{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T01:13:23Z","timestamp":1778721203471,"version":"3.51.4"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T00:00:00Z","timestamp":1774742400000},"content-version":"vor","delay-in-days":87,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,13]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Palm distributions play a central role in the study of point processes and their associated summary statistics. In this work, we characterize the Palm distributions of the superposition of independent point processes, establishing a simple mixture representation depending on the point processes\u2019 Palm distributions and moment measures. We explore two statistical applications enabled by our main result. First, we consider minimum contrast estimation for corrupted point processes. Second, we investigate the class of shot noise Cox processes and derive explicit expressions for their higher-order Palm distributions. In the finite case, we further obtain a tractable expression for the Janossy density, which plays the role of a likelihood function and thus can be used for new likelihood-based inference strategies. Extensions to the superposition of multiple point processes and to higher-order Palm distributions are also presented.<\/jats:p>","DOI":"10.1093\/biomet\/asag021","type":"journal-article","created":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T12:43:30Z","timestamp":1773924210000},"source":"Crossref","is-referenced-by-count":0,"title":["Palm distributions of superposed point processes for statistical inference"],"prefix":"10.1093","volume":"113","author":[{"given":"M","family":"Beraha","sequence":"first","affiliation":[{"name":"Department of Economics, Management and Statistics, University of Milano-Bicocca , Via Bicocca degli Arcimboldi 8 , 20126 Milan, \u00a0 mario.beraha@unimib.it","place":["Italy"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4956-1103","authenticated-orcid":false,"given":"F","family":"Camerlenghi","sequence":"additional","affiliation":[{"name":"Department of Economics, Management and Statistics, University of Milano-Bicocca , Via Bicocca degli Arcimboldi 8 , 20126 Milan,","place":["Italy"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-6789-9262","authenticated-orcid":false,"given":"L","family":"Ghilotti","sequence":"additional","affiliation":[{"name":"Department of Statistical Science, Duke University , 218 Old Chemistry , Durham, North Carolina 27708, \u00a0 lorenzo.ghilotti@duke.edu","place":["U.S.A."]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2026,3,28]]},"reference":[{"key":"2026051320513968300_asag021-B1","author":"Baccelli","year":"2020"},{"key":"2026051320513968300_asag021-B2","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.1093\/jrsssb\/qkaf027","article-title":"Bayesian mixture models with repulsive and attractive atoms","volume":"87","author":"Beraha","year":"2025","journal-title":"J. R. Statist. Soc. B"},{"key":"2026051320513968300_asag021-B3","author":"Beraha","year":"2025"},{"key":"2026051320513968300_asag021-B4","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1002\/asmb.2615","article-title":"Identification of spatial defects in semiconductor manufacturing","volume":"37","author":"Borgoni","year":"2021","journal-title":"Appl. Stoch. Mod. Bus. Indust"},{"key":"2026051320513968300_asag021-B5","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1080\/00949650701709327","article-title":"Reduced Palm distribution generating function for a spatial point process","volume":"78","author":"Chiu","year":"2008","journal-title":"J. Statist. Comp. Simul"},{"key":"2026051320513968300_asag021-B6","doi-asserted-by":"crossref","DOI":"10.1002\/9781118658222","volume-title":"Stochastic Geometry and Its Applications","author":"Chiu","year":"2013","edition":"3rd ed"},{"key":"2026051320513968300_asag021-B7","author":"Choi","year":"2017"},{"key":"2026051320513968300_asag021-B8","volume-title":"An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods","author":"Daley","year":"2003","edition":"2nd ed"},{"key":"2026051320513968300_asag021-B9","doi-asserted-by":"crossref","DOI":"10.1201\/b15326","volume-title":"Statistical Analysis of Spatial and Spatio-Temporal Point Patterns","author":"Diggle","year":"2013"},{"key":"2026051320513968300_asag021-B10","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1111\/rssb.12002","article-title":"Comparing distributions by using dependent normalized random-measure mixtures","volume":"75","author":"Griffin","year":"2013","journal-title":"J. R. Statist. Soc. B"},{"key":"2026051320513968300_asag021-B11","volume-title":"Statistical Analysis and Modelling of Spatial Point Patterns","author":"Illian","year":"2008"},{"key":"2026051320513968300_asag021-B12","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.3150\/13-BEJ521","article-title":"Bayesian inference with dependent normalized completely random measures","volume":"20","author":"Lijoi","year":"2014","journal-title":"Bernoulli"},{"key":"2026051320513968300_asag021-B13","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1214\/07-AAP495","article-title":"Bayesian nonparametric estimators derived from conditional Gibbs structures","volume":"18","author":"Lijoi","year":"2008","journal-title":"Ann. Appl. Prob"},{"key":"2026051320513968300_asag021-B14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v077.i11","article-title":"Spatio-temporal analysis of epidemic phenomena using the R package surveillance","volume":"77","author":"Meyer","year":"2017","journal-title":"J. Statist. Software"},{"key":"2026051320513968300_asag021-B15","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1080\/01621459.2016.1255636","article-title":"Mixture models with a prior on the number of components","volume":"113","author":"Miller","year":"2018","journal-title":"J. Am. Statist. Assoc"},{"key":"2026051320513968300_asag021-B16","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1239\/aap\/1059486821","article-title":"Shot noise Cox processes","volume":"35","author":"M\u00f8ller","year":"2003","journal-title":"Adv. Appl. Prob"},{"key":"2026051320513968300_asag021-B17","doi-asserted-by":"crossref","DOI":"10.1201\/9780203496930","volume-title":"Statistical Inference and Simulation for Spatial Point Processes","author":"M\u00f8ller","year":"2003"},{"key":"2026051320513968300_asag021-B18","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s13595-011-0033-y","article-title":"Point process models for mixed sessile forest stands","volume":"68","author":"Ngo Bieng","year":"2011","journal-title":"Ann. Forest Sci"},{"key":"2026051320513968300_asag021-B19","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1023\/A:1003403601725","article-title":"Space\u2013time point-process models for earthquake occurrences","volume":"50","author":"Ogata","year":"1998","journal-title":"Ann. Inst. Statist. Math"},{"key":"2026051320513968300_asag021-B20","doi-asserted-by":"crossref","first-page":"255","DOI":"10.2307\/3212829","article-title":"The second-order analysis of stationary point processes","volume":"13","author":"Ripley","year":"1976","journal-title":"J. Appl. Prob"},{"key":"2026051320513968300_asag021-B21","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1007\/s10463-013-0431-z","article-title":"Identification and estimation of superposed Neyman-Scott spatial cluster processes","volume":"66","author":"Tanaka","year":"2014","journal-title":"Ann. Inst. Statist. Math"},{"key":"2026051320513968300_asag021-B22","doi-asserted-by":"crossref","first-page":"2382","DOI":"10.1080\/01621459.2023.2257896","article-title":"Spatiotemporal clustering with Neyman-Scott processes via connections to Bayesian nonparametric mixture models","volume":"119","author":"Wang","year":"2023","journal-title":"J. Am. Statist. Assoc"},{"key":"2026051320513968300_asag021-B23","first-page":"623","volume-title":"Proc. 21st Int. Conf. Artificial Intelligence and Statistics, vol. 84 of Proc. Mach. Learn. Res","author":"Xu","year":"2018"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asag021\/67637136\/asag021.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/113\/2\/asag021\/67637136\/asag021.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/113\/2\/asag021\/67637136\/asag021.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:51:48Z","timestamp":1778719908000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/doi\/10.1093\/biomet\/asag021\/8555606"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2,13]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asag021","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026]]},"published":{"date-parts":[[2026]]},"article-number":"asag021"}}