Pith. sign in

REVIEW 3 major objections 5 minor 68 references

Bayesian integrative factor analysis methods, with application in nutrition and genomics data

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This tutorial claims that five Bayesian integrative factor analysis methods perform very differently across data structures, with no single method dominating across simulations and real data.

desk verdict Useful tutorial on Bayesian multi-study factor analysis, but the headline accuracy results for Tetris rest on an oracle-information setup that overstates what the method can do for applied users. read the letter →

arxiv 2506.18479 v1 pith:JFD3BQMS submitted 2025-06-23 stat.AP

Mavis Liang , Blake Hansen , Alejandra Avalos-Pacheco , Roberta De Vito This is my paper
classification stat.AP MSC 62H2562F1562P10
keywords Bayesianfactoranalysismulti-studydataintegrationmodelsspike-and-slabpriorsIndianBuffetProcessMCMCnutritiongenomics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper is a tutorial that claims the choice among five Bayesian integrative factor analysis methods—Perturbed Factor Analysis (PFA), MOM-SS, Subspace Factor Analysis (SUFA), Bayesian Multi-study Factor Analysis (BMSFA), and Tetris—plus two naive baselines (Stack FA and Ind FA) materially changes what researchers learn from multi-study data. Across five simulation scenarios and two real case studies in nutrition and genomics, the methods differ substantially in accuracy, computational cost, and interpretability, and no single method dominates. If this is right, applied researchers need scenario-dependent guidance rather than a one-size-fits-all recommendation. The paper also finds that none of the methods reliably recovers the true number of latent factors across all settings, with eigenvalue-decomposition-based counting working well in low dimensions but underestimating in high-dimensional sparse data.

What carries the argument

The machinery is the covariance decomposition shared by the five methods: each study's marginal covariance is written as $\Sigma_s = \Sigma_\Phi + \Sigma_{\Lambda_s} + \Psi_s$, a common low-rank component plus a study-specific component plus noise. Each model parameterizes $\Sigma_\Phi$ and $\Sigma_{\Lambda_s}$ differently—perturbation matrices for PFA, non-local spike-and-slab loadings for MOM-SS, a shared subspace with study-specific transformations for SUFA, separate common and study-specific loadings for BMSFA, and a binary Indian-Buffet-Process factor-sharing matrix for Tetris—and the comparison is driven by simulation studies scored with the RV coefficient and Frobenius norm, paired with runtime and memory measurements.

What would settle it

Generate data from a realistic multi-study process that none of the five models targets—for example, a factor model with nonlinear loading effects or heavy-tailed noise—and check whether the paper's ranking (BMSFA robust, MOM-SS less accurate in complex settings, PFA failing at high dimension) still holds; or fit all methods to a spike-in dataset with known true shared and study-specific factors and see whether Tetris_fixT without the true T matrix remains competitive.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that Bayesian integrative factor models are complementary rather than interchangeable: performance depends heavily on the structure of the data being integrated. The authors show this by generating data under the assumptions of PFA, MOM-SS, SUFA, and Tetris and measuring how well each model recovers loadings, covariances, and factor counts, then confirming the patterns on real nutrition and gene-expression datasets. Among the specific findings, Tetris_fixT is the most accurate when the data genuinely follow the Tetris model, SUFA and BMSFA offer a good accuracy-efficiency balance in small-to-moderate dimensions, MOM-SS is the fastest but loses precision in complex scenarios, and PFA is accurate but computationally heavy and fails to complete in the high-dimensional genomics scenario. No method estimates the number of factors correctly in every scenario.

Load-bearing premise

The simulation scenarios are assumed to represent the range of real multi-study data structures, and in the Tetris-based scenarios the Tetris_fixT variant is given the exact true factor-sharing matrix, which may inflate its apparent advantage.

