Estimating the Dimension of a Model
1978/03/01 by Gideon Schwarz · 238 citations
Mathematics · #Statistical Methods and Inference
paper · pdf · doi:10.1214/aos/1176344136
openalex publication_date 1978/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/03/27
Abstract
The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.
Cited by
- Beyond j=1: Observational Constraints on Almost-ΛCDM Cosmologies
- A Smooth Transition from Giant Planets to Brown Dwarfs from the Radial Occurrence Distribution
- E-Values For Multiplicity Control In Multiverse Analysis
- Algebraic Signatures for Structural Learning in Probability Tensors
- Time-Domain Axion Searches with Magnetic White Dwarfs
- Turtle shell clustering: A mixture approach to discriminative clustering with applications to flow cytometry and other data
- Improving Decision Quality for Energy System Design via Stochastic Goal Programming with Data-Driven MILPs
- A recursive subspace based method for errors-in-variables model identification of time-varying systems
- Interpretable Anomaly and Drift Detection with Gaussian Mixture Models
- Toward Joint Prediction of a Longitudinal Marker and a Terminal Event: A bivariate discrete-time framework
- A Unified Statistical Framework for Multicopter Propeller Damage Diagnosis Based on Functionally Pooled Models and Bayesian Quantification: Experimental Flight Test Assessment
- How Does Bayesian Causal Discovery Fail? Characterising Structural Consequences in Linear Gaussian Networks under Latent Confounding
- FLINT: Fingerprinting Federated Learning Architectures from 5G PHY-Layer Side Channels
- cpm: A python library for theory-driven modelling in computational psychiatry
- Parsimonious Mixtures of Skewed Bilinear Factor Analyzers
- A comprehensive separation of dark matter and baryonic mass components in galaxy clusters – II: an overview of the mass distribution in Abell S1063
- Decoupling perturbations from background in f(Q) gravity: the square-root correction and the impact on the σ8 tension
- The dark and featureless surface of rocky exoplanet LHS 3844 b from JWST mid-infrared spectroscopy
- Molecular mapping in DNA-PAINT via modified Gaussian Mixture Modeling
- The hyper-systemizing hypothesis: how the tendency to systemize influences conspiracy beliefs and belief inflexibility in clinical and general populations
- From movement to cognitive maps: recurrent neural networks reveal how locomotor development shapes hippocampal spatial coding
- Cardiac-vagal rhythm echoes on the heartbeat’s mechanosensory imprint in the brain
- Stochastic choice drives variability in patch foraging decisions in humans and rats
- On the Exoplanet Yield of Gaia Astrometry
- A Global Perspective on Local Sea Level Changes
- Description length of canonical and microcanonical models
- Discovering cognitive strategies with tiny recurrent neural networks
- The emergence and demise of giant sloths
- How Individual Differences in Empathy Predict Moments of Empathy in Everyday Life
- The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
- Multiphase Structured Latent Curve Models for Count Response Data: A Re-Analysis of the Acquisition of Morphology in English
- SNAP: Sequential Non-Ancestor Pruning for Targeted Causal Effect Estimation With an Unknown Graph
- Is Ockham’s razor losing its edge? New perspectives on the principle of model parsimony
- Exploring the effect of installing collars on snow crab (Chionoecetes opilio) pots in Newfoundland and Labrador: Do collars improve size selectivity?
- An information criterion for detecting periodicities in functional time series
- Regret-Based Federated Causal Discovery with Unknown Interventions
- How the terminal glucoside of the N-glycan donor affects the catalytic efficiency of the eukaryotic oligosaccharyltransferase
- Bayesian Feature Extraction using Gaussian and Diffused-gamma Priors for High Dimensional Spatio-Temporal Data
- Collaborative Optimization of Multiclass Imbalanced Learning: Density-Aware and Region-Guided Boosting
- Brain mechanisms for processing systematic sound-to-meaning mappings for concrete and abstract concepts
- Persistent and anti-persistent stride-to-stride fluctuations: An ARFIMA decomposition consistent with closed-loop sensorimotor control
- On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement
- A Multidimensional Fractional Hawkes Process for Multiple Earthquake Mainshock Aftershock Sequences
- A comparison between initialization strategies for the infinite hidden Markov model
- Momentary energy management profiles: associations with energy, heart rate variability, and motivational states
- Simplex Demixing: Disentangling Multiple Light-Flavor Jets at Colliders
- Sum-Rule-Preserving Non-Factorized Transition-GPD Tomography of N→Δ(1232) Multipole Structure
- Constraining Spatial Curvature with Priors from Swampland Conjectures
- JASPER: Joint Bayesian Analysis of Spatial Expression via Regression
- Ordering-based Causal Discovery via Generalized Score Matching
- Prediction intervals for quantile autoregression
- On the Metric f(R) gravity Viability in Accounting for the Binned Supernovae Data
- What is Stochastic Supervenience?
