Is Gibbs sampling an MCMC method?





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






up vote
4
down vote

favorite












As far as I understand it, it is (at least, that is how Wikipedia defines it). But I've found this statement by Efron* (emphasis added):




Markov chain Monte Carlo (MCMC) is the great success story of modern-day Bayesian statistics. MCMC, and its sister method “Gibbs sampling,” permit the numerical calculation of posterior distributions in situations far too complicated for analytic expression.




and now I'm confused. Is this just a minor difference in terminology, or is Gibbs sampling something other than MCMC?



[*]: Efron 2011, "The Bootstrap and Markov-Chain Monte Carlo"










share|cite|improve this question




























    up vote
    4
    down vote

    favorite












    As far as I understand it, it is (at least, that is how Wikipedia defines it). But I've found this statement by Efron* (emphasis added):




    Markov chain Monte Carlo (MCMC) is the great success story of modern-day Bayesian statistics. MCMC, and its sister method “Gibbs sampling,” permit the numerical calculation of posterior distributions in situations far too complicated for analytic expression.




    and now I'm confused. Is this just a minor difference in terminology, or is Gibbs sampling something other than MCMC?



    [*]: Efron 2011, "The Bootstrap and Markov-Chain Monte Carlo"










    share|cite|improve this question
























      up vote
      4
      down vote

      favorite









      up vote
      4
      down vote

      favorite











      As far as I understand it, it is (at least, that is how Wikipedia defines it). But I've found this statement by Efron* (emphasis added):




      Markov chain Monte Carlo (MCMC) is the great success story of modern-day Bayesian statistics. MCMC, and its sister method “Gibbs sampling,” permit the numerical calculation of posterior distributions in situations far too complicated for analytic expression.




      and now I'm confused. Is this just a minor difference in terminology, or is Gibbs sampling something other than MCMC?



      [*]: Efron 2011, "The Bootstrap and Markov-Chain Monte Carlo"










      share|cite|improve this question













      As far as I understand it, it is (at least, that is how Wikipedia defines it). But I've found this statement by Efron* (emphasis added):




      Markov chain Monte Carlo (MCMC) is the great success story of modern-day Bayesian statistics. MCMC, and its sister method “Gibbs sampling,” permit the numerical calculation of posterior distributions in situations far too complicated for analytic expression.




      and now I'm confused. Is this just a minor difference in terminology, or is Gibbs sampling something other than MCMC?



      [*]: Efron 2011, "The Bootstrap and Markov-Chain Monte Carlo"







      mcmc gibbs






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 8 hours ago









      Gabriel

      1,0281234




      1,0281234






















          2 Answers
          2






          active

          oldest

          votes

















          up vote
          2
          down vote













          The algorithm that is now called Gibbs sampling forms a Markov-chain and uses Monte-Carlo simulation for its inputs, so it does indeed fall within the proper scope of MCMC (Markov-Chain Monte-Carlo) methods. Historically, the method can be traced back at least to the mid-twentieth century, but it was not well-known and was only later popularised by the seminal paper of Geman and Geman (1984) which examined statistical physics in relation to the use of the Gibbs distribution (for some historical references, see Casella and George 1992, p. 167).



          For some reason, thoughout his paper, Efron refers to the Gibbs sampler as if it were outside the scope of MCMC. He does this in the quote you have given, and also in some other parts of the paper. Since his opening reference to the technique refers to the "Gibbs sampler" (given in quotes) it is possible that he is alluding to the historical fact that the original method was developed through the Gibbs distribution in statistical physics, and was not incorporated into the general statistical theory of MCMC until much later. This is my best guess as to why he refers to it this way.



          Given that Bradley Efron is still alive and kicking, it might be worth emailing him and just asking him why he refers to the Gibbs sampler this way. Efron is a really brilliant statistician, so I'm sure he has some good reason for referring to the Gibbs sampler this way, and it would be great to know the reasoning.



          Update: I have taken the liberty of emailing Bradley Efron to ask him about this. I will update this answer if I receive a response.






          share|cite|improve this answer























          • Thank you! I'll wait to see if you get an answer from Dr Efron, if not I'll still select this as the answer.
            – Gabriel
            3 hours ago


















          up vote
          1
          down vote













          Go with Wikipedia. Better yet, go with these MCMC researchers:





          • Tierney (1994), "Markov Chains for Exploring Posterior Distributions";


          • Geyer (2011), "Introduction to Markov Chain Mote Carlo";


          • Robert and Casella (2011), "A Short History of Markov Chain Monte Carlo".


          The Gibbs sampler is an example of a Markov chain Monte Carlo algorithm. Indeed, it is a special case of the Metropolis-Hastings algorithm. Any algorithm that generates random draws from a distribution $pi(theta)$ by simulating a Markov chain that has $pi(theta)$ as its stationary distribution is a Markov chain Monte Carlo algorithm, and that's exactly what the Gibbs sampler does.






          share|cite|improve this answer























            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',
            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
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f379508%2fis-gibbs-sampling-an-mcmc-method%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            2
            down vote













            The algorithm that is now called Gibbs sampling forms a Markov-chain and uses Monte-Carlo simulation for its inputs, so it does indeed fall within the proper scope of MCMC (Markov-Chain Monte-Carlo) methods. Historically, the method can be traced back at least to the mid-twentieth century, but it was not well-known and was only later popularised by the seminal paper of Geman and Geman (1984) which examined statistical physics in relation to the use of the Gibbs distribution (for some historical references, see Casella and George 1992, p. 167).