Editorial extensions

If this is right

  • Applied researchers should choose an integrative factor method based on data dimension and expected factor-sharing structure, not by default preference.
  • Tetris should be reserved for settings where partially shared factors are suspected and a large computational budget is available; BMSFA is a more robust default, and SUFA is efficient when the number of variables is small to moderate.
  • Factor-count estimates are unreliable across methods, so conclusions about the number of latent factors should be validated with multiple approaches or with external evidence.
  • The paper's reproducible R workflow lets other researchers apply and compare the seven methods on their own multi-study datasets.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A fairer comparison of Tetris against the other methods would estimate its factor-sharing matrix from the data rather than supplying the true T matrix in Tetris-based simulations; the performance gap may narrow under misspecification.
  • The no-dominance conclusion is conditional on the five scenario families considered; extending the comparison to non-normal data, missing observations, or unbalanced study designs could reshuffle the rankings.
  • A natural next step the paper leaves implicit is an automated model-selection rule (for example, held-out predictive likelihood) that picks among these methods for a given dataset, since the paper shows none is universally best.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This manuscript presents a tutorial-style comparison of five Bayesian integrative factor analysis methods (PFA, MOM-SS, SUFA, BMSFA, and Tetris) plus two baseline approaches (Stack FA and Ind FA). The authors evaluate the methods through five simulation scenarios, each using a different data-generating process (PFA, MOM-SS, SUFA, and Tetris for the last two), and two real-data applications (HCHS/SOL nutrition data and curatedOvarianData gene expression). The paper includes model formulations, identifiability and post-processing discussions, R code, and computational cost comparisons. The central claim is that no single method dominates across all settings, so applied researchers need scenario-dependent guidance.

Significance. The paper provides a useful practical resource: it compiles model descriptions, implementation details, and reproducible code for a set of recently proposed methods, and it presents a careful simulation design with multiple scenarios and robust similarity metrics (RV coefficient and Frobenius norm). The two real-data applications illustrate the workflow and provide concrete guidance. If its comparative conclusions were fully supported, the paper would be a valuable reference for applied statisticians. However, as detailed in the major comments, the comparison is undermined by an oracle-like advantage given to Tetris_fixT in the two Tetris-based simulation scenarios, and the paper's own real-data results show that automatic Tetris tends to overfit. The overall message about scenario-dependent performance is defensible, but the specific accuracy ranking of Tetris is not.

major comments (3)
  1. [Section 3.1, Scenarios 4 and 5; Section 3.2] In Scenarios 4 and 5, Tetris_fixT is fit using the exact structure T employed during data generation, 'ensuring optimal alignment with the truth' (Section 3.1). This is an oracle condition: the method is handed the true factor-sharing matrix while all other methods receive only the true counts K and J_s. In these same scenarios, the automatic Tetris procedure failed to complete within 24 hours (Section 3.2), so the accuracy results reported for 'Tetris_fixT' are not attributable to the Tetris method that an applied user would run. The statement in Section 3.2 that 'Tetris_fixT produces the most accurate estimates across all quantities due to perfect alignment with the generative model' is therefore effectively a tautology, and it does not support the paper's conclusion that Tetris is highly accurate for unknown latent structures. This is load-bearing because Scenarios 4 and 5 are the only simulations in which a Tetris variant ranks among the most accurate methods.
  2. [Section 3.2; Section 4.2.5; Table 3] The text in Section 3.2 concludes that 'Tetris, while highly accurate, does not scale well' and that 'Tetris_fixT provides a faster and more memory-efficient alternative to Tetris while maintaining competitive accuracy.' This conflates the oracle-informed Tetris_fixT with the automatic Tetris method. In the nutrition case study, Tetris with an estimated T overestimates the number of factors (K = 26) and produces 'nearly empty loaded columns' (Section 4.2.5), and the low MSE for Tetris in Table 3 is explicitly attributed to overfitting. Thus the real-data analysis does not support the claim that Tetris is an accurate automatic method, and the accuracy advantage in Scenarios 4–5 is an artifact of providing the true T.
  3. [Section 3.3, Table 2] The factor-number recovery results do not include Tetris in Scenarios 4 and 5 (because the sampler did not run to completion), and in Scenarios 1–3 Tetris gives poor or unstable estimates of K and J_s (e.g., Scenario 1: estimated K = 1.38 (1.14) with J_s overestimated; Scenario 3: J_s = 0 for all studies). The discussion in Section 3.3 notes that no method recovers the correct number of factors across all scenarios, but the paper elsewhere presents Tetris as 'highly accurate' on the basis of Scenarios 4–5. Since those scenarios only provide evidence for the oracle variant, the paper should clearly separate evidence for automatic Tetris from evidence for Tetris_fixT and should temper the accuracy claims accordingly.
minor comments (5)
  1. [Section 3.1, Scenario 4] The description of Tetris_fixT as a variant that 'pre-specifies the number of factors to improve scalability' understates the oracle nature of the procedure; in Scenarios 4 and 5 it is given the exact T matrix, which encodes the complete sharing structure and is far more informative than the factor counts K and J_s.
  2. [Section 4.2.6, Table 3] The text states that Tetris achieves the lowest MSE of 0.314, while Table 3 reports 0.318; these values should be reconciled.
  3. [Section 2.3.4] The paragraph on BMSFA factor-number determination contains a duplicated sentence ('To determine the number of factors, one can run the sampler...' appears twice) and should be edited.
  4. [Figure 2 caption] The caption describes the panel layout as 'second column... third column... third column'; the final reference should be to the fourth column or to the final panel.
  5. [Throughout] There are spelling errors (e.g., 'covaraince' in Section 2.2, 'visuallization' in Section 4.1) and inconsistent notation for the MOM-SS model name (MOM−SS vs. MOM-SS); these should be fixed in a final polish.

