# Understanding Joint Probability Model

• pamparana
In summary, the conversation discusses a joint probability model involving four random variables and the confusion surrounding the right-hand side of the equation. The expert explains that the right-hand side represents the probability of a conditional on b, multiplied by the probability of b conditional on c and d, and then multiplied by the joint probability of c and d. They also provide a simplified example to demonstrate the concept of marginalization.
pamparana
Hello everyone,

I am trying to understand a paper and am stuck at one place.

The statement says something as follows:

Say we have a, b, c and d which are random variables generated by some model. This leads to the following joint probability model:

p(a, b, c, d) = p(a|b)p(b|c,d)p(c)p(d)

I do not understand the RHS of the equation at all? What is it saying and quite confused as to how it is derived?

Thanks,
Luca

pamparana said:
Say we have a, b, c and d which are random variables generated by some model. This leads to the following joint probability model:

p(a, b, c, d) = p(a|b)p(b|c,d)p(c)p(d)

I do not understand the RHS of the equation at all? What is it saying and quite confused as to how it is derived?
Luca

probability of (a conditional on b) times probability of (b conditional on c,d) times the joint probability of c and d.

You say "some model" If they provided no further information, take it as a given. Conditioning on c,d and multiplying by the joint probability are two different operations.

EDIT: In calculating for conditioning on two or more variables, you try to marginalize one of the variables:

P(A|B,C)=P(A,B,C)/P(B,C)=P(A,B,C)/P(B)P(C|B)=P(C|AB)P(A,B)/P(B)P(C|B)=P(A)P(B|A)P(C|AB)/P(B)PC|B).

This is less complicated then your example with four variables, but it shows the concept of marginalization of P(B) and P(C).

Last edited:

## 1. What is a joint probability model?

A joint probability model is a statistical model that describes the probability of two or more events occurring together. It takes into account the relationship between multiple variables and calculates the probability of their combined outcomes.

## 2. How is a joint probability model different from a conditional probability model?

A joint probability model considers the probability of two or more events occurring together, while a conditional probability model focuses on the probability of one event occurring given that another event has already occurred.

## 3. What is the purpose of using a joint probability model?

The purpose of using a joint probability model is to better understand the relationship between multiple variables and their combined probabilities. This can be helpful in decision making, forecasting, and identifying patterns in data.

## 4. How is a joint probability model calculated?

A joint probability model is calculated by multiplying the individual probabilities of each event together. For example, if event A has a probability of 0.5 and event B has a probability of 0.7, the joint probability of A and B occurring together would be 0.5 x 0.7 = 0.35.

## 5. What are some real-life applications of a joint probability model?

A joint probability model can be applied in various fields such as finance, economics, marketing, and healthcare. For example, it can be used to calculate the likelihood of a certain investment portfolio performing well, the probability of a marketing campaign being successful, or the likelihood of a patient developing a certain disease based on their lifestyle and genetic factors.

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