- Applying Gaussian Mixture Models to Track Reconstruction in Inelastic Scattering Experiments with Active Targets
- Causal Structure Learning for Dynamical Systems with Theoretical Score Analysis
- Parsimonious Ultrametric Manly Mixture Models
- A latent variable model for identifying and characterizing food adulteration
- Doomed Worlds II: Reassessing Suggestions of Orbital Decay for TrES-5 b
- Optimized Architectures for Kolmogorov-Arnold Networks
- Scalable branch-and-bound model selection with non-monotonic criteria including AIC, BIC and Mallows's Cp
- Identifiability and improper solutions in the probabilistic partial least squares regression with unique variance
- From Earths to Super-Earths: Five New Small Planets Transiting M Dwarf Stars
- Seeking Spectroscopic Binaries with Data-Driven Models
- Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model
- Identifiable factor analysis for mixed continuous and binary variables based on the Gaussian-Grassmann distribution
- Validation of a Third Earth-sized Planet in the TOI-2267 Binary System
- A Bayesian Approach for Robust Longitudinal Envelope Models
- Metrics for Optimizing Searches for Orbital Precession and Tidal Decay via Transit- and Occultation-Timing
- Causal symmetrization as an empirical signature of operational autonomy in complex systems
- Health monitoring at the Robert Koch Institute – Effects of a change in study design on sample composition and prevalence estimates due to the start of the ‘Health in Germany’ panel
- Hypothesis-Based Particle Detection for Accurate Nanoparticle Counting and Digital Diagnostics
- Fractional Holographic Dark Energy Driven Reconstruction of f(Q) Gravity and its Cosmological Implications
- The Hidden Cost of Straight Lines: Quantifying Misallocation Risk in Voronoi-based Service Area Models
- Convergence-Divergence Models: Generalizations of Phylogenetic Trees Modeling Gene Flow Over Time
- pvEBayes: An R Package for Empirical Bayes Methods in Pharmacovigilance
- Factors Influencing Cryptocurrency Prices: Evidence from Bitcoin, Ethereum, Dash, Litecoin, and Monero
- Bayes Factor Hypothesis Testing in Meta-Analyses: Practical Advantages and Methodological Considerations
- Softly Symbolifying Kolmogorov-Arnold Networks
- SVEMnet: An R package for Self-Validated Elastic-Net Ensembles and Multi-Response Optimization in Small-Sample Mixture-Process Experiments
- Order Selection in Vector Autoregression by Mean Square Information Criterion
- GRB 240715A: Revealing Novel Intrinsic Mechanism by Different Individual Pulse
- Singular Learning Theory for Factor Analysis
- Robust outlier-adjusted mean-shift estimation of state-space models
- Constraining the Nature of Dark Matter from Tidal Radii of Cluster Galaxy Subhalos
- Causal Discovery on Higher-Order Interactions
- A Dynamical Scalar Field Model for Dark Energy: Addressing the Hubble Tension and Cosmic Evolution
- Estimating the true number of principal components under the random design
- Detecting and quantifying networks of biological kinship via exponential family random graph models
- Exponential f(R) cosmology with massive neutrinos as a dynamical dark energy framework
- Bayesian and Machine-Learning Analyses of Nonminimal f(Q) Gravity and H0 Tension
- On the Development of Probabilistic Projections of Country-level Progress to the UN SDG Indicator of Minimum Proficiency in Reading and Mathematics
- Benchmarking of Clustering Validity Measures Revisited
- Wings over the city: avian and butterfly diversity across a gradient of anthropogenic disturbance
