Path-Following Methods for Maximum a Posteriori Estimators in Bayesian Hierarchical Models: How Estimates Depend on Hyperparameters Article Swipe

View

Zilai Si , Yucong Liu , Alexander Strang ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.1137/22m153330x

Related Topics

Concepts

Hyperparameter Mathematics Estimator Bayesian probability Maximum a posteriori estimation Path (computing) A priori and a posteriori Statistics Bayesian inference Mathematical optimization Econometrics Applied mathematics Maximum likelihood Algorithm Computer science Philosophy Programming language Epistemology

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.1137/22m153330x
OA Status: gold
Cited By: 3
References: 29
Related Works: 10
OpenAlex ID: https://openalex.org/W4400202384

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4400202384

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.1137/22m153330x

Digital Object Identifier
Title: Path-Following Methods for Maximum a Posteriori Estimators in Bayesian Hierarchical Models: How Estimates Depend on Hyperparameters

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2024

Year of publication
Publication date: 2024-07-01

Full publication date if available
Authors: Zilai Si, Yucong Liu, Alexander Strang

List of authors in order
Landing page: https://doi.org/10.1137/22m153330x

Publisher landing page
Open access: Yes

Whether a free full text is available
OA status: gold

Open access status per OpenAlex
OA URL: https://escholarship.org/uc/item/5xn8z9m3

Direct OA link when available
Concepts: Hyperparameter, Mathematics, Estimator, Bayesian probability, Maximum a posteriori estimation, Path (computing), A priori and a posteriori, Statistics, Bayesian inference, Mathematical optimization, Econometrics, Applied mathematics, Maximum likelihood, Algorithm, Computer science, Philosophy, Programming language, Epistemology

