shortcomings. For instance, we can use paper and pencil to add 9,263,891 and 1,421,602 as most of us can’t do this in our heads. Alternatively, we can use a spreadsheet for this computation. In any case, it will not surprise us that the sum of those two numbers is a little over 10.5 million. The computed result is entirely consistent with our intuition. As this paper will show, the formally correct solutions of these probabilistic paradoxes are counterintuitive. In addition to being counterintuitive, there are few tools assisting us in solving them. There is no spreadsheet that allows us to simply plug in the numbers to calculate the result. Although we won’t be able to overcome inherent mental biases and cognitive limitations, we can now provide a very practical new tool for the correct inference in the form of Bayesian networks. Bayesian networks derive their name from Reverend Thomas Bayes, who, in the middle of the 18th century, first stated the rule for computing inverse probabilities. Bayesian networks offer a framework that allows applying Bayes’ Rule for updating beliefs in the same way spreadsheets are very convenient for applying arithmetic operations to many numbers. We will show how restating these vexing problem domains as simple Bayesian networks offers near-instant solutions. Just as spreadsheets help us perform arithmetic operations externally, i.e. outside our head, Bayesian networks offer a reliable structure to precisely perform inferential computations, which we can’t manage in our minds. The visual nature of Bayesian networks furthermore helps (at least a little) in making these paradoxes more intuitive to our own human way of thinking.
The lives of U.S. soldiers in combat depend on complex weapon systems and advanced technologies. ... more The lives of U.S. soldiers in combat depend on complex weapon systems and advanced technologies. In combat conditions, the resources available to support the operation and maintenance of these systems are minimal. Following the failure of a critical system, technical support personnel may take days to arrive via helicopter or ground convoy—leaving soldiers and civilian experts exposed to battlefield risks. To address this problem, the U.S. Army Communications Electronics Command (CECOM) developed a suite of systems, Virtual Logistics Assistance Representative (VLAR), with a single purpose: to enable a combat soldier to maintain critical equipment. The CECOM VLAR team uses an operations research (OR) approach to codifying expert knowledge about Army equipment and applying that knowledge to troubleshooting equipment diagnostics in combat situations. VLAR infuses a classic knowledge-management spiral with OR techniques: from socializing advanced technical concepts and eliciting tacit knowledge, to integratin...
Market driver analysis and product optimization are one of the central tasks in Product Marketing... more Market driver analysis and product optimization are one of the central tasks in Product Marketing and thus relevant to virtually all types of businesses. BayesiaLab provides a uni!ed software platform, which can, based on consumer data, 1. provide deep understanding of the market preference structure 2. directly generate recommendations for prioritized product actions. The proposed approach utilizes Probabilistic Structural Equation Models (PSEM), based on machine learned Bayesian networks. PSEMs provide an ef!cient alternative to Structural Equation Models (SEM), which have been used traditionally in market research.
In this introductory paper, we present Bayesian networks (the paradigm) and BayesiaLab (the softw... more In this introductory paper, we present Bayesian networks (the paradigm) and BayesiaLab (the software tool), from the perspective of the applied researcher. In Chapter 1 we begin with the role of Bayesian networks in today’s world of analytics, juxtaposing them with traditional statistics and more recent innovations in data mining. Once we establish how Bayesian networks fit into the proverbial big picture, we present in Chapter 2 the mathematical formalism that underpins this paradigm. While employing Bayesian networks for research has become remarkably easy with BayesiaLab, we need to emphasize importance of their theory. Only a deep understanding of this theory will allow researchers to fully appreciate the wide-ranging benefits of Bayesian networks. Finally, in Chapter 3, we provide an overview of the BayesiaLab software platform, which leverages the Bayesian networks paradigm to far greater extent than any other tool that has ever been available in this field. We show how the th...
This paper’s intent is to illustrate how Bayesian networks and BayesiaLab can help overcome certa... more This paper’s intent is to illustrate how Bayesian networks and BayesiaLab can help overcome certain limitations of traditional statistical methods in high-dimensional problem domains. We consider the vehicle safety discussion in the recent Final Rule, issued by the Environmental Protection Agency (EPA) and the National Highway Traffic Safety Administration (NHTSA) on future CAFE standards, as an ideal topic for our demonstration purposes. Although this paper is meant to focus on technique as opposed to the subject matter itself, our findings will inevitably generate new insights. However, it is not our intention to challenge the judgement of the EPA/NHTSA Final Rule. Rather, we plan to take an independent look at the overall problem domain while considering the rationale presented in the Final Rule. Instead of merely replicating the existing analyses with different tools, we will draw upon a broader set of variables and use alternative methods to create a complementary view of some ...
The objective of this paper is to provide you with a practical framework for causal effect estima... more The objective of this paper is to provide you with a practical framework for causal effect estimation in the context of policy assessment and impact analysis, and in the absence of experimental data. We will present a range of methods, along with their limitations, including Directed Acyclic Graphs and Bayesian networks. These techniques are intended to help you distinguish causation from association when working with data from observational studies This paper is structured as a tutorial that revolves around a single, seemingly simple example. On the basis of this example, we will illustrate numerous techniques for causal identification and estimation.
