{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/multimodal-nested-sampling-an-efficient-and","title":"Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis","arxiv_id":"0704.3704","date":"2007-04-27","proceeding":null,"authors":["Farhan Feroz","M. P. Hobson"],"abstract":"In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional MCMC sampling methods. Second, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive. The nested sampling method introduced by Skilling (2004), has greatly reduced the computational expense of calculating evidences and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee et al. (2006), but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw et al. (2007), recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical datasets.","url_abs":"https://arxiv.org/abs/0704.3704v3","url_pdf":"https://arxiv.org/pdf/0704.3704v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"multimodal-nested-sampling-an-efficient-and","repo_url":"https://github.com/SuperKam91/gns","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"object-detection","task_name":"Object Detection"},{"task_slug":"object-detection-1","task_name":"object-detection"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=0704.3704","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"0704.3704"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/SuperKam91/gns","reach":null}],"summary":{"ran_draft_wrong":1,"unverified":3},"by_repo_kind":{"listed":{"samples":4,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"dc703b4b8b01e2b2","entry":"getSetupDicts","repo":"SuperKam91/gns","repo_kind":"listed","path":"gns/setup_dicts.py","file_url":"https://github.com/SuperKam91/gns/blob/HEAD/gns/setup_dicts.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"dc703b4b8b01e2b2"}},{"code_sha256_prefix":"d3ec799af4155e93","entry":"NestedRun","repo":"SuperKam91/gns","repo_kind":"listed","path":"gns/nested_run.py","file_url":"https://github.com/SuperKam91/gns/blob/HEAD/gns/nested_run.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d3ec799af4155e93"}},{"code_sha256_prefix":"b87435b5696e91e6","entry":"NestedRunLinear","repo":"SuperKam91/gns","repo_kind":"listed","path":"gns/nested_run.py","file_url":"https://github.com/SuperKam91/gns/blob/HEAD/gns/nested_run.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b87435b5696e91e6"}},{"code_sha256_prefix":"d1abbc84b7b78c02","entry":"NestedRunLog","repo":"SuperKam91/gns","repo_kind":"listed","path":"gns/nested_run.py","file_url":"https://github.com/SuperKam91/gns/blob/HEAD/gns/nested_run.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d1abbc84b7b78c02"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}