- Goodness-of-fit testing of the distribution of posterior classification probabilities for validating model-based clustering
- Higher-Order Causal Structure Learning with Additive Models
- Measuring accretion disc properties in the transitional millisecond pulsar PSR J1023+0038 using XMM-Newton, NuSTAR, NICER and Chandra
- Multi-Faceted Emission Properties of PSR J2129+4119 Observed with FAST
- Uncertainty-Aware Diagnostics for Physics-Informed Machine Learning
- Delta Debugging for Cyber-Physical Systems with Flaky Test Executions
- Mono- and Polyauxic Growth Kinetics: A Semi-Mechanistic Framework for Complex Biological Dynamics
- Compactly supported radial basis functions as probability density functions
- Quantification and statistical comparison of cell-state transition kinetics using a parametric failure-based model
- The T16 Planet Hunt: 10,000 New Planet Candidates from TESS Cycle 1 and the Confirmation of a Hot Jupiter Around TIC 183374187
- Career Adaptability as a Developmental Resource for Sustainable Careers: A Latent Profile Analysis in Emerging Adults
- High Arctic vegetation lowers soil temperatures on sunny days despite low stature
- Evidence for a Nonzero Eccentricity Superpuff Exoplanet WASP-107 b Using JWST Occultation Observation
- <i>Microbotryum crypticum</i>, a new anther smut fungus on <i>Silene miqueliana</i> from Japan
- A Fine-Grained Longitudinal Study of Adolescent Cannabis Use and Its Relation to Cognitive Performance in Young Adulthood
- A multilevel model with heterogeneous variances for snap timing in the National Football League
- Fast-Cooling Synchrotron Prompt Emission from Internal Shocks in GRB 241030A
- Transformers can do Bayesian Clustering
- Building on models—a perspective for computational neuroscience
- Reliable Robotic Task Execution in the Face of Anomalies
- Constraining and Comparing the Dynamical Dark Energy and f(R) Modified Gravity Models with Cosmological Distance Measurements
- Revisiting the 150 MHz Radio Luminosity Function of Star-Forming Galaxies with LOFAR Deep Fields through a Refined Statistical Framework
- Operationalising Extended Cognition: Formal Metrics for Corporate Knowledge and Legal Accountability
- Differentiable Constraint-Based Causal Discovery
- Beyond ΛCDM: Exploring a Dynamical Cosmological Constant Framework Consistent with Late-Time Observations
- Robust Rank Estimation for Noisy Matrices
- Survival of the fittest Cox model: Pivotal variable selection for time-to-event data
- Quantifying Periodicity in Non-Euclidean Random Objects
- Investigating the mysterious nature of 1LHAASO J1740+0948u through deep XMM-Newton observations
- A Simple Method for PMF Estimation on Large Supports
- XRISM Resolves Relativistic Effects from the Innermost Accretion Disk in Serpens X-1
- Dendrograms of Mixing Measures for Softmax-Gated Gaussian Mixture of Experts: Consistency Without Model Sweeps
- Characterizing Agent-Based Model Dynamics via ε-Machines and Kolmogorov-Style Complexity
- Observational Constraints on Chaplygin Gas Models in Non-Minimally Coupled Power Law f(Q) Gravity with Quasars
- Reanalysis of the eclipses of LHS 1140 c: No evidence of an atmosphere and implications for the internal structure of the planet
- Big Bang Nucleosynthesis constraints on space-time noncommutativity
- Is Dark Energy Changing? Probing the Universe's Expansion with present and future astronomical probes
- Generalized Distributions of Host Dispersion Measures in the Fast Radio Burst Cosmology
- Investigating the wCDM Model with Latest DESI BAO Observations
- A General Framework for Joint Multi-State Models
- How Does Transcription-Associated Mutagenesis Shape tRNA Microevolution?
