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Should log-likelihood be high or low?
Log-likelihood values cannot be used alone as an index of fit because they are a function of sample size but can be used to compare the fit of different coefficients. Because you want to maximize the log-likelihood, the higher value is better. For example, a log-likelihood value of -3 is better than -7.
Why is the likelihood not a probability distribution?
In most cases hypotheses represent different values of a parameter in a statistical model, such as the mean of a normal distribution. Since a likelihood is not actually a probability it doesn’t obey various rules of probability; for example, likelihoods need not sum to 1.
What’s the difference between probability and likelihood in Bayes?
The probabilities in the top plot sum to 1, whereas the integral of the continuous likelihood function in the bottom panel is much less than 1; that is, the likelihoods do not sum to 1. The difference between probability and likelihood becomes clear when one uses the probability distribution function in general-purpose programming languages.
How is the likelihood function different from the probability function?
By contrast, the likelihood function is continuous because the probability parameter p can take on any of the infinite values between 0 and 1. The probabilities in the top plot sum to 1, whereas the integral of the continuous likelihood function in the bottom panel is much less than 1; that is, the likelihoods do not sum to 1.
How many possible results are there in Bayes?
There are only 11 possible results (0 to 10 correct predictions). The actual result will always be one and only one of the possible results. Thus, the probabilities that attach to the possible results must sum to 1. Hypotheses, unlike results, are neither mutually exclusive nor exhaustive.
Which is the posterior term in probability and likelihood?
The likelihood term, P(Y|X) is the probability of getting a result for a given value of the parameters. It is what you label probability. The posterior and prior terms are what you describe as likelihoods.