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Risk Analysis Methods for Nuclear War and Nuclear Terrorism (2023)

Chapter: 6 Risk Analysis Methods and Models

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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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6

Risk Analysis Methods and Models

Both quantitative and qualitative analytic methods can play a role in assessing specific components of the risks related to nuclear terrorism and nuclear war. While the analysts who are assessing the overall risks of nuclear war and nuclear terrorism are confronted by significant uncertainties related to lack of direct evidence; complex interdependencies; and changing technologies, policies, and geopolitical context, more narrowly defined risk problems may be more valuable to decision makers.

Risk analysis includes identification of risk management options and analysis of the effect of these options on the base risks. It is outside of the statement of task of this committee to analyze the policy or launch decisions that can be made by the decision makers. However, risk assessments can provide useful information to better inform decision makers.

Often, the questions that confront decision makers involve risks related to components of the overall risks, in particular risks associated with the country’s own systems or capabilities. Such questions might involve scenarios about which a great deal is known and may therefore be more tractable than assessing overall risks. These kinds of questions might include, for example:

  • Do communications in the command-and-control system of nuclear forces work as intended (Paté‐Cornell and Neu 1985)?
  • What is the reliability of a particular country’s nuclear stockpile?
  • What is the probability that a particular model of detector at an automobile border crossing will detect a specific level of radiation (with probabilities of false positives and false negatives)?
Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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  • How quickly does a particular material used in a nuclear weapon degrade?
  • Which nuclear facilities should be inspected and how often?

Such questions might be addressed qualitatively, by structuring the understanding of the system, or quantitatively, by assigning probabilities to the events or failure modes identified in that risk structure. Some risk analyses are based on a combination of models that address both deterministic and probabilistic variables. Analyses often involve integrated models that select the most appropriate technique for each part of the risk analysis process—such as a reliability analysis of a system or subsystem, probability of detection of a sensor suite, the reliability of a communications network or the dynamics of external events. The choice of specific techniques is determined in part by the decisions that the risk analysis is intended to inform, the availability of relevant input, and the desires of the decision maker regarding the form of the results.

OVERVIEW OF METHODS

Table 6-1 briefly summarizes common analysis methods that have been or could be used for assessing the risks of nuclear war and nuclear terrorism. (For more detailed discussions of selected methods for both likelihood and consequence assessments, see Scouras et al. 2021.) In addressing a particular question, analysts may draw on multiple methods and many sources of evidence. This table relies only on publicly available information and is not intended to be exhaustive.

Note that some of the models presented in this table have not yet been applied to nuclear war and nuclear terrorism or published in the open literature. They are presented here as analytical options that can be used to assess the risks. It is important for all models to be validated prior to their use. This can be a time-consuming process but is essential for reliable implementation in any setting.

FIRST-STRIKE STABILITY ANALYSIS

First-strike stability analysis uses models and simulations to examine the nuclear capabilities that would remain on both sides if one side were to carry out a preemptive nuclear strike on the other side and vice versa. These analyses are conducted over a range of possible attacks spanning adversaries and their capabilities (e.g., their weapon systems and alert statuses). The results from these analyses can inform operational and logistical decisions, such as determining options for storing and protecting resources, evaluating possible force structures and alert statuses, assessing different strategic arms control agreement options, and planning scenarios for specific attacks. In particular, these analyses provide a starting point for evaluating response options by each side following the initial strike—a situation

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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that becomes more complex as additional nuclear states develop capabilities and numbers that bring them closer to parity with the current nuclear superpowers.

Many methods can be brought to bear to feed first-strike stability analyses with information. Common examples are drawdown curves, which can be as simple as a representation of remaining blue force weapons after red attacks of varying size. These depend on assumptions about aggressor and defender capabilities and give insight into what aggressor and defender capabilities exist following a first strike. Other factors that could be considered include how preemptive actions could result in destabilizing actions from adversaries (e.g., creating new weapon technologies to counter the reinforcement of existing weapon silos) and how actions can cascade in a multi-actor scenario.

PROBABILISTIC RISK ASSESSMENT

Probabilistic risk analysis (PRA) (also known as probabilistic safety analysis) provides an analytical structure and yields quantitative results. Originally developed for nuclear power plants (NRC 1975), it has been developed further to include human and management errors, as well as the dynamics of systems (e.g., deterioration) and the evolution of external events (e.g., environmental factors). Yet, like all quantitative methods of risk analysis, it can contain large uncertainties and dependencies on underlying assumptions. These uncertainties are reflected to some degree in the resulting risk curves (probability distributions of outcomes), but additional representations are needed to describe the uncertainties in the probabilities and their effects in the results. Functional diagrams, fault trees, event trees, influence diagrams, and dynamic stochastic models are used to represent the underlying structure. When extending a risk analysis to a decision analysis, decision points and approaches are introduced in the model to better understand the inherent uncertainties associated with different options.