Circularity Check

1 steps flagged · score 6.0 of 10

Tetris accuracy conclusions in Scenarios 4–5 rest on Tetris_fixT being given the exact true factor-sharing matrix T; that oracle fit is then summarized as 'Tetris, while highly accurate'.

  1. fitted input called prediction [Section 3.1, Scenario 4; also Scenario 5 and the Section 3.2 summary]
    "Tetris_fixT is fit using the exact structure T employed during data generation, ensuring optimal alignment with the truth. ... In Scenario 4, which mimics the real nutrition data structure (Ns ≫ P), Tetris_fixT produces the most accurate estimates across all quantities due to perfect alignment with the generative model."

    Scenarios 4 and 5 generate data from the Tetris model, whose covariance is Sigma_s = Phi* Ts (Phi*)^top + Psi_s, with T being the binary factor-activation matrix. Tetris_fixT is then handed the exact T used in data generation, while every other method receives only the true counts K and J_s. The subsequent finding that Tetris_fixT is 'most accurate' is therefore not a prediction by Tetris's automatic procedure; the model is given the latent structure it is supposed to infer, so the favorable accuracy result is forced by construction. This oracle-conditioned result is then generalized to the paper's own recommendation that 'Tetris, while highly accurate, does not scale well' — even though Tetris proper failed to complete within 24 hours in these same scenarios.

full rationale

The paper is a comparative tutorial, not a derivation of new theory, and most of its evaluation is self-contained. The model descriptions in Section 2 are standard presentations of existing methods; the real-data MSE comparisons in Section 4 use held-out data and are independent of simulation choices; and Scenarios 1–3 are conventional method-of-truth studies in which all methods receive the same true factor counts. The one load-bearing circular step is the Tetris_fixT evaluation in Scenarios 4 and 5. Because these scenarios generate data from Tetris and then fit Tetris_fixT with the exact true T matrix, the statement that Tetris_fixT is the most accurate 'due to perfect alignment with the generative model' is close to tautological for the factor-sharing structure. The paper acknowledges the oracle condition in the simulation setup but still draws the general conclusion that 'Tetris, while highly accurate' and that Tetris_fixT 'maintains high estimation accuracy,' which extends the oracle result to the automatic Tetris procedure. This partial circularity affects the comparative accuracy claims in the two scenarios designed to mimic the real applications, but it does not invalidate the rest of the empirical comparison. The score reflects that one central 'prediction' reduces by construction, while the remaining simulations and case studies retain independent content.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The paper relies on several arbitrary choices for factor counts, thresholds, and hyperparameters. The most critical is the use of known true factor counts in simulations, which favors methods that require pre-specification. No new entities are introduced.