Top concepts (fields/topics) attached by OpenAlex
Cited by: 3

Total citation count in OpenAlex
Citations by year (recent): 2025: 2, 2024: 1

Per-year citation counts (last 5 years)
References (count): 29

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4400202384
doi	https://doi.org/10.1137/22m153330x
ids.doi	https://doi.org/10.1137/22m153330x
ids.openalex	https://openalex.org/W4400202384
fwci	4.59870138
type	article
title	Path-Following Methods for Maximum a Posteriori Estimators in Bayesian Hierarchical Models: How Estimates Depend on Hyperparameters
biblio.issue	3
biblio.volume	34
biblio.last_page	2230
biblio.first_page	2201
topics[0].id	https://openalex.org/T10136
topics[0].field.id	https://openalex.org/fields/26
topics[0].field.display_name	Mathematics
topics[0].score	0.9995999932289124
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2613
topics[0].subfield.display_name	Statistics and Probability
topics[0].display_name	Statistical Methods and Inference
topics[1].id	https://openalex.org/T10243
topics[1].field.id	https://openalex.org/fields/26
topics[1].field.display_name	Mathematics
topics[1].score	0.9943000078201294
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2613
topics[1].subfield.display_name	Statistics and Probability
topics[1].display_name	Statistical Methods and Bayesian Inference
topics[2].id	https://openalex.org/T11236
topics[2].field.id	https://openalex.org/fields/22
topics[2].field.display_name	Engineering
topics[2].score	0.9876999855041504
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2207
topics[2].subfield.display_name	Control and Systems Engineering
topics[2].display_name	Control Systems and Identification
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C8642999
concepts[0].level	2
concepts[0].score	0.8677676916122437
concepts[0].wikidata	https://www.wikidata.org/wiki/Q4171168
concepts[0].display_name	Hyperparameter
concepts[1].id	https://openalex.org/C33923547
concepts[1].level	0
concepts[1].score	0.7924277186393738
concepts[1].wikidata	https://www.wikidata.org/wiki/Q395
concepts[1].display_name	Mathematics
concepts[2].id	https://openalex.org/C185429906
concepts[2].level	2
concepts[2].score	0.6429193019866943
concepts[2].wikidata	https://www.wikidata.org/wiki/Q1130160
concepts[2].display_name	Estimator
concepts[3].id	https://openalex.org/C107673813
concepts[3].level	2
concepts[3].score	0.624956488609314
concepts[3].wikidata	https://www.wikidata.org/wiki/Q812534
concepts[3].display_name	Bayesian probability
concepts[4].id	https://openalex.org/C9810830
concepts[4].level	3
concepts[4].score	0.583890974521637
concepts[4].wikidata	https://www.wikidata.org/wiki/Q635384
concepts[4].display_name	Maximum a posteriori estimation
concepts[5].id	https://openalex.org/C2777735758
concepts[5].level	2
concepts[5].score	0.5831055045127869
concepts[5].wikidata	https://www.wikidata.org/wiki/Q817765
concepts[5].display_name	Path (computing)
concepts[6].id	https://openalex.org/C75553542
concepts[6].level	2
concepts[6].score	0.5286985635757446
concepts[6].wikidata	https://www.wikidata.org/wiki/Q178161
concepts[6].display_name	A priori and a posteriori
concepts[7].id	https://openalex.org/C105795698
concepts[7].level	1
concepts[7].score	0.447174072265625
concepts[7].wikidata	https://www.wikidata.org/wiki/Q12483
concepts[7].display_name	Statistics
concepts[8].id	https://openalex.org/C160234255
concepts[8].level	3
concepts[8].score	0.43931320309638977
concepts[8].wikidata	https://www.wikidata.org/wiki/Q812535
concepts[8].display_name	Bayesian inference
concepts[9].id	https://openalex.org/C126255220
concepts[9].level	1
concepts[9].score	0.41495370864868164
concepts[9].wikidata	https://www.wikidata.org/wiki/Q141495
concepts[9].display_name	Mathematical optimization
concepts[10].id	https://openalex.org/C149782125
concepts[10].level	1
concepts[10].score	0.38244524598121643
concepts[10].wikidata	https://www.wikidata.org/wiki/Q160039
concepts[10].display_name	Econometrics
concepts[11].id	https://openalex.org/C28826006
concepts[11].level	1
concepts[11].score	0.34210240840911865
concepts[11].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[11].display_name	Applied mathematics
concepts[12].id	https://openalex.org/C49781872
concepts[12].level	2
concepts[12].score	0.3371362090110779
concepts[12].wikidata	https://www.wikidata.org/wiki/Q1045555
concepts[12].display_name	Maximum likelihood
concepts[13].id	https://openalex.org/C11413529
concepts[13].level	1
concepts[13].score	0.31028974056243896
concepts[13].wikidata	https://www.wikidata.org/wiki/Q8366
concepts[13].display_name	Algorithm
concepts[14].id	https://openalex.org/C41008148
concepts[14].level	0
concepts[14].score	0.18929266929626465
concepts[14].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[14].display_name	Computer science
concepts[15].id	https://openalex.org/C138885662
concepts[15].level	0
concepts[15].score	0.0
concepts[15].wikidata	https://www.wikidata.org/wiki/Q5891
concepts[15].display_name	Philosophy
concepts[16].id	https://openalex.org/C199360897
concepts[16].level	1
concepts[16].score	0.0
concepts[16].wikidata	https://www.wikidata.org/wiki/Q9143
concepts[16].display_name	Programming language
concepts[17].id	https://openalex.org/C111472728
concepts[17].level	1
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q9471
concepts[17].display_name	Epistemology
keywords[0].id	https://openalex.org/keywords/hyperparameter
keywords[0].score	0.8677676916122437