The first step in a PRA is to characterize the functions of the system, and which ones are essential to the success of its operations, as well as the external events that affect the reliability of the different components. This is done through a functional diagram representing system functions in series or in parallel and through event trees or fault trees (Paté-Cornell 2009).

Fault trees are often used to identify failure modes when analyzing the failure probabilities of engineered systems (Aven 2008; Rausand and Hoyland 2003), but they are not generally necessary for other kinds of systems. Event trees are based on the specification of events contributing to the considered outcome (e.g., total failure of the system). They include probabilities and dependencies to provide the probabilities of the different scenarios based on the failure modes, thus a probability distribution of the outcomes (Paté‐Cornell 1984). As noted above, PRA has evolved considerably since its introduction in 1974—now including, for instance,

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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TABLE 6-1 Risk Analysis Methods

Method Applicability and Strengths Limitations Examples of Use for Risks of Nuclear War or Nuclear Terrorism
First-Strike Stability Analysis This method compares the surviving nuclear forces of both actors for the two cases in which (1) one actor attacks the nuclear forces of the other side first, and (2) the other actor strikes first. This method is limited to the contribution of force structure and posture to incentives to strike first in a crisis; it ignores myriad other relevant factors. This method can be used to evaluate different force structures and alert statuses. It can also be used to assess different strategic arms control agreement options.

Resources: Cimbala and Scouras (2002); Scouras (2019)
Probabilistic Risk Assessment (PRA) PRA was originally developed for engineered systems but has been applied to other fields and to interactions between intelligent adaptive actors and other nontechnical risk analyses. PRA provides an analytical structure and yields quantitative results with quantified uncertainties.

Classical statistics and Bayesian probabilities can be used to reflect uncertainties in available information.
The major challenges of applying PRA to the risks of nuclear war are identifying the scenarios, and assessing their probabilities and consequences. These probabilities have to be communicated to decision makers in a way that they understand, recognizing that it can be challenging to grasp and represent the complex structure and functions of a system and the interactions among actors.

While the quantitative results from PRA can be converted into qualitative results, nuance can be lost in the process.
The Department of Homeland Security has used PRA to assess the risks of nuclear terrorism. PRA can be used to analyze terrorist pathways to nuclear weapons use and potential defender responses. It can be used to evaluate the risks associated with defender capabilities, acquisition of materials, production of sufficient material, weaponization of that material, reliability of technical systems involved in nuclear weapons maintenance and signal communication, transportation to the target area, final deployment at the target, exposure and other effects of nuclear weapons use, ability of the public health system to provide effective medical countermeasures, and potential human health and economic consequences from an attack.

Resources: Paté-Cornell and Guikema (2002); Paté-Cornell and Neu (1985)
Order-of-Magnitude Estimates An order-of-magnitude estimate provides a simplified framework for estimating overall risks for nuclear war and nuclear terrorism. This begins with upper and lower bounds, which are then incrementally decreased and increased respectively until a range of values is identified that cannot be ruled out easily. This intuitive approach is subject to the challenges typical of expert elicitation.

This approach has not yet been widely tested.
Resources: Hellman (2011); Scouras et al. (2021)
Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Method Applicability and Strengths Limitations Examples of Use for Risks of Nuclear War or Nuclear Terrorism
Nuclear Effects Simulation Built on mathematical models, deterministic or probabilistic simulations use data (e.g., weapons yield, weather condition, wind speed) to estimate effects of nuclear weapons. Nuclear effects simulation models are based on available test data and the nature of many long-term effects that are not well known. The resolution and accuracy of these models vary. These simulations can be used in war games involving nuclear terrorism or limited use of nuclear weapons.

Resources: Bele (n.d.); Nasstrom et al. (2007)
Game Theoretical Approaches Game theory, or game analysis, is a standard approach for situations with intelligent adversaries. Game theory analysis is limited by the knowledge of what the adversaries know, want, and have. Representing these limitations is critical to the value of the results. As with probabilistic methods, uncertainties are introduced in the analysis and represented in the results. Game theory was arguably the basis for the mutually assured destruction policy during the Cold War.