free parameters (5)
  • Factor counts K and Js = Set to known true values in simulations; set to arbitrary upper bounds in real data analyses (e.g., K=6, Js=2 for…
    The paper specifies factor counts for each model in each simulation scenario. These are not estimated but chosen to match true or reasonable values. In real data analyses, they are selected via eigenvalue thresholds or default settings, which involve arbitrary choices.
  • EVD threshold (5% variance) = 0.05
    Used to determine number of factors for Stack FA, Ind FA, and BMSFA. This is a post-hoc choice that affects estimated factor counts and downstream results.
  • PFA cutoff (adaptive truncation) = 0.001 (in nutrition data)
    Threshold for loading magnitude to prune factors. This is a tuning parameter that affects estimated K and model complexity.
  • SUFA qmax and Js heuristic = qmax=6 in nutrition; Js=K/S heuristic
    Maximum shared factors and study-specific factors are pre-specified, affecting identifiability and results.
  • Tetris IBP hyperparameters alpha_T, beta_T = alpha=1.25*S, beta=1
    These control the expected number of factors in the Indian Buffet Process. The paper recommends adjusting them but uses defaults.
assumptions (3)
  • domain assumption Multi-study data consist of the same variables measured across independent groups or studies.
    Section 2.1 defines the scope of the tutorial. The methods are not designed for multi-platform data where the same subjects are measured under different modalities.
  • standard math The latent factor models are identifiable up to orthogonal rotation, and post-processing resolves this.
    Section 2.4 discusses rotational invariance and alignment methods, but the paper relies on the assumption that these post-processing steps yield meaningful point estimates.
  • domain assumption The simulation data-generating processes represent realistic conditions for real data.
    Section 3.1 describes scenarios based on PFA, MOM-SS, SUFA, and Tetris. The conclusions about method performance are only as valid as these assumptions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Bayesian integrative factor analysis methods, with application in nutrition and genomics data." pith.science (2026). https://pith.science/paper/JFD3BQMS

@misc{pith2026250618479,
  author       = {Pith},
  title        = {Pith review of: Bayesian integrative factor analysis methods, with application in nutrition and genomics data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JFD3BQMS}},
  note         = {Machine review of arXiv:2506.18479}
}
read the original abstract

High-dimensional data are crucial in biomedical research. Integrating such data from multiple studies is a critical process that relies on the choice of advanced statistical models, enhancing statistical power, reproducibility, and scientific insight compared to analyzing each study separately. Factor analysis (FA) is a core dimensionality reduction technique that models observed data through a small set of latent factors. Bayesian extensions of FA have recently emerged as powerful tools for multi-study integration, enabling researchers to disentangle shared biological signals from study-specific variability. In this tutorial, we provide a practical and comparative guide to five advanced Bayesian integrative factor models: Perturbed Factor Analysis (PFA), Bayesian Factor Regression with non-local spike-and-slab priors (MOM-SS), Subspace Factor Analysis (SUFA), Bayesian Multi-study Factor Analysis (BMSFA), and Bayesian Combinatorial Multi-study Factor Analysis (Tetris). To contextualize these methods, we also include two benchmark approaches: standard FA applied to pooled data (Stack FA) and FA applied separately to each study (Ind FA). We evaluate all methods through extensive simulations, assessing computational efficiency and accuracy in the estimation of loadings and number of factors. To bridge theory and practice, we present a full analytical workflow, with detailed R code, demonstrating how to apply these models to real-world datasets in nutrition and genomics. This tutorial is designed to guide applied researchers through the landscape of Bayesian integrative factor analysis, offering insights and tools for extracting interpretable, robust patterns from complex multi-source data. All code and resources are available at: https://github.com/Mavis-Liang/Bayesian_integrative_FA_tutorial

Figures

Figures reproduced from arXiv: 2506.18479 by the authors.

Figure 1
Figure 1. Data Integration Scenarios: multi-study data which observes the same set of variables across multiple groups of subjects (left), multi-platform data which observes multiple sets of variables on the same subjects (right). In this tutorial, we focus on methods designed for the multi-study setting, while recognizing that future extensions are needed to unify multi-study and multi-platform approaches under a common fram… view at source ↗
Figure 2
Figure 2. Measuring accuracy of different Bayesian integrative factor models in estimating factor loadings and marginal covariance matrices, across five simulation scenarios with correctly specified numbers of factors. The first column lists out the settings of a scenario, the second column shows the RV coefficient between estimated and true common loadings (Φ), the third column shows the RV or study-specific loadings (Λs), a… view at source ↗
Figure 3
Figure 3. Computational efficiency of Bayesian integrative factor models, evaluated under correctly specified numbers of factors across the five simulation scenarios. The runtime (in seconds) and peak memory usage (in MiB) are recorded for each model. 36 [PITH_FULL_IMAGE:figures/full_fig_p036_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Heatmaps of the factor loading matrices for each method. Rows correspond to nutrients, and columns to latent factors. Loadings in blue (orange) represent negative (positive) associations. 37 [PITH_FULL_IMAGE:figures/full_fig_p037_4.png]
Figure 5
Figure 5. Figure 5: Shared gene co-expression network based on ΣbΦ across the ovarian cancer studies for different methods obtained using Gephi [Bastian et al., 2009]. We include edges between two genes if the corresponding element in the shared covariance matrix ΣbΦ is greater than a thr…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