- Morpheme knowledge is shaped by information available through orthography
- Revisiting the Orbital Dynamics of the Hot Jupiter WASP-12 b with New Transit Times
- A subsampling approach for large data sets when the Generalised Linear Model is potentially misspecified
- Frequency-Domain Analysis of Time Series with Network-Structured Dependence: Application to Global Bank Connectedness
- Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning
- Environment-Aware Indoor LoRaWAN Path Loss: Parametric Regression Comparisons, Shadow Fading, and Calibrated Fade Margins
- Optimality and computational barriers in variable selection under dependence
- Observation of undepleted phosphine in the atmosphere of a low-temperature brown dwarf
- Beyond CPL: Evidence for dynamical dark energy in three-parameter models
- A z≃0.4 Little Red Dot analog: An Extended Starburst with an Overmassive Black hole
- What is in the model? A Comparison of variable selection criteria and model search approaches
- A competitive edge: how social cues and spatial congruence influence joint attention in addressed or witnessed interactions
- Bayesian Model Comparison and Significance: Widespread Errors and how to Correct Them
- A Unified Probabilistic Framework for Dictionary Learning with Parsimonious Activation
- The Optimal Magnitude of Government Spending: Evidence from Cambodia
- Predictability and Statistical Memory in Classical Sonatas and Quartets
- What’s the optimal usage pattern? Latent profile analysis of Chinese young adults’ social networking site use and its association with subjective well-being
- Anthropogenic climate change leads to a pronounced reorganisation of wintertime North Atlantic atmospheric circulation regimes
- The Orbital Eccentricities of Planets in the Kinematic Thin and Thick Galactic Disks
- Achieving just transition through convergence in the Carbon Efficiency of Social Progress
- Tail-robust estimation of factor-adjusted vector autoregressive models for high-dimensional time series
- Modeling Psychological Profiles in Volleyball via Mixed-Type Bayesian Networks
- Mixtures Closest to a Given Measure: A Semidefinite Programming Approach
- Einstein@Home Searches for Gamma-ray Pulsars in the Inner Galaxy
- Online Sequential Leveraging Sampling Method for Streaming Autoregressive Time Series with Application to Seismic Data
- Cosmological Dynamics of Matter Creation with Modified Chaplygin Gas and Bulk Viscosity
- Decomposing Co-Movements in Matrix-Valued Time Series: A Pseudo-Structural Reduced-Rank Approach
- Generalized Nonnegative Structured Kruskal Tensor Regression
- Statistical Constraints on Albedo Structure in Asteroid Families from NEOWISE Measurements
- Selfnormalization for relevant inference with supremum-type statistics
- Evaluating the Vergence-Accommodation Conflict in Gaze-Based 3D Target Selection
- A dark-matter-sensitive orientation clock near rotating black holes
- A Cluster-Analytic Approach to Constraint Typologies and Technical Efficiency among Maize Farmers in Himachal Pradesh
- Neural mechanisms of negative emotionality and cognitive control: The role of frontal midline theta
- Too Hot, Too Wet: Bayesian Spatial Modeling of Climate‐Driven Salmonella Risk in New South Wales, Australia, 1991–2022
- Growth patterns of blackthroat seaperch Doederleinia berycoides cohorts in relation to dominant year classes in the western Japan Sea
- Clustering longitudinal data: comparison of model-based and distance-based approaches using simulated and real-world data in psychiatric research
- Concatenation, Conflict, and Complexity: Genealogical Heterogeneity Mimics Substitutional Heterogeneity for Nucleotide Model Selection
- The First Dedicated Survey of Atmospheric Escape from Planets Orbiting F Stars
- HD 164604 c: A Second Giant Planet on a 15 Yr Orbit and Constraints on the Planet–Planet Mutual Inclination*
- More rumination, better cows: Exploring genetic parameters of daily rumination time in Holstein dairy cows around first calving
- Constraining deviations from ΛCDM in the Hubble expansion rate
- Early Evidence for Polar Orbits of Sub-Saturns around Hot Stars
- Subspace Clustering of Subspaces: Unifying Canonical Correlation Analysis and Subspace Clustering
- Enhanced Survival Trees
- On the Fe xxii Emission in the X-ray spectrum of NGC 1068
- Covariance-Corrected WAIC for Bayesian Sequential Data Models
- Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMs
- Revealing Multimodal Causality with Large Language Models
- Bayesian distributionally robust variational inequalities: regularization and quantification
- Automated Constitutive Model Discovery by Pairing Sparse Regression Algorithms with Model Selection Criteria