Resources: Brams (2001); Ice et al. (2019); Kucik and Paté-Cornell (2012); O’Neill (1994); Schelling (1960, 1980)
Adversarial Risk Analysis (ARA) ARA can be used to model the strategic choices of an intelligent opponent. It might apply to situations in which one has a small number of actors and fairly accurate knowledge about the goals, capabilities, and decision making of those actors. The model also includes uncertainties—for example, those represented by Bayesian probabilities. ARA may be more effective in modeling scenarios with a small number of actors (e.g., a nuclear threat by North Korea against the United States), but it would not be easy to use when assessing the possible actions of opportunistic terrorists. ARA is relatively new, but older versions of the method have been applied in the context of game analyses. ARA has not been directly used in many complex settings. As an extension of game analysis, however, it has been used to model and simulate counterterrorism policies, considering alternative decisions of a government and a terrorist group.

Resources: Banks et al. (2015); Rios Insua et al. (2012)
Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×
Agent-Based Models Agent-based models are based on rules that determine the interactions among actors. They can also reflect uncertainties of each actor about the motivations and potential responses of others to actions of the actor. These models can be difficult to identify and validate as the rule sets may change over time. It is difficult to test the goodness-of-fit of agent-based models for particular applications since relevant statistics are seldom available.

The models should include uncertainties relevant to the decisions made by the actors and the interaction rules.
Some attempts have been made to apply agent-based models to understand approaches to deter the development and use of nuclear weapons.

Resources: Banks and Hooten (2021); Carley et al. (2018)
Multi-Attribute Models Multi-attribute models specify the key attributes of the preferences of an actor and then assess the behavior of actors that pose the largest risk. These models rely on expert opinions from policy and intelligence experts. These models have been used by the Sandia National Laboratories global risk and decision analysis team.

Resources: Bauer et al. (1999); Caskey and Ezell (2021); Caskey et al. (2018)
Network Models Network models use network analysis to explore multiple alternatives at nodes representing key events and scenarios in the path from start to end. These models can be deterministic or probabilistic and used to identify the shortest path to a given outcome, which can help focus intelligence resources. General cases may be difficult to address depending on the description of scenarios. As applications become more complex and the options multiply, the combinatorial complexity makes these methods more difficult to use. Their implementation depends on the analysts’ computational capabilities. Network models can be used to assess the nuclear capability of a nation state or terrorist organization from program start to operational readiness. These models are useful in thinking through a set of specific nuclear threats and risk scenarios.

Resources: Freeman (2010); McIntosh and Storey (2018)
Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Method Applicability and Strengths Limitations Examples of Use for Risks of Nuclear War or Nuclear Terrorism
Nuclear Force Exchange Models Nuclear force exchange models can be used to assess the potential effectiveness of nuclear attacks and can be part of a first-strike stability analysis.

These models can use weapon-specific technical information (e.g., planning factors) to estimate nuclear force capabilities.
These model outputs depend on users developing possible attack strategies, potentially imbedding biases or inaccurately reflecting relevant scenarios. These models have been used to assess conflict scenarios, such as the North American Trade Organization vs. Warsaw Pact, North Korea, and variations of bilateral compared with trilateral arms agreements.

Resource: Hafemeister (2014)
Conventional Force Models Conventional force models can be used to assess the potential effectiveness of conventional force attacks. These models can be used to compare the effectiveness and consequences of a conventional force attack with a nuclear attack.

These models can use weapon-specific technical information to estimate conventional force capabilities.
These model outputs depend on users developing possible attack strategies, potentially imbedding biases or inaccurately reflecting relevant scenarios. The variety of conventional weapons and possible scenarios compound these challenges. These models are used broadly to assess potential conflict scenarios.

Resources: Ali et al. (2007); Betts (1985); Larson (2019); Stockfish (1975)
Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×

a system’s evolution and deterioration, as well as the human and organizational errors that affect the failures of the system components or constitute failure modes in themselves (Murphy and Paté-Cornell 1996).

In more detail, a combination of fault trees and event trees can be used to characterize the reliability of a system. Fault trees are constructed using inductive or top-down logic starting with a hypothesized failure or undesired event (the top event) and working backward to identify the combinations of basic events that could give rise to that top event. In the context of this report, the top event might be a successful terrorist attack on a nuclear plant, and the basic events could be a forcible breach of plant security or the radicalization of an employee. A fault tree includes a logic diagram that shows Boolean representations of the basic components (i.e., by two values—for example, by true or false, or by 0 or 1, happens or not), as well as the Boolean relationship between the basic events and the top event (a system or subsystem failure) and the possible causes of that event (the sets of component failures called failure modes). The tree itself represents how the states of the system’s components (basic events) relate to the state of the system as a whole, using logic gates. Probabilities are then used to assess the chances of the different failure modes and of failure of the system.

