Does Approximate Bayesian Computation (ABC) follow the Likelihood Principle?What is an “uninformative prior”? Can we ever have one with truly no information?ABC. How can it avoid the likelihood function?Parameter Estimation for intractable Likelihoods / Alternatives to approximate Bayesian computationDistance metric for Approximate Bayesian Computation (ABC) regressionApproximate Bayesian computation: where to start from?Simple linear regression using Approximate Bayesian Computation (ABC)In what situations would one use Approximate Bayesian Computation instead of Bayesian inference?Using maximum Likelihood regression to get closer to the true posterior when doing Approximate Bayesian Computation : contradiction?Approximate Bayesian Computation for parameters estimation in ODE-based modelApproximate bayesian computation: model selection on nested modelsProof of Approximate / Exact Bayesian Computation
Can I use a neutral wire from another outlet to repair a broken neutral?
Blender 2.8 I can't see vertices, edges or faces in edit mode
Took a trip to a parallel universe, need help deciphering
Can a rocket refuel on Mars from water?
Do I have a twin with permutated remainders?
Can I ask the recruiters in my resume to put the reason why I am rejected?
Will google still index a page if I use a $_SESSION variable?
What exploit are these user agents trying to use?
How can I make my BBEG immortal short of making them a Lich or Vampire?
1960's book about a plague that kills all white people
Doing something right before you need it - expression for this?
How can I tell someone that I want to be his or her friend?
Western buddy movie with a supernatural twist where a woman turns into an eagle at the end
Neighboring nodes in the network
Were any external disk drives stacked vertically?
What's the point of deactivating Num Lock on login screens?
Why "Having chlorophyll without photosynthesis is actually very dangerous" and "like living with a bomb"?
Why is Collection not simply treated as Collection<?>
How badly should I try to prevent a user from XSSing themselves?
What reasons are there for a Capitalist to oppose a 100% inheritance tax?
Is it possible to download Internet Explorer on my Mac running OS X El Capitan?
Reserved de-dupe rules
Why does Kotter return in Welcome Back Kotter
Why is it a bad idea to hire a hitman to eliminate most corrupt politicians?
Does Approximate Bayesian Computation (ABC) follow the Likelihood Principle?
What is an “uninformative prior”? Can we ever have one with truly no information?ABC. How can it avoid the likelihood function?Parameter Estimation for intractable Likelihoods / Alternatives to approximate Bayesian computationDistance metric for Approximate Bayesian Computation (ABC) regressionApproximate Bayesian computation: where to start from?Simple linear regression using Approximate Bayesian Computation (ABC)In what situations would one use Approximate Bayesian Computation instead of Bayesian inference?Using maximum Likelihood regression to get closer to the true posterior when doing Approximate Bayesian Computation : contradiction?Approximate Bayesian Computation for parameters estimation in ODE-based modelApproximate bayesian computation: model selection on nested modelsProof of Approximate / Exact Bayesian Computation
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
I know that ABC is commonly used when the likelihood is intractable, so likelihood principle is not an interest in that case. But, I am curious whether the ABC satisfies the likelihood principle when the likelihood function is tractable. ABC is a generative procedure to sample parameters from posterior, and likelihood principle says that the inference on the parameter should be solely determined by likelihood part ignoring the term of the observation.
I think that if I generate fake samples from a parameter, the generating process is crucially affected by the term of observation, which might be ignored in the likelihood principle.
It's confusing, because I think that the ABC does not follow the likelihood principle, but it is well-known that Bayesian stat follows it.
Am I missing something?
bayesian computational-statistics abc
asked 2 days ago
Minsuk ShinMinsuk Shin
663
$endgroup$
add a comment |
$begingroup$
I know that ABC is commonly used when the likelihood is intractable, so likelihood principle is not an interest in that case. But, I am curious whether the ABC satisfies the likelihood principle when the likelihood function is tractable. ABC is a generative procedure to sample parameters from posterior, and likelihood principle says that the inference on the parameter should be solely determined by likelihood part ignoring the term of the observation.
I think that if I generate fake samples from a parameter, the generating process is crucially affected by the term of observation, which might be ignored in the likelihood principle.
It's confusing, because I think that the ABC does not follow the likelihood principle, but it is well-known that Bayesian stat follows it.
