Can probability distributions be used as an alternative for regression models? Suppose you have 3 variables: height, weight and salary. Can you first attempt to fit a 3 dimensional probability distribution to this data - then, if someone gives you a height and weight measurement, could you use the probability distribution to estimate the probability of observing a range of salaries for a fixed value of weight and height?
This would in effect produce a conditional probability distribution for this specific combination and you can take the expected value of this distribution  to predict the most likely salary?
Here was my thought: once the 3 dimensional distribution was fit to this data, for a height = 180 cm and weight = 100 kg:
Probabilith (Salary = $10,000 | height = 180 cm, weight = 100 kg)  = 0.2
Probabilith (Salary = $10,500 | height = 180 cm, weight = 100 kg)  = 0.1
Probabilith (Salary = $9,000 | height = 180 cm, weight = 100 kg)  = 0.01
Etc.
Evaluating many such values of salary combinations, you can derive a posterior distribution. There would be no need for beta regression coefficients in this approach.
Is this correct?
Or this is a flawed idea and is it better to just fit a regression model to this problem?
Thanks!

I am fairly sure it's valid to treat regression model as a joint probability distribution. Let $s,h,w$ be salary, height, weight, then a linear regression
$$
  s = \beta_0 + \beta_1h + \beta_2w + \epsilon \\
  \epsilon \sim N(0, \sigma^2)
$$
where $\beta_0, \beta_1, \beta_2$ are regression coefficients posits the distribution
$$
  s \sim N(\beta_0 + \beta_1h + \beta_2w, \sigma^2)
$$
The mean salary for a specific combination of weight and height is exactly what is being modelled in a linear regression, and this is also exactly what a conditional expectation of salary for a given weight and height would aim to provide in your approach.
Of course the accuracy of this prediction depends on the normality of the error term $\epsilon$; if this assumption is violated then predictions will not be accurate.