68 extracted references · 61 canonical work pages

  1. [1]

    C., Buettner, F., Huber, W., and Stegle, O

    Argelaguet, R., Velten, B., Arnol, D., Dietrich, S., Zenz, T., Marioni, J. C., Buettner, F., Huber, W., and Stegle, O. (2018). Multi-omics factor analysis—a framework for unsupervised integration of multi-omics data sets. Molecular systems biology , 14(6):e8124

    work page 2018

  2. [2]

    A mann, C., Boysen-Hogrefe, J., and Pape, M. (2016). Bayesian analysis of static and dynamic factor models: An ex-post approach towards the rotation problem. Journal of Econometrics , 192(1):190--206

    work page 2016

  3. [3]

    Avalos-Pacheco, A., Rossell, D., and Savage, R. S. (2022). Heterogeneous large datasets integration using Bayesian factor regression. Bayesian analysis , 17(1):33--66

    work page 2022

  4. [4]

    and Reichel, L

    Baglama, J. and Reichel, L. (2005). Augmented implicitly restarted lanczos bidiagonalization methods. SIAM Journal on Scientific Computing , 27(1):19--42

    work page 2005

  5. [5]

    and Ng, S

    Bai, J. and Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica , 70(1):191--221

    2002

  6. [6]

    Bartlett, M. S. (1937). The statistical conception of mental factors. British journal of Psychology , 28(1):97

    work page 1937

  7. [7]

    Bastian, M., Heymann, S., and Jacomy, M. (2009). Gephi: an open source software for exploring and manipulating networks. In Proceedings of the international AAAI conference on web and social media , volume 3, pages 361--362

    work page 2009

  8. [8]

    and Dunson, D

    Bhattacharya, A. and Dunson, D. B. (2011). Sparse bayesian infinite factor models. Biometrika , 98(2):291--306

    work page 2011

Show all 68 references
  1. [9]

    S., and Dunson, D

    Bhattacharya, A., Pati, D., Pillai, N. S., and Dunson, D. B. (2015). Dirichlet--laplace priors for optimal shrinkage. Journal of the American Statistical Association , 110(512):1479--1490

    2015

  2. [10]

    K., Laird, M

    Breuer, K., Foroushani, A. K., Laird, M. R., Chen, C., Sribnaia, A., Lo, R., Winsor, G. L., Hancock, R. E., Brinkman, F. S., and Lynn, D. J. (2013). Innatedb: systems biology of innate immunity and beyond—recent updates and continuing curation. Nucleic acids research , 41(D1):...

    2013

  3. [11]

    M., Chang, J., Lucas, J

    Carvalho, C. M., Chang, J., Lucas, J. E., Nevins, J. R., Wang, Q., and West, M. (2008). High-dimensional sparse factor modeling: applications in gene expression genomics. Journal of the American Statistical Association , 103(484):1438--1456

    2008

  4. [12]

    Cattell, R. (2012). The scientific use of factor analysis in behavioral and life sciences . Springer Science & Business Media

    2012

  5. [13]

    K., Dunson, D

    Chandra, N. K., Dunson, D. B., and Xu, J. (2024). Inferring covariance structure from multiple data sources via subspace factor analysis. Journal of the American Statistical Association , 26(just-accepted):1--25

    2024

  6. [14]

    and Gevaert, O

    Cheerla, A. and Gevaert, O. (2019). Deep learning with multimodal representation for pancancer prognosis prediction. Bioinformatics , 35(14):i446--i454

    2019

  7. [15]

    Darton, R. A. (1980). Rotation in factor analysis. Journal of the Royal Statistical Society Series D: The Statistician , 29(3):167--194

    1980

  8. [16]

