Influence diagram

An influence diagram is a graphical tool used to model decision-making in a situation of uncertainty. It is composed of several elements including rectangles, arrows, and numbers, which represent different factors that influence the outcome of the decision. The rectangles represent variables, such as the decision to be made, the probabilities associated with the different outcomes, and the costs associated with each outcome. The arrows represent the relationships between the variables and the numbers associated with the arrows represent the strength of the relationship. The influence diagram can be used to help identify the most likely outcomes of a decision and to determine the best course of action.

Example of Influence diagram

An example of an influence diagram is shown below. It is used to model a decision about whether or not to invest in a risky stock. The rectangles represent the variables associated with the decision, such as the expected return on the investment, the risk associated with the investment, and the cost of the investment. The arrows represent the relationships between these variables and the numbers associated with the arrows represent the strength of the relationship. The influence diagram can be used to identify the most likely outcome of the decision and to determine the best course of action.

In this example, the expected return is represented by the rectangle labeled ‘Expected Return’ and the risk associated with the investment is represented by the rectangle labeled ‘Risk’. The arrows connecting the rectangles represent the relationships between the variables and the numbers associated with the arrows represent the strength of the relationship. The influence diagram can be used to identify the most likely outcome of the decision and to determine the best course of action.

Formula of Influence diagram

The formula for influence diagram is as follows: $P(A)=\sum _{i}^{n}P(A|X_{i})P(X_{i})$

Where P(A) is the probability of the decision, P(A|X_i) is the probability of the decision given the variable X_i and P(X_i) is the probability of the variable X_i. This formula can be used to calculate the probability of the decision given a set of variables.

When to use Influence diagram

An influence diagram can be used to help make decisions in situations of uncertainty. It can help identify the most likely outcomes of a decision and to determine the best course of action. It can be used to model a wide range of decisions, such as financial decisions, medical decisions, and engineering decisions.

Types of Influence diagram

• Probabilistic influence diagrams are used to model decision-making in a situation of uncertainty. In these diagrams, the rectangles represent the variables associated with the decision, the arrows represent the relationships between the variables, and numbers associated with the arrows represent the strength of the relationship. The influence diagram can be used to calculate the expected value of a decision and to determine the best course of action.
• Causal influence diagrams are used to model the cause and effect relationships between different variables. These diagrams are composed of rectangles representing the variables, arrows representing the relationships between the variables, and numbers associated with the arrows representing the strength of the relationship. The influence diagram can be used to identify the most likely outcomes of a decision and to determine the best course of action.
• Utility influence diagrams are used to model the utility of a decision. In these diagrams, the rectangles represent the variables associated with the decision, the arrows represent the relationships between the variables, and numbers associated with the arrows represent the strength of the relationship. The influence diagram can be used to calculate the expected utility of a decision and to determine the best course of action.

Steps of Influence diagram

• First, identify the decision to be made and the variables that will influence the outcome. These variables can include the probabilities of different outcomes, the costs associated with each outcome, and any other factors that will impact the decision.
• Next, draw the influence diagram. Each variable should be represented by a rectangle, and the relationships between the variables should be represented by arrows. The numbers associated with the arrows represent the strength of the relationship between the two variables.
• Once the influence diagram has been created, it can be used to determine the most likely outcome of the decision. The probability of each outcome can be calculated using the numbers associated with the arrows, and the costs associated with each outcome can be calculated using the numbers associated with the rectangles.
• Finally, the best course of action can be determined by comparing the costs and probabilities of each outcome. The outcome with the lowest cost and the highest probability is the most likely to be the best course of action.

Advantages of Influence diagram

• Influence diagram are a visual representation of a decision making process, making it easier for decision makers to understand the different variables and their relationships.
• Influence diagrams can be used to analyze the risk associated with different decisions.
• They can be used to identify the most likely outcomes of a decision and to determine the best course of action.
• Influence diagrams can be used to compare different options and their associated costs and risks.

Disadvantages of Influence diagram

• Influence diagrams can be complicated to construct, especially when there are a large number of variables.
• They can be time consuming to maintain.
• They may not provide a complete or accurate picture of the situation due to the complexity of the relationships between variables.

Limitations of Influence diagram

Despite the usefulness of influence diagrams, there are some limitations. Firstly, influence diagrams are limited by the complexity of the system being modeled. They are most useful for relatively simple systems, such as those with only a few variables and a few relationships between them. Secondly, influence diagrams are limited by the amount of data available. If the data is incomplete or uncertain, the accuracy of the influence diagram will be limited. Lastly, influence diagrams are limited by the user's ability to interpret the results. If the user does not understand the meaning of the elements in the diagram or the relationships between them, the results may be misinterpreted.

Other approaches related to Influence diagram

The influence diagram is closely related to other approaches such as decision trees, Bayesian networks, and Markov Decision Processes (MDPs). All of these approaches are used to model decision-making under uncertainty. Decision trees are used to identify the best course of action by considering all the possible outcomes and their associated probabilities. Bayesian networks are used to model the relationship between different variables and their associated probabilities. Markov Decision Processes are used to identify the optimal course of action by considering all the possible states and their associated rewards or costs.

In summary, an influence diagram is a graphical tool used to model decision-making in a situation of uncertainty. It is closely related to other approaches such as decision trees, Bayesian networks, and Markov Decision Processes, which are all used to model decision-making under uncertainty.

Influence diagram — recommended articles

Multidimensional scaling — Probability theory — Hierarchical regression analysis — Multicollinearity — Autocorrelation — Standardized regression coefficients — Principal component analysis — Support vector machine — Coefficient of determination

References

• Sanner, S. (2010). Relational dynamic influence diagram language (rddl): Language description. Unpublished ms. Australian National University, 32, 27.
• Fatisson, J., Oswald, V., & Lalonde, F. (2016). Influence diagram of physiological and environmental factors affecting heart rate variability: an extended literature overview. Heart international, 11(1), heartint-5000232.