Timeline for What is the difference between "priors" and "likelihood"?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 29, 2012 at 9:51 | comment | added | Andrew | Thanks for your replies, I have found the answer and your comments very useful to further my understanding. | |
| May 22, 2012 at 9:29 | vote | accept | Andrew | ||
| May 20, 2012 at 2:21 | comment | added | probabilityislogic | a frequentist does not "only use the data" its just that the method of using prior information is different, such as the parameterisation they want unbiasness or fisher efficient estimator. prior information for frequentist usually comes in the from of choice of hypothesis to compare, statistic to use, and significance level. | |
| May 19, 2012 at 23:32 | answer | added | Nick | timeline score: 9 | |
| May 19, 2012 at 23:30 | comment | added | Michael R. Chernick | Bayesians and frequentist both use the likelihood for inference. The idfference is that the Bayesians add a prior and use a posterior distribution for inference while the frequentists only use the data. Their interpretation of probability is fundamentally different. | |
| May 19, 2012 at 23:24 | comment | added | Michael R. Chernick | The Bayesian cannot determine a probability distribution for the parameter based on the likelihood alone. But prior to collecting the data they can form an opinion about the parameter and express it in terms of a probability that the call a prior because it is derived prior to collecting data. Then they can combine the prior with the likelihood to get a posterior distribution for the parameter. It is called posterior because it is obtained after observing the data. In this context applying Bayes rulegives the posterior as an appropriately normalized product of prior with likelihood. | |
| May 19, 2012 at 23:15 | comment | added | Michael R. Chernick | @Macro technically you gave a complete answer to the question. Since Andrew is probably not familiar with the Bayesian methodology or at least the terminology i think it is appropriate to elaborate a little. Bayesians do inference based on treating unknown models parameters as having probabilities. The likelihood is a probability density for the data given a value for the parameter. The likelihood can be used by frequentists to do inference about the parameter without making assumptions about the parameter. | |
| May 19, 2012 at 22:51 | comment | added | Macro | The likelihood is the joint density of the data, given a parameter value and the prior is the marginal distribution of the parameter. Something tells me you're asking something more though-- can you elaborate? | |
| May 19, 2012 at 22:48 | history | asked | Andrew | CC BY-SA 3.0 |