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Many studies have extended the choice of link functions to avoid possible misspecification and to improve the model fit to the data. We introduce the\n                    <jats:italic>p<\/jats:italic>\n                    -generalized Gaussian distribution (\n                    <jats:italic>p<\/jats:italic>\n                    -GGD) to binary regression in a Bayesian framework. The\n                    <jats:italic>p<\/jats:italic>\n                    -GGD has received considerable attention due to its flexibility in modeling the tails, while generalizing, for instance, over the standard normal distribution where\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$p=2$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    or the Laplace distribution where\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$p=1$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . Here, we extend from maximum likelihood estimation (MLE) to Bayesian posterior estimation using Markov Chain Monte Carlo (MCMC) sampling for the model parameters\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\beta$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03b2<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and the link function parameter\n                    <jats:italic>p<\/jats:italic>\n                    . We use simulated and real-world data to verify the effect of different parameters\n                    <jats:italic>p<\/jats:italic>\n                    on the estimation results, and how logistic regression and probit regression can be incorporated into a broader framework. To make our Bayesian methods scalable in the case of large data, we also incorporate coresets to reduce the data before running the complex and time-consuming MCMC analysis. This allows us to perform very efficient calculations while retaining the original posterior parameter distributions up to little distortions both, in practice, and with theoretical guarantees.\n                  <\/jats:p>","DOI":"10.1007\/s11634-024-00599-1","type":"journal-article","created":{"date-parts":[[2024,7,4]],"date-time":"2024-07-04T03:01:54Z","timestamp":1720062114000},"page":"109-143","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Scalable Bayesian p-generalized probit and logistic regression"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6424-9137","authenticated-orcid":false,"given":"Zeyu","family":"Ding","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simon","family":"Omlor","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katja","family":"Ickstadt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Munteanu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,4]]},"reference":[{"key":"599_CR1","unstructured":"Ahn S, Balan AK, Welling M (2012) Bayesian posterior sampling via stochastic gradient Fisher scoring. 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