Mdthbs

As a discovery writer, how to complete unfinished novel (which is highly diverted from original plot ) after a time-gap

Who are the people reviewing far more papers than they're submitting for review?

What is the maximum viable speed for a projectile within earth's atmosphere?

Debussy as term for bathroom?

What's the purpose of autocorrelation?

Twelve Minesweeper mines that make twelve 4s

Very lazy puppy

How often is duct tape used during crewed space missions?

Borrowing observations for prior probability in Bayesian Inference

Should I inform my future product owner that there is a good chance that a team member will leave the company soon?

Quick Kurodoko Puzzle: Threes and Triples

Is it safe to unplug a blinking USB drive after 'safely' ejecting it?

What are sources for Magic Items that are not adventure-specific?

Is the name of an interval between two notes unique and absolute?

All numbers in a 5x5 Minesweeper grid

Make Interviewee Comfortable in Potentially Intimate Environment

Tips for remembering the order of parameters for ln?

Madrid to London w/ Expired 90/180 days stay as US citizen

Exam design: give maximum score per question or not?

Why does Canada require a minimum rate of climb for ultralights of 300 ft/min?

Do you add your strength modifier once or twice to an unarmed strike?

What to do as a player when ranger animal companion dies

Is a global DNS record a security risk for phpMyAdmin?

What was the deeper meaning of Hermione wanting the cloak?

Borrowing observations for prior probability in Bayesian Inference

Bayesian inference for multinomial distribution with asymmetric prior knowledge?Prior for Bayesian Inference on Failure Rate in Poisson DistributionHelp with Bayesian inference in OpenBugsBayesian inference for a conditional probabilityBayesian Inference: Feeding Posterior back in as Prior

.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0;
}

2

$begingroup$

For the purposes of Bayesian Inference, is it assumed that the historical observations used for the prior probability values must be from the exact entity for which you are looking to calculate the posterior probability?

By way of an example, say I am an automobile insurer. I take on a new covered entity, a 22 year old male from the midwest. In the first week, this new covered entity files a claim for an accident, we don't know who was at fault. I have no prior observational data on this covered entity, but I am curious how likely it is that they are "average" in their attention to safety, and just had a bad day. Can I borrow historical observations from other covered entities who are statistically similar (22 years old, male, live in the midwest, drive with the same frequency, etc) and use it to calculate my prior probabilities for the Bayesian Inference? My assumption is yes, but in that case, I am curious of the following:

Are there any assumptions that will be violated in doing this?

How can I weight the "more similar" historical observations (22 years old, midwest, male) differently than my "less similar" historical observations (23 years old, midwest, female, drives less frequently)?

probability bayesian inference prior posterior

share|cite|improve this question

asked 8 hours ago

Alt182Alt182

5133 bronze badges

$endgroup$

add a comment
 | 

2

$begingroup$

For the purposes of Bayesian Inference, is it assumed that the historical observations used for the prior probability values must be from the exact entity for which you are looking to calculate the posterior probability?

By way of an example, say I am an automobile insurer. I take on a new covered entity, a 22 year old male from the midwest. In the first week, this new covered entity files a claim for an accident, we don't know who was at fault. I have no prior observational data on this covered entity, but I am curious how likely it is that they are "average" in their attention to safety, and just had a bad day. Can I borrow historical observations from other covered entities who are statistically similar (22 years old, male, live in the midwest, drive with the same frequency, etc) and use it to calculate my prior probabilities for the Bayesian Inference? My assumption is yes, but in that case, I am curious of the following:

Are there any assumptions that will be violated in doing this?

How can I weight the "more similar" historical observations (22 years old, midwest, male) differently than my "less similar" historical observations (23 years old, midwest, female, drives less frequently)?

probability bayesian inference prior posterior

share|cite|improve this question

asked 8 hours ago

Alt182Alt182

5133 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

For the purposes of Bayesian Inference, is it assumed that the historical observations used for the prior probability values must be from the exact entity for which you are looking to calculate the posterior probability?