A detailed fault tree might involve numerous events or be decomposed to examine the role of each subsystem in a system’s failure. The failure modes (minimum combinations of component failures leading to system failure) can be identified from the logical functions of the fault tree. The probability of the top event can then be computed as a function of the probabilities of these failure modes, accounting for the effects of external events and the human errors that may affect the failure probabilities of several components and subsystems. To construct the fault tree itself, one needs a description of the system’s function, which is provided by a functional block diagram. Boolean results allow for the identification of failure modes, whose probabilities can then be assessed to yield the chances of the top event (system failure). In technical systems, fault trees allow identification of the combinations of events and the Boolean variables (0 or 1) that constitute the failure modes. Once the failure modes have been identified, one can compute their probabilities, including dependencies and external events.

Event trees are deductive (in contrast with fault trees) and based on random events and random variables and their probability distributions (Paté‐Cornell 1984). The results of a fault tree analysis and the probabilities of failure modes can be included in an event tree to assess the probability distribution of different possible outcomes (including system failure, or a range of losses in a successful terrorist attack). Event trees are widely applicable to analyses of a spectrum of scenarios, including terrorist nuclear attacks). They are constructed using deductive logic. The process may start by hypothesizing the initiating event of a failure scenario, such as terrorists’ acquisition of fissile material or an alarm indicating the possibility of

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×

an incoming intercontinental ballistic missile. It then works forward to identify all possible combinations of subsequent events (whether successes, failures, or multi-outcome results) and their probabilities, conditional on what precedes them in the tree, to determine which combinations of events would lead to undesirable outcomes and their probabilities. WASH-1400 (NRC 1975), one of the first applications of PRA to an engineered system, introduced fault trees and event trees in the nuclear technical realm. Dynamic models representing an anticipation of future evolutions, both of systems and of the external events that affect their operations, are now part of PRAs and especially relevant to the assessment of nuclear risks.

An event tree represents the events following an initiating event and decomposes the scenarios by showing all possible pathways to outcomes. For example, risk analysts in the Department of Homeland Security use an event tree methodology when analyzing potential nuclear terrorism attack scenarios. Monte Carlo simulation, based on the generation of random values of different events and factors and the functions in which they appear, can be used to generate multiple realizations of a given loss function and provide a final set of likelihoods and consequences realizations for the set of scenarios. Similarly, the National Nuclear Security Administration noted in communication to the committee that knowledge about nuclear devices and pathways to their development allows the overall probability of a given scenario to be decomposed into probabilities of acquisition, processing, fabrication, and use of nuclear materials in an analysis of risks. “Since there may be higher confidence in one of these terms over another, the partitioning approach enables resources to focus on improving the quantification of those terms where the greatest uncertainty or highest potential for impact to a risk assessment may exist, and subsequently redirect USG [U.S. government] efforts after achieving an acceptable level of confidence.”1

The combination of fault trees and event trees is useful when considering technical systems because their functions can be combined to provide a final risk result. Event trees are useful if one wants to display the chronological order of events and the dependencies among uncertain factors. The events in an event tree do not have to be in chronological order. The probabilities on any branch are conditioned on the realizations of the random variables that precede the events in the tree regardless of the timing. Their order can thus be chosen as a function of the structure of the information available. Event trees therefore display dependencies among events (e.g., if the quality of emergency response depends on environmental conditions). This type of dependency is readily apparent since the failure probabilities of each component or occurrences of various events are shown on the relevant branches. For these reasons, event trees are good for facilitating communication about the

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1 L. Leonard, Department of Homeland Security, “Response to NASEM Questions on DHS Risk Assessments,” Washington, DC, September 15, 2021.

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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effects of the assumptions made in the risk model. However, because both successes and failures are explicitly shown and can have more than two realizations, event-tree models can rapidly become extremely large.