    De Vito, R., Bellio, R., Trippa, L., and Parmigiani, G. (2019). Multi-study factor analysis. Biometrics , 75(1):337--346

    2019

  9. [17]

    De Vito, R., Bellio, R., Trippa, L., and Parmigiani, G. (2021). Bayesian multistudy factor analysis for high-throughput biological data. The annals of applied statistics , 15(4):1723--1741

    2021

  10. [18]

    A., Bainter, S

    De Vito, R., Stephenson, B., Sotres-Alvarez, D., Siega-Riz, A.-M., Mattei, J., Parpinel, M., Peters, B. A., Bainter, S. A., Daviglus, M. L., Van Horn, L., et al. (2022). Shared and ethnic background site-specific dietary patterns in the hispanic community health study/study of...

    2022

  11. [19]

    Doan, A., Halevy, A., and Ives, Z. (2012). Principles of data integration . Elsevier

    2012

  12. [20]

    Durante, D. (2017). A note on the multiplicative gamma process. Statistics & Probability Letters , 122:198--204

    2017

  13. [21]

    Edefonti, V., De Vito, R., Salvatori, A., Bravi, F., Patel, L., Dalmartello, M., and Ferraroni, M. (2020). Reproducibility of a posteriori dietary patterns across time and studies: a scoping review. Advances in Nutrition , 11(5):1255--1281

    2020

  14. [22]

    Edefonti, V., Hashibe, M., Ambrogi, F., Parpinel, M., Bravi, F., Talamini, R., Levi, F., Yu, G., Morgenstern, H., Kelsey, K., et al. (2012). Nutrient-based dietary patterns and the risk of head and neck cancer: a pooled analysis in the international head and neck cancer epidem...

    2012

  15. [23]

    Falcon, S., Morgan, M., and Gentleman, R. (2007). An introduction to bioconductor’s expressionset class

    2007

  16. [24]

    Fr \"u hwirth-Schnatter, S., Hosszejni, D., and Lopes, H. F. (2024). Sparse bayesian factor analysis when the number of factors is unknown. Bayesian Analysis , 1(1):1--44

    2024

  17. [25]

    F., Riester, M., Haibe-Kains, B., Risch, T., Tyekucheva, S., Jazic, I., Wang, X

    Ganzfried, B. F., Riester, M., Haibe-Kains, B., Risch, T., Tyekucheva, S., Jazic, I., Wang, X. V., Ahmadifar, M., Birrer, M. J., Parmigiani, G., et al. (2013). curatedovariandata: clinically annotated data for the ovarian cancer transcriptome. Database , 2013

    2013

  18. [26]

    Garrett-Mayer, E., Parmigiani, G., Zhong, X., Cope, L., and Gabrielson, E. (2008). Cross-study validation and combined analysis of gene expression microarray data. Biostatistics , 9(2):333--354

    2008

  19. [27]

    Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by browne and draper)

    2006

  20. [28]

    B., Stern, H

    Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1995). Bayesian data analysis . Chapman and Hall/CRC

    1995

  21. [29]

    George, E. I. and McCulloch, R. E. (1993). Variable selection via gibbs sampling. Journal of the American Statistical Association , 88(423):881--889

    1993

  22. [30]

    and Dunson, D

    Ghosh, J. and Dunson, D. B. (2009). Default prior distributions and efficient posterior computation in bayesian factor analysis. Journal of Computational and Graphical Statistics , 18(2):306--320

    2009

  23. [31]

    Giussani, M., Landoni, E., Merlino, G., Turdo, F., Veneroni, S., Paolini, B., Cappelletti, V., Miceli, R., Orlandi, R., Triulzi, T., et al. (2018). Extracellular matrix proteins as diagnostic markers of breast carcinoma. Journal of cellular physiology , 233(8):6280--6290

    2018

  24. [32]

    N., De Vito, R., Trippa, L., and Parmigiani, G

    Grabski, I. N., De Vito, R., Trippa, L., and Parmigiani, G. (2023a). Bayesian combinatorial multistudy factor analysis. The annals of applied statistics , 17(3):2212

    2023

  25. [33]

    N., Vito, R

    Grabski, I. N., Vito, R. D., Trippa, L., and Parmigiani, G. (2023b). Bayesian Combinatorial Multi - Study Factor Analysis . The annals of applied statistics . (in press)