ABSTRACT There are a number of paradoxes and fallacies that keep recurring as popular and mind-be... more ABSTRACT There are a number of paradoxes and fallacies that keep recurring as popular and mind-bending puzzles in the media. Although there is (now) complete agreement among scientists on how to resolve them, the correct answers are often perplexing to the casual observer and still cause bewilderment. We will start off with the fallacy of the transposed conditional, which has become rather infamous and is better known as Prosecutor’s Fallacy. As the name implies, it is a problem often encountered in courts of law, and there are numerous cases of incorrect convictions as a result of this fallacy. No less serious are the potential consequences of Simpson’s Paradox, for instance, when determining the treatment effect of a new drug under study. The effect of a drug on two subgroups may appear as the complete opposite of the treatment effect on the whole group. On a much lighter note, the Monty Hall Problem has its origin in a television game show and might perhaps be the most difficult puzzle to comprehend intuitively, even when explicit proof is provided. Respected mathematicians and statisticians have struggled with this problem, and some of them have boldly proclaimed wrong solutions. The counterintuitive nature of these probabilistic problems relates to the cognitive limits of human inference. More specifically, we are dealing with the problem of updating beliefs given new evidence, i.e. carrying out inference. This cognitive challenge may seem surprising, given that humans are exceptionally gifted in discovering causal structures in their everyday environment. Discovering causality in the world is quite literally child’s play, as babies start understanding the world through a combination of observation and experimentation. Our human intuition is actually quite good when it comes to reasoning from cause to effect; our qualitative perception of such relationships (even under uncertainty) is often compatible with formal computations. However, when it comes to reasoning under uncertainty in the opposite direction, from effect to cause, i.e. diagnosis, or when combining multiple pieces of evidence, conventional wisdom frequently fails catastrophically. Even worse, the correct inference in such situations is often completely counterintuitive to people and feels utterly wrong to them. It is not an exaggeration to say that their sense of reason is violated. For more traditional computations, such as arithmetics, we have many tools that help us address our mental shortcomings. For instance, we can use paper and pencil to add 9,263,891 and 1,421,602 as most of us can’t do this in our heads. Alternatively, we can use a spreadsheet for this computation. In any case, it will not surprise us that the sum of those two numbers is a little over 10.5 million. The computed result is entirely consistent with our intuition. As this paper will show, the formally correct solutions of these probabilistic paradoxes are counterintuitive. In addition to being counterintuitive, there are few tools assisting us in solving them. There is no spreadsheet that allows us to simply plug in the numbers to calculate the result. Although we won’t be able to overcome inherent mental biases and cognitive limitations, we can now provide a very practical new tool for the correct inference in the form of Bayesian networks. Bayesian networks derive their name from Reverend Thomas Bayes, who, in the middle of the 18th century, first stated the rule for computing inverse probabilities. Bayesian networks offer a framework that allows applying Bayes’ Rule for updating beliefs in the same way spreadsheets are very convenient for applying arithmetic operations to many numbers. We will show how restating these vexing problem domains as simple Bayesian networks offers near-instant solutions. Just as spreadsheets help us perform arithmetic operations externally, i.e. outside our head, Bayesian networks offer a reliable structure to precisely perform inferential computations, which we can’t manage in our minds. The visual nature of Bayesian networks furthermore helps (at least a little) in making these paradoxes more intuitive to our own human way of thinking.
Market driver analysis and product optimization are one of the central tasks in Product Marketing... more Market driver analysis and product optimization are one of the central tasks in Product Marketing and thus relevant to virtually all types of businesses. BayesiaLab provides a uni!ed software platform, which can, based on consumer data, 1. provide deep understanding of the market preference structure 2. directly generate recommendations for prioritized product actions. The proposed approach utilizes Probabilistic Structural Equation Models (PSEM), based on machine learned Bayesian networks. PSEMs provide an ef!cient alternative to Structural Equation Models (SEM), which have been used traditionally in market research.
The objective of this paper is to provide you with a practical framework for causal effect estima... more The objective of this paper is to provide you with a practical framework for causal effect estimation in the context of policy assessment and impact analysis, and in the absence of experimental data. We will present a range of methods, along with their limitations, including Directed Acyclic Graphs and Bayesian networks. These techniques are intended to help you distinguish causation from association when working with data from observational studies This paper is structured as a tutorial that revolves around a single, seemingly simple example. On the basis of this example, we will illustrate numerous techniques for causal identification and estimation.
In this introductory paper, we present Bayesian networks (the paradigm) and BayesiaLab (the softw... more In this introductory paper, we present Bayesian networks (the paradigm) and BayesiaLab (the software tool), from the perspective of the applied researcher. In Chapter 1 we begin with the role of Bayesian networks in today’s world of analytics, juxtaposing them with traditional statistics and more recent innovations in data mining. Once we establish how Bayesian networks fit into the proverbial big picture, we present in Chapter 2 the mathematical formalism that underpins this paradigm. While employing Bayesian networks for research has become remarkably easy with BayesiaLab, we need to emphasize importance of their theory. Only a deep understanding of this theory will allow researchers to fully appreciate the wide-ranging benefits of Bayesian networks. Finally, in Chapter 3, we provide an overview of the BayesiaLab software platform, which leverages the Bayesian networks paradigm to far greater extent than any other tool that has ever been available in this field. We show how the th...
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