Bayesian Machine

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About Bayesian Machine

Bayesian Machine is an enlightening project that employs a Bayesian framework to investigate beliefs about various topics. We utilize multiple AI chatbots to autonomously explore questions, update their beliefs, and reach conclusions based on evidence.

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Method

In this Bayesian exploration, we engage multiple AI chatbots in a unique investigative process. Here's a simplified example of how it works:

Example: Determining Gender

Let's say a chatbot is trying to determine if a person is male or female, starting with a 51% belief they're male based on global statistics.

  1. The chatbot asks: "Do you have long hair?"
    Answer: Yes
    Updated belief: 85.2% female (long hair is more common in females)
  2. Next question: "Do you regularly wear makeup?"
    Answer: No
    Updated belief: 63.4% female (not wearing makeup is more common in males, but the prior female probability was high)
  3. The chatbot asks: "Have you ever been diagnosed with color blindness?"
    Answer: No
    Updated belief: 65.9% female (color blindness is slightly more common in males)
  4. Final question: "Have you ever grown a full beard?"
    Answer: Yes
    Updated belief: 99.979% male (ability to grow a full beard is a strong male indicator)

The chatbot concludes the person is male with 99.979% confidence, demonstrating how Bayesian inference can handle seemingly contradictory evidence and how some factors are more decisive than others.

Bayesian Mathematics Explanation

For the mathematically inclined, here's how we apply Bayes' theorem in our process:

Bayes' theorem is expressed as:

P(A|B) = [P(B|A) * P(A)] / P(B)

Where:

  • P(A|B) is the posterior probability of A given B
  • P(B|A) is the likelihood of B given A
  • P(A) is the prior probability of A
  • P(B) is the marginal likelihood of B

In our gender determination example, for the question about growing a full beard:

P(Male | Full Beard) = [P(Full Beard | Male) * P(Male)] / [P(Full Beard | Male) * P(Male) + P(Full Beard | Female) * P(Female)]

Plugging in our estimated probabilities:

P(Male | Full Beard) = (0.9 * 0.341) / (0.9 * 0.341 + 0.0001 * 0.659) ≈ 0.99979

This calculation dramatically shifts our belief towards male, illustrating the power of Bayesian inference in updating probabilities based on new evidence.

In our actual process:

  1. Each chatbot begins with an initial belief about a specific question.
  2. The chatbot then formulates questions to gather more information.
  3. We use Perplexity to search for answers to these questions, providing the chatbot with current, relevant data.
  4. Upon receiving this information, the chatbot updates its belief using Bayesian inference.
  5. This process of questioning, data gathering, and belief updating continues until the chatbot reaches a high level of certainty or we decide to conclude the investigation.

This method allows for a transparent view of how beliefs evolve based on new evidence, mimicking a rational approach to knowledge acquisition and belief formation.

"In the spirit of the Enlightenment, we seek to illuminate the path of knowledge through rational inquiry and empirical evidence."