            For some reason, thoughout his paper, Efron refers to the Gibbs sampler as if it were outside the scope of MCMC. He does this in the quote you have given, and also in some other parts of the paper. Since his opening reference to the technique refers to the "Gibbs sampler" (given in quotes) it is possible that he is alluding to the historical fact that the original method was developed through the Gibbs distribution in statistical physics, and was not incorporated into the general statistical theory of MCMC until much later. This is my best guess as to why he refers to it this way.



            Given that Bradley Efron is still alive and kicking, it might be worth emailing him and just asking him why he refers to the Gibbs sampler this way. Efron is a really brilliant statistician, so I'm sure he has some good reason for referring to the Gibbs sampler this way, and it would be great to know the reasoning.



            Update: I have taken the liberty of emailing Bradley Efron to ask him about this. I will update this answer if I receive a response.






            share|cite|improve this answer























            • Thank you! I'll wait to see if you get an answer from Dr Efron, if not I'll still select this as the answer.
              – Gabriel
              3 hours ago















            up vote
            2
            down vote













            The algorithm that is now called Gibbs sampling forms a Markov-chain and uses Monte-Carlo simulation for its inputs, so it does indeed fall within the proper scope of MCMC (Markov-Chain Monte-Carlo) methods. Historically, the method can be traced back at least to the mid-twentieth century, but it was not well-known and was only later popularised by the seminal paper of Geman and Geman (1984) which examined statistical physics in relation to the use of the Gibbs distribution (for some historical references, see Casella and George 1992, p. 167).



            For some reason, thoughout his paper, Efron refers to the Gibbs sampler as if it were outside the scope of MCMC. He does this in the quote you have given, and also in some other parts of the paper. Since his opening reference to the technique refers to the "Gibbs sampler" (given in quotes) it is possible that he is alluding to the historical fact that the original method was developed through the Gibbs distribution in statistical physics, and was not incorporated into the general statistical theory of MCMC until much later. This is my best guess as to why he refers to it this way.



            Given that Bradley Efron is still alive and kicking, it might be worth emailing him and just asking him why he refers to the Gibbs sampler this way. Efron is a really brilliant statistician, so I'm sure he has some good reason for referring to the Gibbs sampler this way, and it would be great to know the reasoning.



            Update: I have taken the liberty of emailing Bradley Efron to ask him about this. I will update this answer if I receive a response.






            share|cite|improve this answer























            • Thank you! I'll wait to see if you get an answer from Dr Efron, if not I'll still select this as the answer.
              – Gabriel
              3 hours ago













            up vote
            2
            down vote










            up vote
            2
            down vote









            The algorithm that is now called Gibbs sampling forms a Markov-chain and uses Monte-Carlo simulation for its inputs, so it does indeed fall within the proper scope of MCMC (Markov-Chain Monte-Carlo) methods. Historically, the method can be traced back at least to the mid-twentieth century, but it was not well-known and was only later popularised by the seminal paper of Geman and Geman (1984) which examined statistical physics in relation to the use of the Gibbs distribution (for some historical references, see Casella and George 1992, p. 167).



            For some reason, thoughout his paper, Efron refers to the Gibbs sampler as if it were outside the scope of MCMC. He does this in the quote you have given, and also in some other parts of the paper. Since his opening reference to the technique refers to the "Gibbs sampler" (given in quotes) it is possible that he is alluding to the historical fact that the original method was developed through the Gibbs distribution in statistical physics, and was not incorporated into the general statistical theory of MCMC until much later. This is my best guess as to why he refers to it this way.



            Given that Bradley Efron is still alive and kicking, it might be worth emailing him and just asking him why he refers to the Gibbs sampler this way. Efron is a really brilliant statistician, so I'm sure he has some good reason for referring to the Gibbs sampler this way, and it would be great to know the reasoning.



            Update: I have taken the liberty of emailing Bradley Efron to ask him about this. I will update this answer if I receive a response.






            share|cite|improve this answer














            The algorithm that is now called Gibbs sampling forms a Markov-chain and uses Monte-Carlo simulation for its inputs, so it does indeed fall within the proper scope of MCMC (Markov-Chain Monte-Carlo) methods. Historically, the method can be traced back at least to the mid-twentieth century, but it was not well-known and was only later popularised by the seminal paper of Geman and Geman (1984) which examined statistical physics in relation to the use of the Gibbs distribution (for some historical references, see Casella and George 1992, p. 167).