    2023

  26. [34]

    Griffiths, T. L. and Ghahramani, Z. (2011). The indian buffet process: An introduction and review. Journal of Machine Learning Research , 12(4)

    2011

  27. [35]

    Hansen, B., Avalos-Pacheco, A., Russo, M., and De Vito, R. (2024). Fast variational inference for bayesian factor analysis in single and multi-study settings. Journal of Computational and Graphical Statistics , 34(1):1--42

    2024

  28. [36]

    Horn, R. A. and Johnson, C. R. (2012). Matrix analysis . Cambridge university press

    2012

  29. [37]

    Hu, T., Chitnis, N., Monos, D., and Dinh, A. (2021). Next-generation sequencing technologies: An overview. Human immunology , 82(11):801--811

    2021

  30. [38]

    Hu, Y. (2005). Efficient, high-quality force-directed graph drawing. Mathematica journal , 10(1):37--71

    2005

  31. [39]

    G., Næs, T., and Liland, K

    Indahl, U. G., Næs, T., and Liland, K. H. (2018). A similarity index for comparing coupled matrices. Journal of Chemometrics , e3049

    2018

  32. [40]

    Johnson, V. E. and Rossell, D. (2010). On the use of non-local prior densities in bayesian hypothesis tests. Journal of the Royal Statistical Society Series B: Statistical Methodology , 72(2):143--170

    2010

  33. [41]

    Johnson, V. E. and Rossell, D. (2012). Bayesian model selection in high-dimensional settings. Journal of the American Statistical Association , 107(498):649--660

    2012

  34. [42]

    Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika , 23(3):187--200

    1958

  35. [43]

    and Ghahramani, Z

    Knowles, D. and Ghahramani, Z. (2007). Infinite sparse factor analysis and infinite independent components analysis. In International conference on independent component analysis and signal separation , pages 381--388. Springer

    2007

  36. [44]

    M., Kalsbeek, W

    LaVange, L. M., Kalsbeek, W. D., Sorlie, P. D., Avil \'e s-Santa, L. M., Kaplan, R. C., Barnhart, J., Liu, K., Giachello, A., Lee, D. J., Ryan, J., et al. (2010). Sample design and cohort selection in the hispanic community health study/study of latinos. Annals of epidemiology...

    2010

  37. [45]

    and Song, X.-Y

    Lee, S.-Y. and Song, X.-Y. (2002). Bayesian selection on the number of factors in a factor analysis model. Behaviormetrika , 29(1):23--39

    2002

  38. [46]

    T., Scharpf, R

    Leek, J. T., Scharpf, R. B., Bravo, H. C., Simcha, D., Langmead, B., Johnson, W. E., Geman, D., Baggerly, K., and Irizarry, R. A. (2010). Tackling the widespread and critical impact of batch effects in high-throughput data. Nature Reviews Genetics , 11(10):733--739

    2010

  39. [47]

    Legramanti, S., Durante, D., and Dunson, D. B. (2020). Bayesian cumulative shrinkage for infinite factorizations. Biometrika , 107(3):745--752

    2020

  40. [48]

    Lopes, H. F. and West, M. (2004). Bayesian model assessment in factor analysis. Statistica Sinica , pages 41--67

    2004

  41. [49]

    M., and Werb, Z

    Lu, P., Weaver, V. M., and Werb, Z. (2012). The extracellular matrix: a dynamic niche in cancer progression. Journal of cell biology , 196(4):395--406

    2012

  42. [50]

    Mardis, E. R. (2013). Next-generation sequencing platforms. Annual review of analytical chemistry , 6(1):287--303

    2013

  43. [51]

    D., D \'e jean, S., and Salse, J

    Mardoc, E., Sow, M. D., D \'e jean, S., and Salse, J. (2024). Genomic data integration tutorial, a plant case study. BMC genomics , 25(1):66

    2024

  44. [52]

    Neal, R. M. (2012). Mcmc using hamiltonian dynamics. arXiv preprint arXiv:1206.1901

    2012 arXiv

  45. [53]

    Owen, A. B. and Wang, J. (2016). Bi-cross-validation for factor analysis

    2016

  46. [54]

    and Ntzoufras, I

    Papastamoulis, P. and Ntzoufras, I. (2022). On the identifiability of bayesian factor analytic models. Statistics and Computing , 32(2):23