Fault and event trees are used to develop a probability distribution of the consequences of the scenarios. The probabilities of the output quantity of interest (e.g., losses) reflect the uncertainties of individual component failures. Event trees include both systematic (epistemic) and random (aleatory) uncertainties in the form of marginal or conditional probabilities: see Appendix B for more discussion of these types of uncertainties. While they are included in event-tree analysis, systematic (epistemic) uncertainties—for example, those resulting from disagreements among experts or imperfect knowledge—can be separately described to a decision maker, and the effect of these uncertainties can be assessed, through such methods as a sensitivity analysis. This is important as the two types of uncertainty have different implications for decision making. Although aleatory uncertainty cannot be reduced (e.g., the result of the roll of the dice), a high level of systematic (epistemic) uncertainty may imply that more research or intelligence gathering might be desirable (if feasible) before deciding about options for risk reduction. Yet it should be understood and communicated that more information may actually increase uncertainties—for example, if a new failure mode is discovered in the process of a risk analysis—which may be an important consideration for the decision maker.

As noted above, these methods are often used to analyze the failure probabilities of outcomes, including failure of particular systems or subsystems, both technical and social. These methods have been applied in many fields, including nuclear power plants, aerospace systems such as the space shuttle, chemical and petrochemical facilities, and medical procedures. They can even support qualitative analysis: for example, Barrett and colleagues (2013a) use a simplified fault tree representation to structure an analysis of inadvertent nuclear war.

While the general form of a probabilistic risk assessment for nuclear power plants today is not dramatically different from that used in the Reactor Safety Study (NRC 1975), substantial improvements in methodology have been developed to enable the method to handle more complex and realistic situations. But many nuclear threat scenarios are quite complex, and the application of probabilistic risk assessment may be difficult.

Risk analysis seeks to identify the actions that minimize the expected loss. When there is both great uncertainty about the probabilities of events and the magnitude of the consequences, probabilistic risk assessment will represent these uncertainties as probability distributions of outcomes based on the limited information available. Yet, one should recognize that some decision makers may have difficulties relating these probabilities to the decisions that they have to make, and that both the analytical methods and the results have to be carefully explained.

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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ORDER-OF-MAGNITUDE ESTIMATES

One intuitive approach to assessing the overall probability of nuclear war, proposed by Hellman (2011), can generate results with a wide range of uncertainty. Hellman briefed the committee on his approach, which begins by considering an extreme case: a probability of 1 percent per day. He argues that this is clearly too high; in his words, “we would not expect to live out the next year.” By the same token, a probability of 1 in 1,000,000 per year is, in his view, clearly too small. Hellman then argues for increasing the lower bound and decreasing the upper bound, an order of magnitude at a time, until a range of values is identified that cannot easily be ruled out. He argues that even an estimate covering two orders of magnitude of uncertainty can be policy relevant.

Hellman uses historical events such as the 1962 Cuban missile crisis and adaptations of expert elicitation to develop his intuitive estimate that the probability of nuclear war is 1 percent per year to an order of magnitude. While the method described above does not constitute a PRA, as described in this report, Hellman suggests that some form of PRA of the overall risks of nuclear war could be used to further develop the rough probabilities into estimates of overall risks of nuclear war, albeit with large uncertainties (Scouras et al. 2021).2

This intuitive approach merits further investigation as a means to estimate the overall risks for nuclear war. It has not yet been widely tested.

NUCLEAR EFFECTS SIMULATIONS

Nuclear effects simulations use mathematical and statistical models to estimate the effects of nuclear weapons. These simulations can help inform the understanding of how a detonation would impact a particular location, which can inform decision making. However, these simulations can contain large uncertainties because they often depend on sparse real-world data and a limited understanding of many long-term effects.

While these simulations can be designed to account for many types of effects, they often combine location-specific information (e.g., buildings, populations, transit systems) with the anticipated effects from a detonation (e.g., the blast wave, intense heat, radiation, and radioactive fallout) to estimate the total impact. Longer-term effects, such as the toll on human social, emotional, and physical health, as well as the long-term economic costs resulting from cleanup and rebuilding, are less well understood and so difficult to include.

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2 The policy use of risk estimates with very large uncertainties is a more appropriate subject for Phase II of this study, which will examine the interplay between the result of risk analyses and national security strategy more directly.

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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This type of information can be helpful for scenario planning, but it is not generally well suited for precise calculations of impacts.

GAME THEORETICAL APPROACHES

Increasingly, analyses require some model of an adversary. Such analyses depend on both the characteristics and actions of users and attackers.

Approaches that involve multiple decision makers, typically adversaries, can be understood as games against one or more adversaries (Paté-Cornell 2009; Schelling 1960). Such approaches often focus on questions with uncertain answers: What do the adversaries know? What do they want? What do they have? Information to address these questions can come from a variety of open sources as well as the intelligence community and other experts.