Am I missing something?
bayesian computational-statistics abc
asked 2 days ago
Minsuk ShinMinsuk Shin
663
$endgroup$
add a comment |
$begingroup$
I know that ABC is commonly used when the likelihood is intractable, so likelihood principle is not an interest in that case. But, I am curious whether the ABC satisfies the likelihood principle when the likelihood function is tractable. ABC is a generative procedure to sample parameters from posterior, and likelihood principle says that the inference on the parameter should be solely determined by likelihood part ignoring the term of the observation.
I think that if I generate fake samples from a parameter, the generating process is crucially affected by the term of observation, which might be ignored in the likelihood principle.
It's confusing, because I think that the ABC does not follow the likelihood principle, but it is well-known that Bayesian stat follows it.
Am I missing something?
bayesian computational-statistics abc
asked 2 days ago
Minsuk ShinMinsuk Shin
663
$endgroup$
I know that ABC is commonly used when the likelihood is intractable, so likelihood principle is not an interest in that case. But, I am curious whether the ABC satisfies the likelihood principle when the likelihood function is tractable. ABC is a generative procedure to sample parameters from posterior, and likelihood principle says that the inference on the parameter should be solely determined by likelihood part ignoring the term of the observation.
I think that if I generate fake samples from a parameter, the generating process is crucially affected by the term of observation, which might be ignored in the likelihood principle.
It's confusing, because I think that the ABC does not follow the likelihood principle, but it is well-known that Bayesian stat follows it.
Am I missing something?
bayesian computational-statistics abc
bayesian computational-statistics abc
asked 2 days ago
Minsuk ShinMinsuk Shin
663
asked 2 days ago
Minsuk ShinMinsuk Shin
663
edited 2 days ago
Minsuk Shin
asked 2 days ago
Minsuk ShinMinsuk Shin
663
asked 2 days ago
Minsuk ShinMinsuk Shin
663
asked 2 days ago
Minsuk ShinMinsuk Shin
663
663
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The "when the likelihood function is tractable" is somewhat self-defeating, as the reason for using ABC is that it is intractable.
As for the likelihood principle, ABC is definitely not respecting it, since it requires a simulation of the data from its sampling distribution. It thus uses the frequentist properties of that distribution rather than the likelihood itself. Except in the (unrealistic) limiting case when the tolerance is exactly zero and the distance is based on the sufficient statistic, the ABC thus fails to agree with the likelihood principle.
In my humble opinion, this is a minor issue when compared with the major problems faced by ABC, unless you can provide an example with dire (There are also exact Bayesian approaches that do not agree with the likelihood principle, witness the Jeffreys or matching priors.)
answered 2 days ago
Xi'anXi'an
59.1k897365
$endgroup$
$begingroup$
Thank you for the answer. I totally agree with the point that likelihood principle thing is a minor problem in ABC. I was just curious, and wanted to make sure that I am not missing something. I am not criticizing the usefulness of ABC, and I believe that in many applications with intractable likelihood ABC might be an only option.
$endgroup$
– Minsuk Shin
yesterday
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
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/3.0/"u003ecc by-sa 3.0 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
);
);
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
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f400719%2fdoes-approximate-bayesian-computation-abc-follow-the-likelihood-principle%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The "when the likelihood function is tractable" is somewhat self-defeating, as the reason for using ABC is that it is intractable.
As for the likelihood principle, ABC is definitely not respecting it, since it requires a simulation of the data from its sampling distribution. It thus uses the frequentist properties of that distribution rather than the likelihood itself. Except in the (unrealistic) limiting case when the tolerance is exactly zero and the distance is based on the sufficient statistic, the ABC thus fails to agree with the likelihood principle.
In my humble opinion, this is a minor issue when compared with the major problems faced by ABC, unless you can provide an example with dire (There are also exact Bayesian approaches that do not agree with the likelihood principle, witness the Jeffreys or matching priors.)
answered 2 days ago
Xi'anXi'an
59.1k897365
$endgroup$
$begingroup$
Thank you for the answer. I totally agree with the point that likelihood principle thing is a minor problem in ABC. I was just curious, and wanted to make sure that I am not missing something. I am not criticizing the usefulness of ABC, and I believe that in many applications with intractable likelihood ABC might be an only option.
$endgroup$
– Minsuk Shin
yesterday
add a comment |
$begingroup$
The "when the likelihood function is tractable" is somewhat self-defeating, as the reason for using ABC is that it is intractable.