- Strategic Play and Home Advantage: Coaches' Tactical Impact in Serie A
- Possible Evidence for the Presence of Volatiles on the Warm Super-Earth TOI-270 b
- Convergence and Generalization of Anti-Regularization for Parametric Models
- Unit-Modified Weibull Distribution and Quantile Regression Model
- Effects of Matter Lagrangian in f(Q,T) Gravity: The Accelerating Cosmological Model
- The Morgan-Pitman Test of Equality of Variances and its Application to Machine Learning Model Evaluation and Selection
- MMM: Clustering Multivariate Longitudinal Mixed-type Data
- Experimental Uncertainty Propagation in Neural Network Extraction in Hadronic Physics
- KOO Method-based Consistent Clustering for Group-wise Linear Regression with Graph Structure
- CLAE: A High‐Fidelity Nanopore Sequencing Strategy for Read‐Level Viral Variant Detection and Environmental RNA Virus Discovery
- Systematic attribution of heatwaves to the emissions of carbon majors
- High-Pass Filtering and Gaussian Process Regularization: Stellar Activity Characterization Techniques Applied to the 55 Cancri Planetary System
- Clustering methods for Categorical Time Series and Sequences : A scoping review
- A dense dark matter core of the subhalo in the strong lensing system JVAS B1938+666
- Automated Hierarchical Graph Construction for Multi-source Electronic Health Records
- Simplicial clustering using the α--transformation
- Generalized Tensor Completion with Non-Random Missingness
- Uniform Information Density and Syntactic Reduction: Revisiting that-Mentioning in English Complement Clauses
- Time Series Analysis of DECAL Sensor Noise for the Generation of Truly Random Numbers
- Automatic Screening of Parkinson's Disease from Visual Explorations
- hdMTD: An R Package for High-Dimensional Mixture Transition Distribution Models
- Learning from financial rewards and punishments reduces the in-group bias in social approach without changing the in-group bias in impressions
- Hybrid Topic-Semantic Labeling and Graph Embeddings for Unsupervised Legal Document Clustering
- Agegraphic dark energy from entropy of the anti-de Sitter black hole
- Developing an impact index for the Australian Fire Danger Rating System: predicting potential structure loss from wildfires
- Normalized Maximum Likelihood Code-Length on Riemannian Manifold Data Spaces
- Interpretability of linear regression models of glassy dynamics
- Pivotal inference for linear predictions in stationary processes
- Probing the H0 Tension with Holographic Dark Energy in Unimodular Gravity: Insights from DESI DR2
- A Spectroscopic Hunt for Post-Red Supergiants in the Large Magellanic Cloud II: Turbulent Line Broadening in the Spectra of LMC Yellow Supergiants
- Growth Index in the γδCDM model
- CPL-parametrized cosmic expansion in Galileon gravity: Constraints from recent data
- Bimanual Robot-Assisted Dressing: A Spherical Coordinate-Based Strategy for Tight-Fitting Garments
- A novel approach to generate distributions
- Matters Arising: Spatial correlation in economic analysis of climate change
- Anomaly Detection for IoT Global Connectivity
- Particle physics models of interacting bosonic dark energy and fermionic dark matter in Einstein scalar Gauss-Bonnet gravity
- Parametrizing the Hubble function instead of dark energy: Many possibilities
- Cosmological Parameter Estimation using Particle Swarm Optimization
- Looking into the Unknown: Exploring Action Discovery for Segmentation of Known and Unknown Actions
- Cluster-specific ranking and variable importance for Scottish regional deprivation via vine mixtures
- Leveraging Minute-by-Minute Soccer Match Event Data to Adjust Team's Offensive Production for Game Context
- Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learning
- Validation of TESS Planet Candidates with Multi-Color Transit Photometry and TRICERATOPS+
- Actionable Counterfactual Explanations Using Bayesian Networks and Path Planning with Applications to Environmental Quality Improvement
- Distribution-free data-driven smooth tests without χ2
- To Vary or Not To Vary: A Flexible Empirical Bayes Factor for Testing Variance Components
- Effective Phantom Divide Crossing with Standard and Negative Quintessence
- Discovery of a Little Red Dot candidate at z\gtrsim10 in COSMOS-Web based on MIRI-NIRCam selection
- A Comprehensive Study of the Energy and Redshift Distributions of the Fast Radio Burst Population Based on the First CHIME/FRB Catalog
- How to embed any likelihood into SBI: Application to Planck + Stage IV galaxy surveys and Dynamical Dark Energy
- A Bayesian Ensemble Projection of Climate Change and Technological Impacts on Future Crop Yields
- NIRPS detection of delayed atmospheric escape from the warm and misaligned Saturn-mass exoplanet WASP-69b
Related