likelihood
probability is the _________________ that an event will occur
In statistics, likelihood refers to the probability of observing a set of data given a particular statistical model that is used to describe the data-generating process. It is a function that quantifies how well the observations fit the model. The likelihood function is used to estimate the parameters of the model, by finding the values of the parameters that maximize the likelihood.
For example, consider a coin flipping experiment where we flip a coin 10 times and observe that it lands heads up 6 times. We can use a binomial distribution to model the probability of observing k heads in n flips, where the parameter p represents the probability of getting heads on any given flip.
The likelihood function for this scenario would be the probability of observing 6 heads in 10 flips given a value of p. We would write this as:
L(p|6,10) = (10 choose 6) * p^6 * (1-p)^4
We can use this function to estimate the value of p that maximizes the likelihood of observing 6 heads in 10 flips. This is typically done using maximum likelihood estimation (MLE).
In summary, the likelihood function quantifies how well a given statistical model fits the observed data, and is used to estimate the model parameters using maximum likelihood estimation.
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