keywords[0].display_name	Hyperparameter
keywords[1].id	https://openalex.org/keywords/mathematics
keywords[1].score	0.7924277186393738
keywords[1].display_name	Mathematics
keywords[2].id	https://openalex.org/keywords/estimator
keywords[2].score	0.6429193019866943
keywords[2].display_name	Estimator
keywords[3].id	https://openalex.org/keywords/bayesian-probability
keywords[3].score	0.624956488609314
keywords[3].display_name	Bayesian probability
keywords[4].id	https://openalex.org/keywords/maximum-a-posteriori-estimation
keywords[4].score	0.583890974521637
keywords[4].display_name	Maximum a posteriori estimation
keywords[5].id	https://openalex.org/keywords/path
keywords[5].score	0.5831055045127869
keywords[5].display_name	Path (computing)
keywords[6].id	https://openalex.org/keywords/a-priori-and-a-posteriori
keywords[6].score	0.5286985635757446
keywords[6].display_name	A priori and a posteriori
keywords[7].id	https://openalex.org/keywords/statistics
keywords[7].score	0.447174072265625
keywords[7].display_name	Statistics
keywords[8].id	https://openalex.org/keywords/bayesian-inference
keywords[8].score	0.43931320309638977
keywords[8].display_name	Bayesian inference
keywords[9].id	https://openalex.org/keywords/mathematical-optimization
keywords[9].score	0.41495370864868164
keywords[9].display_name	Mathematical optimization
keywords[10].id	https://openalex.org/keywords/econometrics
keywords[10].score	0.38244524598121643
keywords[10].display_name	Econometrics
keywords[11].id	https://openalex.org/keywords/applied-mathematics
keywords[11].score	0.34210240840911865
keywords[11].display_name	Applied mathematics
keywords[12].id	https://openalex.org/keywords/maximum-likelihood
keywords[12].score	0.3371362090110779
keywords[12].display_name	Maximum likelihood
keywords[13].id	https://openalex.org/keywords/algorithm
keywords[13].score	0.31028974056243896
keywords[13].display_name	Algorithm
keywords[14].id	https://openalex.org/keywords/computer-science
keywords[14].score	0.18929266929626465
keywords[14].display_name	Computer science
language	en
locations[0].id	doi:10.1137/22m153330x
locations[0].is_oa	False
locations[0].source.id	https://openalex.org/S928796702
locations[0].source.issn	1052-6234, 1095-7189
locations[0].source.type	journal
locations[0].source.is_oa	False
locations[0].source.issn_l	1052-6234
locations[0].source.is_core	True
locations[0].source.is_in_doaj	False
locations[0].source.display_name	SIAM Journal on Optimization
locations[0].source.host_organization	https://openalex.org/P4310320508
locations[0].source.host_organization_name	Society for Industrial and Applied Mathematics
locations[0].source.host_organization_lineage	https://openalex.org/P4310320508
locations[0].source.host_organization_lineage_names	Society for Industrial and Applied Mathematics
locations[0].license
locations[0].pdf_url
locations[0].version	publishedVersion
locations[0].raw_type	journal-article
locations[0].license_id
locations[0].is_accepted	True
locations[0].is_published	True
locations[0].raw_source_name	SIAM Journal on Optimization
locations[0].landing_page_url	https://doi.org/10.1137/22m153330x
locations[1].id	pmh:oai:escholarship.org:ark:/13030/qt5xn8z9m3
locations[1].is_oa	True
locations[1].source
locations[1].license	cc-by
locations[1].pdf_url
locations[1].version	submittedVersion
locations[1].raw_type	article
locations[1].license_id	https://openalex.org/licenses/cc-by
locations[1].is_accepted	False
locations[1].is_published	False
locations[1].raw_source_name	SIAM Journal on Optimization, vol 34, iss 3
locations[1].landing_page_url	https://escholarship.org/uc/item/5xn8z9m3
indexed_in	crossref
authorships[0].author.id	https://openalex.org/A5027115378
authorships[0].author.orcid
authorships[0].author.display_name	Zilai Si
authorships[0].countries	US
authorships[0].affiliations[0].institution_ids	https://openalex.org/I111979921
authorships[0].affiliations[0].raw_affiliation_string	Department of Industrial Engineering & Management Sciences, Northwestern University, Evanston, IL 60208 USA.
authorships[0].institutions[0].id	https://openalex.org/I111979921
authorships[0].institutions[0].ror	https://ror.org/000e0be47
authorships[0].institutions[0].type	education
authorships[0].institutions[0].lineage	https://openalex.org/I111979921
authorships[0].institutions[0].country_code	US
authorships[0].institutions[0].display_name	Northwestern University
authorships[0].author_position	first
authorships[0].raw_author_name	Zilai Si
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	Department of Industrial Engineering & Management Sciences, Northwestern University, Evanston, IL 60208 USA.
authorships[1].author.id	https://openalex.org/A5025152292
authorships[1].author.orcid	https://orcid.org/0000-0002-3753-9670
authorships[1].author.display_name	Yucong Liu
authorships[1].countries	US
authorships[1].affiliations[0].institution_ids	https://openalex.org/I130701444
authorships[1].affiliations[0].raw_affiliation_string	School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332 USA.
authorships[1].institutions[0].id	https://openalex.org/I130701444
authorships[1].institutions[0].ror	https://ror.org/01zkghx44
authorships[1].institutions[0].type	education
authorships[1].institutions[0].lineage	https://openalex.org/I130701444
authorships[1].institutions[0].country_code	US
authorships[1].institutions[0].display_name	Georgia Institute of Technology
authorships[1].author_position	middle
