Accordingly, the conditional probability distribution can be written as follows:

For any , the function is called a conditional probability distribution of given .

In the symmetric formulation above, this is done simply by adding conditional probability distributions for these additional variables.

A Bayesian statistician often seeks the conditional probability distribution of a random quantity given the data.

Thus, the conditional probability distribution is:

"But those methods require a priori knowledge of conditional probability distribution," Mr. Pap said.

The question Bayes addressed was: what is the conditional probability distribution of p, given the numbers of successes and failures so far observed.

Within a probabilistic framework, this is done by modeling the conditional probability distribution , which can be used for predicting from .

To find the conditional probability distribution of 'p' given the data, one uses Bayes theorem, which some call the 'Bayes-Laplace rule'.

In probability theory and statistics, a conditional variance is the variance of a conditional probability distribution.

Conditional probability distribution / (2:DC)

Consider the problem of estimating a deterministic (not Bayesian) parameter from noisy or corrupt data related through the conditional probability distribution .

That is, an -only policy specifies, for each possible random event , a conditional probability distribution for selecting a control action given that .

A likelihood function arises from a conditional probability distribution considered as a function of its distributional parameterization argument, conditioned on the data argument.

A discrete memoryless single-relay channel can be modelled as four finite sets, and , and a conditional probability distribution on these sets.

In this case, the absence of DIF is determined by the fact that the conditional probability distribution of Y is not dependent on group membership.

Having found the conditional probability distribution of p given the data, one may then calculate the conditional probability, given the data, that the sun will rise tomorrow.

When is a conditional probability distribution and the loss function is the negative log likelihood: , then empirical risk minimization is equivalent to maximum likelihood estimation.

Describe the network with a graphical model, identifying the observed variables (data) and unobserved variables (parameters and latent variables ) and their conditional probability distributions.

The conditional probability distribution of X given X is the probability distribution of X when X is known to be a particular value.

Similarly, two random variables are independent if the conditional probability distribution of either given the observed value of the other is the same as if the other's value had not been observed.

Liftings are used to produce disintegrations of measures, for instance conditional probability distributions given continuous random variables, and fibrations of Lebesgue measure on the level sets of a function.

A stochastic process has the Markov property if the conditional probability distribution of future states of the process depends only upon the present state, not on the sequence of events that preceded it.

Quantities such as regression coefficients, are statistical parameters in the above sense, since they index the family of conditional probability distributions that describe how the dependent variables are related to the independent variables.

In probability theory, a conditional expectation (also known as conditional expected value or conditional mean) is the expected value of a real random variable with respect to a conditional probability distribution.