Game theoretical approaches can be conducted qualitatively, which approach allows identification of the various options available to the different sides under variable circumstances, based on expert opinions. The task is to identify (qualitatively) the moves that are most likely to be chosen by other sides, without quantitative support of the probabilities and consequences of the different scenarios or of the preferences of the decision makers. The doctrine of mutually assured destruction that prevailed during the Cold War is one example of the use of qualitative analysis, along with the quantification of scenarios and options.

Quantitative game theory has been used in security studies (Bier 2005; Bier and Azaiez 2008; Bier et al. 2007; Zhuang and Bier 2007), and quantitative game analysis methods can include behavioral games, as well as games on hierarchical and nested networks. A key component of these models is the response of each side to a move from another. The model is thus dynamic and allows simulation of the long-term effects of a defense policy or strategy by modeling the alternative actions of both sides (Kucik and Paté-Cornell 2012). Network theory, and influence diagrams in particular, thus plays an important role in this context, as it represents explicitly the formal notion of interaction. The use of networks and influence diagrams implies fundamental insights about interactions, which are sparse, have different strengths, can be directed or asymmetric, and can vary in time.

MODELING OF ADVERSARIES

Explicit Bayesian Modeling

Modeling an opponent is something human beings do regularly, either implicitly or explicitly. In the domain of counterterrorism, a Bayesian model of the effectiveness of policy from a government to interdict or counter the actions of a

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×

terrorist group was constructed based on two influence diagrams representing the decision of each of the two sides at each time unit in a determined time horizon (Kucik and Paté-Cornell 2012). The model was applied to the counterinsurgency measures of the Philippine government faced with a terrorist group in the island of Mindanao with input from the U.S. Army and the Philippine Army. It was then used to simulate the effects of chosen paths at each time by each side over 3 years, and the results for that time period were compared to the actual situation. Bayesian modeling of opponent interactions is thus possible on a similar pattern for nuclear conflicts between nations, but it is likely to be more difficult, given the uncertainties involved, when trying to model organized multinational terrorist organizations.

Other game analyses involving several actors that act over time can be constructed on a similar pattern, but with different assumptions (e.g., not only rationality in the classic economic sense) regarding the preferences of the different sides.

Adversarial Risk Analysis

Adversarial risk analysis (ARA) is an alternative to classical game theory that uses Bayesian subjective distributions to model the goals, resources, beliefs, and reasoning of the opponent. In this framework, subjective probability distributions can be used for all unknown quantities, which results in a distribution over the opponent’s actions that accounts for uncertainty. While ARA reduces the need for common knowledge, it can be computationally expensive (Banks et al. 2022).

ARA is relatively new, but older versions of the method have been applied in the context of game analyses. ARA may be more effective in modeling scenarios with a small number of opponents (e.g., a nuclear threat by North Korea against the United States), but it would not be easy to use when assessing the possible actions of opportunistic terrorists.

OTHER MODELS

Agent-Based Models

Agent-based models study the behavior of systems of virtual entities that interact with each other and their environment according to prescribed rules. A classic example of these models is the principal-agent model, involving, for instance, a supervisor and a subordinate. The composed dynamics of agent interactions can be then used to study interesting patterns that one observes, while providing a certain amount of causal understanding (using rules of interaction) of why these patterns arise. Agent-based models have been used to explore cellular automata, interacting particle systems (Banks and Hooten 2021), and traffic flows on roadways (Barrett

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×

et al. 2002; Nagel et al. 1999). In this traffic model, the agents are endowed with multiple behavioral rules, including carrying out a daily itinerary, deciding modes of transportation, finding the best way to get to their destination, and driving on the road while avoiding accidents. In other words, the virtual vehicles interact with each other and their environment (e.g., the road network, the weather, and the time of day) according to rules that determine spacing, speed, route choice, and other factors.