    2022

  47. [55]

    S., and Dunson, D

    Pati, D., Bhattacharya, A., Pillai, N. S., and Dunson, D. (2014). Posterior contraction in sparse bayesian factor models for massive covariance matrices

    2014

  48. [56]

    Poworoznek, E., Anceschi, N., Ferrari, F., and Dunson, D. (2021). Efficiently resolving rotational ambiguity in bayesian matrix sampling with matching. arXiv preprint arXiv:2107.13783

    2021 arXiv

  49. [57]

    and Escoufier, Y

    Robert, P. and Escoufier, Y. (1976). A unifying tool for linear multivariate statistical methods: the rv-coefficient. Journal of the Royal Statistical Society Series C: Applied Statistics , 25(3):257--265

    1976

  50. [58]

    and George, E

    Ro c kov \'a , V. and George, E. I. (2016). Fast bayesian factor analysis via automatic rotations to sparsity. Journal of the American Statistical Association , 111(516):1608--1622

    2016

  51. [59]

    S., and Dunson, D

    Roy, A., Borg, J. S., and Dunson, D. B. (2021a). Bayesian time-aligned factor analysis of paired multivariate time series. Journal of Machine Learning Research , 22(250):1--27

    2021

  52. [60]

    H., and Dunson, D

    Roy, A., Lavine, I., Herring, A. H., and Dunson, D. B. (2021b). Perturbed factor analysis: Accounting for group differences in exposure profiles. The annals of applied statistics , 15(3):1386--1404

    2021

  53. [61]

    Schiavon, L., Canale, A., and Dunson, D. B. (2022). Generalized infinite factorization models. Biometrika , 109(3):817--835

    2022

  54. [62]

    T., Sweeney, E

    Shinohara, R. T., Sweeney, E. M., Goldsmith, J., Shiee, N., Mateen, F. J., Calabresi, P. A., Jarso, S., Pham, D. L., Reich, D. S., Crainiceanu, C. M., et al. (2014). Statistical normalization techniques for magnetic resonance imaging. NeuroImage: Clinical , 6:9--19

    2014

  55. [63]

    P., Gautier, B., Rohart, F., Vacher, M., Tebbutt, S

    Singh, A., Shannon, C. P., Gautier, B., Rohart, F., Vacher, M., Tebbutt, S. J., and L \^e Cao, K.-A. (2019). Diablo: an integrative approach for identifying key molecular drivers from multi-omics assays. Bioinformatics , 35(17):3055--3062

    2019

  56. [64]

    J., and Gevaert, O

    Steyaert, S., Pizurica, M., Nagaraj, D., Khandelwal, P., Hernandez-Boussard, T., Gentles, A. J., and Gevaert, O. (2023). Multimodal data fusion for cancer biomarker discovery with deep learning. Nature machine intelligence , 5(4):351--362

    2023

  57. [65]

    Sun, Q., Zhao, H., Zhang, C., Hu, T., Wu, J., Lin, X., Luo, D., Wang, C., Meng, L., Xi, L., et al. (2017). Gene co-expression network reveals shared modules predictive of stage and grade in serous ovarian cancers. Oncotarget , 8(26):42983

    2017

  58. [66]

    D., Soni, S., McSkane, M., Baba, H., and Lenz, H.-J

    Tokunaga, R., Zhang, W., Naseem, M., Puccini, A., Berger, M. D., Soni, S., McSkane, M., Baba, H., and Lenz, H.-J. (2018). Cxcl9, cxcl10, cxcl11/cxcr3 axis for immune activation--a target for novel cancer therapy. Cancer treatment reviews , 63:40--47

    2018

  59. [67]

    Wang, J., Li, D., Cang, H., and Guo, B. (2019). Crosstalk between cancer and immune cells: Role of tumor-associated macrophages in the tumor microenvironment. Cancer medicine , 8(10):4709--4721

    2019

  60. [68]

    V., Verhaak, R

    Wang, X. V., Verhaak, R. G., Purdom, E., Spellman, P. T., and Speed, T. P. (2011). Unifying gene expression measures from multiple platforms using factor analysis. PloS one , 6(3):e17691

    2011

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.