By way of an example, say I am an automobile insurer. I take on a new covered entity, a 22 year old male from the midwest. In the first week, this new covered entity files a claim for an accident, we don't know who was at fault. I have no prior observational data on this covered entity, but I am curious how likely it is that they are "average" in their attention to safety, and just had a bad day. Can I borrow historical observations from other covered entities who are statistically similar (22 years old, male, live in the midwest, drive with the same frequency, etc) and use it to calculate my prior probabilities for the Bayesian Inference? My assumption is yes, but in that case, I am curious of the following:

Are there any assumptions that will be violated in doing this?

How can I weight the "more similar" historical observations (22 years old, midwest, male) differently than my "less similar" historical observations (23 years old, midwest, female, drives less frequently)?

probability bayesian inference prior posterior

share|cite|improve this question

asked 8 hours ago

Alt182Alt182

5133 bronze badges

$endgroup$

share|cite|improve this question

asked 8 hours ago

Alt182Alt182

5133 bronze badges

share|cite|improve this question

asked 8 hours ago

Alt182Alt182

5133 bronze badges

asked 8 hours ago

Alt182Alt182

5133 bronze badges

asked 8 hours ago

Alt182Alt182

5133 bronze badges

2 Answers
2

active

oldest

votes

3

$begingroup$

Prior distributions can come from anywhere as long as the information content impinges on the problem at hand.

For example, if you have developed a new variety of green beans, it is highly reasonable to take information on caloric content from existing green bean varietals. If you were interested in forming a prior on corporate bankruptcy rates, the spread between B+++ and D could act as rough bounding information as the default rate must be less than that spread.

Last year's overall batting average for the major leagues could be used as a prior for the batting average of a new rookie, although absent any other information, it should likely be the case that the average should be shifted downward since rookies tend to have lower averages than seasoned players.

There are no assumptions that would be violated by that.

The best weight would be to ask an experienced actuary.

share|cite|improve this answer

answered 7 hours ago

Dave HarrisDave Harris

4,32555 silver badges1717 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your response. Interesting to consider.
  $endgroup$
  – Alt182
  5 hours ago
  

  
  
  
  

add a comment
 | 

1

$begingroup$

I would look into hierarchical models that allow you "learn" the prior. Hierarchical models allow you give each entity their own unique models parameters, but they can be informed in part by the parameters of other entities.

The extent to which they are informed depends on how much data you have for that entity and how similar entities are to each other.

share|cite|improve this answer

answered 7 hours ago

TrynnaDoStatTrynnaDoStat

5,79411 gold badge1515 silver badges3636 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks! Any specific statistical packages in Python or R that do this nicely?
  $endgroup$
  – Alt182
  5 hours ago
  

  
  
  
  

add a comment
 | 

Your Answer

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "65"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/4.0/"u003ecc by-sa 4.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f427647%2fborrowing-observations-for-prior-probability-in-bayesian-inference%23new-answer', 'question_page');
}
);

Post as a guest

Name

Email

Required, but never shown

3

$begingroup$

Prior distributions can come from anywhere as long as the information content impinges on the problem at hand.

For example, if you have developed a new variety of green beans, it is highly reasonable to take information on caloric content from existing green bean varietals. If you were interested in forming a prior on corporate bankruptcy rates, the spread between B+++ and D could act as rough bounding information as the default rate must be less than that spread.

Last year's overall batting average for the major leagues could be used as a prior for the batting average of a new rookie, although absent any other information, it should likely be the case that the average should be shifted downward since rookies tend to have lower averages than seasoned players.

There are no assumptions that would be violated by that.

The best weight would be to ask an experienced actuary.

share|cite|improve this answer

answered 7 hours ago

Dave HarrisDave Harris

4,32555 silver badges1717 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your response. Interesting to consider.
  $endgroup$
  – Alt182
  5 hours ago
  

  
  
  
  

add a comment
 | 

3

$begingroup$

Prior distributions can come from anywhere as long as the information content impinges on the problem at hand.