In the context of nuclear threats and consequences, agent-based models can be developed to understand and assess risks for a nuclear event. The social, economic, and health impacts of an improvised nuclear device as a part of the national planning scenario can be also studied using agent-based models (Barrett et al. 2013c; Parikh et al. 2013). Agent-based models have also been developed to study the social, behavioral, and economic impact of the use of nuclear weapons (Swarup et al. 2013). Such a model might develop a detailed representation of a group of individuals or an organization, understand the pathways by which they can obtain fissile material, and represent intent and their ability to compute the consequences of their actions. In other words, one can build a rich representation of the underlying processes and constraints that might lead an organization/country to carry out a nuclear attack. However, the model’s output depends on the factors considered and the completeness of that set. In addition, it would have to be mapped to a probability distribution, and this has been a significant challenge for agent-based models in general (Heard 2014). Agent-based models that forecast weather may be calibrated on the basis of their empirical accuracy, but there are almost no data that could be used to calibrate nuclear risks. In other words, while events, interactions, and consequences can be represented, the associated information and data to calibrate these models, validate the social theories, and quantify the uncertainty are challenging given the lack of statistical data. Additional challenges stem from the computational resources that would be required to couple models at different scale and fidelity. Additional information, including expert opinion, would then be needed to address this key aspect of the model.

Multi-Attribute Models

Multi-attribute models specify the key attributes of the preferences of a decision maker, such as a nuclear state or a nuclear terrorist group, and then assess their behavior that would cause the biggest risks to the United States or its allies. Each of these criteria may be weighted according to the perceived importance placed on them by the adversaries. Different objectives or possible actions may be in conflict with one another in a multi-attribute model. These models can be structured in many different ways, such as with multi-attribute utility functions (Bauer et al. 1999; Keeney and Raiffa 1976) or using an analytical hierarchy process (Andrews

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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et al. 2008). Both deterministic and stochastic network models are used to estimate nuclear capabilities of nuclear states. Subject-matter experts, such as political scientists or intelligence experts, help define preferences of nuclear adversaries in order to populate these models to predict the behavior of high-risk terrorist groups.

Network Models

Influence diagrams (a generalization of Bayesian networks to include decisions) represent a decision analysis based on risk analysis; these often have the same fundamental inputs and outputs as event trees, but also include decision nodes and the value function of the decision maker. Like the Bayesian networks, they show the dependencies among random variables and events, as well as the resulting distributions of input and outcomes and the values attached to them by the decision maker. In both Bayesian networks and influence diagrams, the model has to include a set of numerical tables representing the dependencies among the factors and the resulting distribution of the consequences, as well as the diagram. As the system evolves and the risks change, stochastic processes representing that evolution need to be introduced in the analysis.

Pathway Models

Pathway and network models are used to identify the potential activities that an adversary could perform to obtain a nuclear weapon or delivery system. They can represent multiple variables and decision nodes in the pathway to a user’s decision and its consequences. For example, for nuclear weapons delivery systems, once the potential activities (paths) that an adversary could take are identified, intelligence systems can look for potential signals of these activities.

Network Analysis

Complex networks exist throughout society, including transportation and communication networks. Network science deals with principles that govern the design, analysis, control, and optimization of networks. Recent quantitative changes in computing and communications have created new opportunities for collecting, integrating, accessing, and analyzing information related to such networks, and these enhance analysts’ ability to formulate, analyze, and implement policies pertaining to them. As networks become pervasive, they reduce the time it takes to transmit information between various agents or organizations. Furthermore, they introduce new connections between systems—together creating challenges for resilient decision making in the event a nuclear war or terrorist activity.

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×

Real-world networks are large, heterogeneous, and evolve over time, and their dynamics, behavior, and network structure are interdependent. Reasoning, predicting, and controlling these networks are challenging because the dimension reduction techniques commonly used to analyze physical systems are difficult to apply.

Network analysis seeks to assess the relationships and interdependencies among connected entities. These approaches have been applied to problems related to nuclear and other forms of terrorism, as well as nuclear deterrence (Carley et al. 2018; Morgan et al. 2017) and the consequences of a nuclear explosion on the power grid (Barrett et al. 2013b). Much like agent-based models, dynamic multilevel network analysis can be used to represent sensor networks for detecting the movement of nuclear material (Cazalas 2018; Srikrishna et al. 2005) or to identify central actors that might be involved in the exchange of nuclear material or information.

Nuclear Force Exchange Models

Nuclear force exchange models can approximate the potential effectiveness of a nuclear attack by estimating the expected physical damage, including pre-launch survivability, in-flight survivability, weapon reliability, and probability of damage (incorporating factors such as accuracy, yield, and height at burst). While some of these models are deterministic with one expected outcome, most are probabilistic and provide a range of possible outcomes that depend on the given force structure and other characteristics. Some analyses use input from a variety of models and resources, including submodels that capture detailed phenomena about known variables (e.g., missile trajectory, detonation reliability, blast impact characteristics), as well as existing damage calculators that are used across organizations.