            For some reason, thoughout his paper, Efron refers to the Gibbs sampler as if it were outside the scope of MCMC. He does this in the quote you have given, and also in some other parts of the paper. Since his opening reference to the technique refers to the "Gibbs sampler" (given in quotes) it is possible that he is alluding to the historical fact that the original method was developed through the Gibbs distribution in statistical physics, and was not incorporated into the general statistical theory of MCMC until much later. This is my best guess as to why he refers to it this way.



            Given that Bradley Efron is still alive and kicking, it might be worth emailing him and just asking him why he refers to the Gibbs sampler this way. Efron is a really brilliant statistician, so I'm sure he has some good reason for referring to the Gibbs sampler this way, and it would be great to know the reasoning.



            Update: I have taken the liberty of emailing Bradley Efron to ask him about this. I will update this answer if I receive a response.







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited 4 hours ago

























            answered 4 hours ago









            Ben

            19.5k22295




            19.5k22295












            • Thank you! I'll wait to see if you get an answer from Dr Efron, if not I'll still select this as the answer.
              – Gabriel
              3 hours ago


















            • Thank you! I'll wait to see if you get an answer from Dr Efron, if not I'll still select this as the answer.
              – Gabriel
              3 hours ago
















            Thank you! I'll wait to see if you get an answer from Dr Efron, if not I'll still select this as the answer.
            – Gabriel
            3 hours ago




            Thank you! I'll wait to see if you get an answer from Dr Efron, if not I'll still select this as the answer.
            – Gabriel
            3 hours ago












            up vote
            1
            down vote













            Go with Wikipedia. Better yet, go with these MCMC researchers:





            • Tierney (1994), "Markov Chains for Exploring Posterior Distributions";


            • Geyer (2011), "Introduction to Markov Chain Mote Carlo";


            • Robert and Casella (2011), "A Short History of Markov Chain Monte Carlo".


            The Gibbs sampler is an example of a Markov chain Monte Carlo algorithm. Indeed, it is a special case of the Metropolis-Hastings algorithm. Any algorithm that generates random draws from a distribution $pi(theta)$ by simulating a Markov chain that has $pi(theta)$ as its stationary distribution is a Markov chain Monte Carlo algorithm, and that's exactly what the Gibbs sampler does.






            share|cite|improve this answer



























              up vote
              1
              down vote













              Go with Wikipedia. Better yet, go with these MCMC researchers:





              • Tierney (1994), "Markov Chains for Exploring Posterior Distributions";


              • Geyer (2011), "Introduction to Markov Chain Mote Carlo";


              • Robert and Casella (2011), "A Short History of Markov Chain Monte Carlo".


              The Gibbs sampler is an example of a Markov chain Monte Carlo algorithm. Indeed, it is a special case of the Metropolis-Hastings algorithm. Any algorithm that generates random draws from a distribution $pi(theta)$ by simulating a Markov chain that has $pi(theta)$ as its stationary distribution is a Markov chain Monte Carlo algorithm, and that's exactly what the Gibbs sampler does.






              share|cite|improve this answer

























                up vote
                1
                down vote










                up vote
                1
                down vote









                Go with Wikipedia. Better yet, go with these MCMC researchers:





                • Tierney (1994), "Markov Chains for Exploring Posterior Distributions";


                • Geyer (2011), "Introduction to Markov Chain Mote Carlo";


                • Robert and Casella (2011), "A Short History of Markov Chain Monte Carlo".


                The Gibbs sampler is an example of a Markov chain Monte Carlo algorithm. Indeed, it is a special case of the Metropolis-Hastings algorithm. Any algorithm that generates random draws from a distribution $pi(theta)$ by simulating a Markov chain that has $pi(theta)$ as its stationary distribution is a Markov chain Monte Carlo algorithm, and that's exactly what the Gibbs sampler does.






                share|cite|improve this answer














                Go with Wikipedia. Better yet, go with these MCMC researchers:





                • Tierney (1994), "Markov Chains for Exploring Posterior Distributions";


                • Geyer (2011), "Introduction to Markov Chain Mote Carlo";


                • Robert and Casella (2011), "A Short History of Markov Chain Monte Carlo".


                The Gibbs sampler is an example of a Markov chain Monte Carlo algorithm. Indeed, it is a special case of the Metropolis-Hastings algorithm. Any algorithm that generates random draws from a distribution $pi(theta)$ by simulating a Markov chain that has $pi(theta)$ as its stationary distribution is a Markov chain Monte Carlo algorithm, and that's exactly what the Gibbs sampler does.







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited 3 hours ago

























                answered 4 hours ago









                bamts

                48329




                48329






























                    draft saved

                    draft discarded




















































                    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.





                    Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                    Please pay close attention to the following guidance:


                    • 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.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f379508%2fis-gibbs-sampling-an-mcmc-method%23new-answer', 'question_page');
                    }
                    );

                    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







                    Popular posts from this blog

                    A CLEAN and SIMPLE way to add appendices to Table of Contents and bookmarks

                    Calculate evaluation metrics using cross_val_predict sklearn

                    Insert data from modal to MySQL (multiple modal on website)