authorships[1].raw_author_name	Yucong Liu
authorships[1].is_corresponding	False
authorships[1].raw_affiliation_strings	School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332 USA.
authorships[2].author.id	https://openalex.org/A5036898670
authorships[2].author.orcid	https://orcid.org/0000-0001-6618-631X
authorships[2].author.display_name	Alexander Strang
authorships[2].countries	US
authorships[2].affiliations[0].institution_ids	https://openalex.org/I95457486
authorships[2].affiliations[0].raw_affiliation_string	Department of Statistics, The University of California, Berkeley, CA 94720 USA.
authorships[2].institutions[0].id	https://openalex.org/I95457486
authorships[2].institutions[0].ror	https://ror.org/01an7q238
authorships[2].institutions[0].type	education
authorships[2].institutions[0].lineage	https://openalex.org/I95457486
authorships[2].institutions[0].country_code	US
authorships[2].institutions[0].display_name	University of California, Berkeley
authorships[2].author_position	last
authorships[2].raw_author_name	Alexander Strang
authorships[2].is_corresponding	False
authorships[2].raw_affiliation_strings	Department of Statistics, The University of California, Berkeley, CA 94720 USA.
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://escholarship.org/uc/item/5xn8z9m3
open_access.oa_status	gold
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Path-Following Methods for Maximum a Posteriori Estimators in Bayesian Hierarchical Models: How Estimates Depend on Hyperparameters
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T03:46:38.306776
primary_topic.id	https://openalex.org/T10136
primary_topic.field.id	https://openalex.org/fields/26
primary_topic.field.display_name	Mathematics
primary_topic.score	0.9995999932289124
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2613
primary_topic.subfield.display_name	Statistics and Probability
primary_topic.display_name	Statistical Methods and Inference
related_works	https://openalex.org/W1503532423, https://openalex.org/W2150865841, https://openalex.org/W4309133645, https://openalex.org/W1967494390, https://openalex.org/W2138865713, https://openalex.org/W3013496002, https://openalex.org/W2169353922, https://openalex.org/W2465363361, https://openalex.org/W2896820906, https://openalex.org/W3128856671
cited_by_count	3
counts_by_year[0].year	2025
counts_by_year[0].cited_by_count	2
counts_by_year[1].year	2024
counts_by_year[1].cited_by_count	1
locations_count	2
best_oa_location.id	pmh:oai:escholarship.org:ark:/13030/qt5xn8z9m3
best_oa_location.is_oa	True
best_oa_location.source
best_oa_location.license	cc-by
best_oa_location.pdf_url
best_oa_location.version	submittedVersion
best_oa_location.raw_type	article
best_oa_location.license_id	https://openalex.org/licenses/cc-by
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name	SIAM Journal on Optimization, vol 34, iss 3
best_oa_location.landing_page_url	https://escholarship.org/uc/item/5xn8z9m3
primary_location.id	doi:10.1137/22m153330x
primary_location.is_oa	False
primary_location.source.id	https://openalex.org/S928796702
primary_location.source.issn	1052-6234, 1095-7189
primary_location.source.type	journal
primary_location.source.is_oa	False
primary_location.source.issn_l	1052-6234
primary_location.source.is_core	True
primary_location.source.is_in_doaj	False
primary_location.source.display_name	SIAM Journal on Optimization
primary_location.source.host_organization	https://openalex.org/P4310320508
primary_location.source.host_organization_name	Society for Industrial and Applied Mathematics
primary_location.source.host_organization_lineage	https://openalex.org/P4310320508
primary_location.source.host_organization_lineage_names	Society for Industrial and Applied Mathematics
primary_location.license
primary_location.pdf_url
primary_location.version	publishedVersion
primary_location.raw_type	journal-article
primary_location.license_id
primary_location.is_accepted	True
primary_location.is_published	True
primary_location.raw_source_name	SIAM Journal on Optimization
primary_location.landing_page_url	https://doi.org/10.1137/22m153330x
publication_date	2024-07-01
publication_year	2024
referenced_works	https://openalex.org/W3217655848, https://openalex.org/W2143628714, https://openalex.org/W1999092643, https://openalex.org/W2291795049, https://openalex.org/W2887011717, https://openalex.org/W2799274016, https://openalex.org/W3107024450, https://openalex.org/W2980939245, https://openalex.org/W2071706611, https://openalex.org/W2910526316, https://openalex.org/W2164452299, https://openalex.org/W2119883478, https://openalex.org/W2097323375, https://openalex.org/W2063978378, https://openalex.org/W2109449402, https://openalex.org/W2056636001, https://openalex.org/W4294541781, https://openalex.org/W2061810505, https://openalex.org/W2171303908, https://openalex.org/W1965169081, https://openalex.org/W2101095383, https://openalex.org/W1982652137, https://openalex.org/W2497431972, https://openalex.org/W2157076315, https://openalex.org/W2135046866, https://openalex.org/W2066986830, https://openalex.org/W2108894973, https://openalex.org/W2146031909, https://openalex.org/W3098745759
referenced_works_count	29
abstract_inverted_index
cited_by_percentile_year.max	97
cited_by_percentile_year.min	90
countries_distinct_count	1
institutions_distinct_count	3
citation_normalized_percentile.value	0.90107695
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	True