1. Bayes’ Theorem

I think it is very important to discuss the background of Bayes’ Theorem and its connection to probability. At its core, Bayes’ Theorem revolves around the concept of belief and its spectrum, highlighting how probabilities can represent degrees of belief rather than certainties. This foundation allows for a clear way to quantify and update our understanding of uncertain events.

Belief is not deterministic; rather, it exists on a spectrum of probabilities, representing varying degrees of certainty. This concept is grounded in probability theory, where an event space contains all possible outcomes of a scenario. Each event is assigned a probability value within the range of 0 to 1, where 0 indicates an impossible event and 1 represents absolute certainty. The total sum of probabilities for all possible events within this space equals 1, ensuring a complete representation. Additionally, the negation of an event (its complement) is calculated as 1 − 𝑃 ( 𝑒 𝑣 𝑒 𝑛 𝑡 ), maintaining consistency within the concept.

What about the possibilities?

I am not sure if they can be described as "even," but it is clear that the precision of distributed assignments is far from vague. In fact, they are more exact and structured compared to the basic adverbs, offering a clearer way for understanding probabilities.

What are the rules?

1. No possibility is measured by 0, and absolute truth is measured by 1. For example, 2 + 2 = 4 is 1.
2. p = 1 - q, where q can be referred to as the negation of p.
3. Conjunction and Disjunction: P + Q or P × Q.

What is Bayes’ Theorem?

It is one of the most important theorems in probability theory and has been widely used in statistics.

P(A|B) = (P(B|A) ⋅ P(A)) / P(B)

It is especially used in evidence collection to diagnose diseases.

What do I think?

It is crucial to grasp the fundamental relationship between the known and unknown properties, as this is at the core of Bayes’ Theorem. Given its extensive application across numerous fields over the years, developing a solid understanding of this theorem is not just valuable but essential. It enables us to bridge gaps in knowledge by systematically updating our beliefs in light of new evidence.