# Confusing use of notation in expressing probability distribution

• sarikan
In summary, the conversation discusses the use of notation in a text about Bayesian statistics. The notation in question uses the conditional probability notation to describe a random variable with a normal distribution. This can be confusing, as it may suggest that the mean and variance are random variables, when in fact they are parameters of the density function. The question is whether there is a way to interpret this notation in a unifying manner, without distinguishing between a simple description of a probability distribution and a conditional distribution. The response suggests that using a different marker for the parameters may be more appropriate in a Bayesian context.
sarikan
Hi,
I'm trying to follow a text about Bayesian statistics, and the author is using the following notation to describe a random variable which has normal distribution:

p(x | µ, σ2) = (Gaussian density function here)

In a Bayesian text, this notation is confusing, since it makes me think about mean and variance as random variables, but they are not random variables. They are simply the parameters of the density function, and this is just using the conditional probability notation for expressing something else, namely saying that "x is distributed normally, with this mean and this variance"
This is not the case where you have p(a|b) = p(b|a).p(a)/p(b)

My question is, is there a unifying way of thinking about the first notation so that I don't have to distinguish between the case where I simply have description of a probability distribution, and the case where it is about conditional distribution? I could not get my head around the idea of interpreting mean and variance as variables on which the random variable is conditioned on. Is this really a different use of the same notation, or am I missing something here?

I hope I can describe my problem, and apologies if this is not clear enough. Your response would be much appreciated!

Regards

The first notation is unfortunate, since it is not a conditional probability. It would be better to use something other than | as a marker for the parameters.

Indeed. Especially in a Bayesian text. Thanks for the response.

Kind regards

## 1. What is the purpose of using notation in expressing probability distribution?

Notation is used to represent the probability of a certain event occurring in a mathematical form. It helps to simplify complex problems and make them more manageable. It also allows for a standardized way of communicating probability distributions among scientists and researchers.

## 2. What are some common notations used in expressing probability distribution?

Some common notations include P(x), which represents the probability of an event x occurring, and F(x), which represents the cumulative probability function. Other notations like μ and σ2 represent the mean and variance of a normal distribution, while λ represents the rate parameter of a Poisson distribution.

## 3. Why is the use of notation sometimes confusing in expressing probability distribution?

The use of notation can be confusing because different notations may be used for the same concept, depending on the context and field of study. Additionally, some notations may have different meanings in different branches of mathematics, leading to confusion and misinterpretation.

## 4. What are some tips for avoiding confusion when using notation in expressing probability distribution?

Some tips include clearly defining all notations used in a particular study or problem, using consistent notation throughout the study, and avoiding using multiple notations for the same concept. It is also helpful to provide a key or legend to explain any unfamiliar or non-standard notations used.

## 5. How can a scientist effectively communicate the use of notation in expressing probability distribution?

To effectively communicate the use of notation, a scientist should provide a clear and concise explanation of the notation used, its meaning, and any assumptions or limitations associated with it. It is also helpful to provide examples and visuals to illustrate the notation and its application in the context of the study.

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