As for the likelihood principle, ABC is definitely not respecting it, since it requires a simulation of the data from its sampling distribution. It thus uses the frequentist properties of that distribution rather than the likelihood itself. Except in the (unrealistic) limiting case when the tolerance is exactly zero and the distance is based on the sufficient statistic, the ABC thus fails to agree with the likelihood principle.
In my humble opinion, this is a minor issue when compared with the major problems faced by ABC, unless you can provide an example with dire (There are also exact Bayesian approaches that do not agree with the likelihood principle, witness the Jeffreys or matching priors.)
answered 2 days ago
Xi'anXi'an
59.1k897365
$endgroup$
$begingroup$
Thank you for the answer. I totally agree with the point that likelihood principle thing is a minor problem in ABC. I was just curious, and wanted to make sure that I am not missing something. I am not criticizing the usefulness of ABC, and I believe that in many applications with intractable likelihood ABC might be an only option.
$endgroup$
– Minsuk Shin
yesterday
add a comment |
$begingroup$
The "when the likelihood function is tractable" is somewhat self-defeating, as the reason for using ABC is that it is intractable.
As for the likelihood principle, ABC is definitely not respecting it, since it requires a simulation of the data from its sampling distribution. It thus uses the frequentist properties of that distribution rather than the likelihood itself. Except in the (unrealistic) limiting case when the tolerance is exactly zero and the distance is based on the sufficient statistic, the ABC thus fails to agree with the likelihood principle.
In my humble opinion, this is a minor issue when compared with the major problems faced by ABC, unless you can provide an example with dire (There are also exact Bayesian approaches that do not agree with the likelihood principle, witness the Jeffreys or matching priors.)
answered 2 days ago
Xi'anXi'an
59.1k897365
$endgroup$
The "when the likelihood function is tractable" is somewhat self-defeating, as the reason for using ABC is that it is intractable.
As for the likelihood principle, ABC is definitely not respecting it, since it requires a simulation of the data from its sampling distribution. It thus uses the frequentist properties of that distribution rather than the likelihood itself. Except in the (unrealistic) limiting case when the tolerance is exactly zero and the distance is based on the sufficient statistic, the ABC thus fails to agree with the likelihood principle.
In my humble opinion, this is a minor issue when compared with the major problems faced by ABC, unless you can provide an example with dire (There are also exact Bayesian approaches that do not agree with the likelihood principle, witness the Jeffreys or matching priors.)
answered 2 days ago
Xi'anXi'an
59.1k897365
edited 2 days ago
answered 2 days ago
Xi'anXi'an
59.1k897365
answered 2 days ago
Xi'anXi'an
59.1k897365
answered 2 days ago
Xi'anXi'an
59.1k897365
59.1k897365
$begingroup$
Thank you for the answer. I totally agree with the point that likelihood principle thing is a minor problem in ABC. I was just curious, and wanted to make sure that I am not missing something. I am not criticizing the usefulness of ABC, and I believe that in many applications with intractable likelihood ABC might be an only option.
$endgroup$
– Minsuk Shin
yesterday
add a comment |
$begingroup$
Thank you for the answer. I totally agree with the point that likelihood principle thing is a minor problem in ABC. I was just curious, and wanted to make sure that I am not missing something. I am not criticizing the usefulness of ABC, and I believe that in many applications with intractable likelihood ABC might be an only option.
$endgroup$
– Minsuk Shin
yesterday
$begingroup$
Thank you for the answer. I totally agree with the point that likelihood principle thing is a minor problem in ABC. I was just curious, and wanted to make sure that I am not missing something. I am not criticizing the usefulness of ABC, and I believe that in many applications with intractable likelihood ABC might be an only option.
$endgroup$
– Minsuk Shin
yesterday
$begingroup$
Thank you for the answer. I totally agree with the point that likelihood principle thing is a minor problem in ABC. I was just curious, and wanted to make sure that I am not missing something. I am not criticizing the usefulness of ABC, and I believe that in many applications with intractable likelihood ABC might be an only option.
$endgroup$
– Minsuk Shin
yesterday
add a comment |
Thanks for contributing an answer to Cross Validated!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f400719%2fdoes-approximate-bayesian-computation-abc-follow-the-likelihood-principle%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
