Why can you not get a value greater than 1 when we measure probability?
Probabilities are measured over intervals, not single points. That is, the area under the curve between two distinct points defines the probability for that interval. This means that the height of the probability function can in fact be greater than one.
Can the probability density function be greater than 1?
A pf gives a probability, so it cannot be greater than one. A pdf f(x), however, may give a value greater than one for some values of x, since it is not the value of f(x) but the area under the curve that represents probability.
How is posterior probability related to prior probability?
The posterior probability distribution is the probability distribution of an unknown quantity, treated as a random variable, conditional on the evidence obtained from an experiment or survey. . . The two are related as follows: . The posterior probability is therefore proportional to the product Likelihood · Prior probability .
What is the posterior predictive distribution in 3.5?
3.5 Posterior predictive distribution The prior predictive distribution is a collection of datasets generated from the model (the likelihood and the priors). After we have seen the data and obtained the posterior distributions of the parameters, we can now use the posterior distributions to generate future data from the model.
How to calculate the posterior probability of spotting a girl?
Given all this information, the posterior probability of the observer having spotted a girl given that the observed student is wearing trousers can be computed by substituting these values in the formula:
When to ignore dependent variable in posterior predict?
(Bear in mind that if we fit a model with sample_prior = “only”, the dependent variable is ignored and posterior_predict will give us samples from the prior predictive distribution).