A Chat with GPT: Causality, Bayesian Networks, and Path Diagrams Arguments For and Against

Bram Adams -

ive been reading judea pearl's book of why. he makes the case that causality exists and that staticticians are wrong when they say causality is just when correlation is 1. he also says that bayseian networks are a precursor to path diagrams and that subjectivity can evolve into objectivity.

Me:

create a markdown table for and against this argument

GPT:

Arguments For Arguments Against
1. Causality is more than just correlation: Pearl argues that causality goes beyond mere correlation, as it involves understanding the underlying mechanisms and relationships between variables. 1. Correlation can be a useful proxy for causation: While correlation does not equal causation, in some cases it can serve as a good indicator of causal relationships when other information is lacking or difficult to obtain.
2. Bayesian networks provide a foundation for path diagrams: According to Pearl, Bayesian networks help lay the groundwork for understanding causal relationships through graphical models known as path diagrams, which visually represent these connections. 2. Limitations of Bayesian networks and path diagrams: Critics may argue that while these tools are helpful in visualizing complex systems, they may not always capture all nuances or accurately represent real-world situations where multiple factors interact simultaneously.
3.Subjectivity evolving into objectivity: Pearl suggests that by incorporating subjective beliefs into probabilistic models (such as Bayesian networks), we can refine our understanding over time and eventually arrive at objective conclusions about causal relationships. 3.Potential biases in subjective beliefs: Opponents might argue that relying on subjective beliefs could introduce biases or inaccuracies into analyses, potentially leading to incorrect conclusions about causality.

Me:

can you elaborate on 1 and 3 in the against column?

GPT:

  1. Correlation can be a useful proxy for causation: While correlation does not equal causation, in some cases it can serve as a good indicator of causal relationships when other information is lacking or difficult to obtain. Critics argue that although correlation alone cannot prove causality, it still provides valuable insights into potential causal relationships between variables. In situations where experimental manipulation is impossible or unethical (e.g., studying the effects of smoking on health), strong correlations might be the best available evidence to suggest possible causal links. However, relying solely on correlation could lead to false conclusions if confounding factors are not accounted for.
  2. Potential biases in subjective beliefs: Opponents might argue that relying on subjective beliefs could introduce biases or inaccuracies into analyses, potentially leading to incorrect conclusions about causality. Subjective beliefs may be influenced by personal experiences, cultural backgrounds, and cognitive biases which could skew our understanding of cause-and-effect relationships. For example, confirmation bias may lead individuals to seek out information that supports their pre-existing beliefs while ignoring contradictory evidence. By incorporating these biased subjective beliefs into probabilistic models like Bayesian networks without proper scrutiny and validation against objective data sources, we risk perpetuating misconceptions and drawing erroneous conclusions about the true nature of causal relationships in complex systems.

Me:

draw a path diagram for an example where these biases could occur and ruin the validity of the experiment

GPT:

In this example, let's consider a study investigating the relationship between exercise (X), diet quality (Z), and weight loss (Y). The true causal relationships are as follows: both exercise and diet quality independently contribute to weight loss. However, due to subjective beliefs or biases, the researcher might believe that only exercise directly affects weight loss while diet quality influences exercise habits.

Here is a path diagram representing this biased belief:

  ┌───────┐       ┌────────┐
  │ Diet  ├──────►│Exercise│
  └───────┘       └────────┘
         ╲          ╱
           ╲        ╱ 
            ▼      ▼  
          ┌─────────┐
          │WeightLoss│
          └─────────┘

In this incorrect path diagram, there is an arrow from "Diet" to "Exercise," suggesting that diet quality affects one's ability or willingness to engage in physical activity. Additionally, there is an arrow from "Exercise" to "Weight Loss," indicating that engaging in physical activity leads to losing weight.

However, the true causal structure should look like this:

   ┌───────┐       ┌────────┐
   │ Diet  │       │Exercise│
   └───────┘       └────────┘ 
         ↓           ↓       
         ├──►╭◀-----╯        
             ◎               
             ▼              
        ╭━━━━━━━╮           
        | Weight Loss |
        ╰━━━━━━━╯

In the correct path diagram above, both "Diet" and "Exercise" have direct arrows pointing towards "Weight Loss," showing their independent contributions without any influence on each other.

By relying on biased beliefs when constructing the initial path diagram for analysis, researchers may draw inaccurate conclusions about causality. In our example scenario with flawed assumptions about how variables interact could lead them to overestimate the importance of exercise while underestimating or ignoring the role of diet quality in promoting weight loss.

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