These models can be used as part of a first-strike stability analysis or as a standalone assessment of the risks of a nuclear attack.

Conventional Force Models

Like nuclear force exchange models, conventional force models can be used to assess the potential effectiveness of conventional force attacks, accounting for known variables and uncertainties and yielding deterministic or probabilistic outcomes. However, the abundance of available conventional weapons and the expanded delivery options greatly expand the possible modeling scenarios. Mission planning and other decisions are also complicated by the plethora of factors and options. It is important to note, however, that only some weapons and systems are assumed to affect nuclear stability.

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×

Relative Risk

Relative risk expresses the differences in risk among a set of scenarios or mitigation strategies. This kind of assessment uses some of the methods described above to frame risk information in a way that may be more understandable and thus more useful to decision makers. However, to compute relative risks, one generally has to start from the value of an absolute risk, then assess the effects of changing the values of the relative factors.

Artificial Intelligence and Nuclear Risks

Artificial intelligence (AI)3 is a rapidly developing technology that is revolutionizing the analysis of large datasets and is being widely explored in military and intelligence applications, with particular interest in its support of fast decision making (Schmidt et al. 2021). Associations identified by AI systems are typically based on empirical correlation and they can offer unexpected insights into the relationships between variables. However, they can also produce results that are profoundly biased or simply incorrect (e.g., CRS 2021; Kumar et al. 2019). Because only limited data are available, decision making regarding a nuclear crisis and the use or threat of the use of nuclear weapons may not be well suited for AI.

In the case of deep learning, the processing typically includes nonlinear steps, such as thresholding, whereby variables are downweighted or completely dropped if their values lie outside certain ranges. Correlations can develop in unanticipated and nonlinear ways, with small perturbations resulting in large changes during the analysis. In contrast with many traditional pattern-recognition processes that are linear and can be run backward and undone, processing nonlinearities can effectively prevent deep-learning algorithms from being reversed in order to understand what determines the outcome. The availability of massive amounts of computer processing has been an asset for AI, but also serves as a liability because of increased reliance on cloud and edge computing, which create opportunities for adversary exploitation (CRS 2021; West and Allen 2020).

However, there are at least two types of nuclear-relevant applications in which AI might be implemented to varying degrees to support nuclear decision making: surveillance, warning, and reconnaissance; and communications (Hruby and Miller 2021). The use of AI in an adversarial manner, to challenge human analysis and judgment in wargaming and related activities intended to improve crisis management, could be another helpful role for AI systems.

___________________

3 AI primarily refers to machine learning, including such approaches as supervised or reinforcement learning and deep learning; see CRS (2021) and West and Allen (2020) for brief, nontechnical summaries.

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×

AI continues to evolve rapidly, and much effort is being made to use physics, as well as insights from the behavioral and social sciences, to improve AI results. However, progress along these lines has been surprisingly difficult, and many of the failures are still poorly understood. Pressures for rapid decision making, as well as the lack of relevant training examples, increase these vulnerabilities of AI, as do the challenges for appropriate interfacing between human and machine-based decision making. The lack of transparency and accountability compound these risks.

CONCLUSION

CONCLUSION 6-1: Different methods of risk assessment are more or less well suited for different situations and goals. For risk management problems that involve significant uncertainties and a need to make resource-constrained decisions, assessing the risk variations associated with different options can help inform decision making. The results of relative risk assessments may be more useful and easier to communicate to a decision maker than the absolute risk.

Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
×
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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Suggested Citation:"6 Risk Analysis Methods and Models." National Academies of Sciences, Engineering, and Medicine. 2023. Risk Analysis Methods for Nuclear War and Nuclear Terrorism. Washington, DC: The National Academies Press. doi: 10.17226/26609.
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The assessment of risk is complex and often controversial. It is derived from the existence of a hazard, and it is characterized by the uncertainty of possible undesirable events and their outcomes. Few outcomes are as undesirable as nuclear war and nuclear terrorism. Over the decades, much has been written about particular situations, policies, and weapons that might affect the risks of nuclear war and nuclear terrorism. The nature of the concerns and the risk analysis methods used to evaluate them have evolved considerably over time.

At the request of the Department of Defense, Risk Analysis Methods for Nuclear War and Nuclear Terrorism discusses risks, explores the risk assessment literature, highlights the strengths and weaknesses of risk assessment approaches, and discusses some publicly available assumptions that underpin U.S. security strategies, all in the context of nuclear war and nuclear terrorism.

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