Actuarial Outpost Continuous Prior?
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#1
11-16-2017, 10:34 PM
 verdun11 SOA Join Date: Dec 2015 College: University of North Carolina Posts: 21
Continuous Prior?

Hi everyone,

Going through credibility now and am finding the continuous prior distribution to be fairly challenging. I understand the discrete distribution, but am really struggling with the continuous, and how the discrete transitions into the continuous. How should I conceptually be thinking about the continuous prior?
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#2
11-17-2017, 10:45 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,166

If you could give a specific example, it might be helpful.
#3
11-25-2017, 04:39 PM
 dkamka Member CAS SOA Join Date: Jul 2010 Location: basement of SOA (Schaumburg) Studying for Predictive Analytics& FAP College: Roosevelt University Alumnus '10 Favorite beer: Jawa Juice Posts: 475

Quote:
 Originally Posted by verdun11 Hi everyone, Going through credibility now and am finding the continuous prior distribution to be fairly challenging. I understand the discrete distribution, but am really struggling with the continuous, and how the discrete transitions into the continuous. How should I conceptually be thinking about the continuous prior?
The conditional model is how we calculate probabilities, but it's conditional on a parameter whose pdf is the continuous prior distribution. In order to use given data, you need to plus in each data value to the original continous pdf and multiple by the prior distribution. Integrate over the domain of the prior pdf and divide that into the product of the conditional pdf*prior pdf. This gives you the posterior distribution. In order to calculate moments or probabilities of the posterior, just use the posterior pdf as usual. In order to find predictive moments or probabilities use the conditional moment or probability of the original model*posterior pdf and evaluate as usual.
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