For example, if you have developed a new variety of green beans, it is highly reasonable to take information on caloric content from existing green bean varietals. If you were interested in forming a prior on corporate bankruptcy rates, the spread between B+++ and D could act as rough bounding information as the default rate must be less than that spread.

Last year's overall batting average for the major leagues could be used as a prior for the batting average of a new rookie, although absent any other information, it should likely be the case that the average should be shifted downward since rookies tend to have lower averages than seasoned players.

There are no assumptions that would be violated by that.

The best weight would be to ask an experienced actuary.

share|cite|improve this answer

answered 7 hours ago

Dave HarrisDave Harris

4,32555 silver badges1717 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your response. Interesting to consider.
  $endgroup$
  – Alt182
  5 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

Prior distributions can come from anywhere as long as the information content impinges on the problem at hand.

For example, if you have developed a new variety of green beans, it is highly reasonable to take information on caloric content from existing green bean varietals. If you were interested in forming a prior on corporate bankruptcy rates, the spread between B+++ and D could act as rough bounding information as the default rate must be less than that spread.

Last year's overall batting average for the major leagues could be used as a prior for the batting average of a new rookie, although absent any other information, it should likely be the case that the average should be shifted downward since rookies tend to have lower averages than seasoned players.

There are no assumptions that would be violated by that.

The best weight would be to ask an experienced actuary.

share|cite|improve this answer

answered 7 hours ago

Dave HarrisDave Harris

4,32555 silver badges1717 bronze badges

$endgroup$

share|cite|improve this answer

answered 7 hours ago

Dave HarrisDave Harris

4,32555 silver badges1717 bronze badges

answered 7 hours ago

Dave HarrisDave Harris

4,32555 silver badges1717 bronze badges

answered 7 hours ago

Dave HarrisDave Harris

4,32555 silver badges1717 bronze badges

1

$begingroup$

I would look into hierarchical models that allow you "learn" the prior. Hierarchical models allow you give each entity their own unique models parameters, but they can be informed in part by the parameters of other entities.

The extent to which they are informed depends on how much data you have for that entity and how similar entities are to each other.

share|cite|improve this answer

answered 7 hours ago

TrynnaDoStatTrynnaDoStat

5,79411 gold badge1515 silver badges3636 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks! Any specific statistical packages in Python or R that do this nicely?
  $endgroup$
  – Alt182
  5 hours ago
  

  
  
  
  

add a comment
 | 

1

$begingroup$

I would look into hierarchical models that allow you "learn" the prior. Hierarchical models allow you give each entity their own unique models parameters, but they can be informed in part by the parameters of other entities.

The extent to which they are informed depends on how much data you have for that entity and how similar entities are to each other.

share|cite|improve this answer

answered 7 hours ago

TrynnaDoStatTrynnaDoStat

5,79411 gold badge1515 silver badges3636 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks! Any specific statistical packages in Python or R that do this nicely?
  $endgroup$
  – Alt182
  5 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

I would look into hierarchical models that allow you "learn" the prior. Hierarchical models allow you give each entity their own unique models parameters, but they can be informed in part by the parameters of other entities.

The extent to which they are informed depends on how much data you have for that entity and how similar entities are to each other.

share|cite|improve this answer

answered 7 hours ago

TrynnaDoStatTrynnaDoStat

5,79411 gold badge1515 silver badges3636 bronze badges

$endgroup$

share|cite|improve this answer

answered 7 hours ago

TrynnaDoStatTrynnaDoStat

5,79411 gold badge1515 silver badges3636 bronze badges

answered 7 hours ago

TrynnaDoStatTrynnaDoStat

5,79411 gold badge1515 silver badges3636 bronze badges

answered 7 hours ago

TrynnaDoStatTrynnaDoStat

5,79411 gold badge1515 silver badges3636 bronze badges