The four pillars of open science

An open review of Gorgolewski & Poldrack (PP2016)

the 4 pillars of open science.png

The four pillars of open science are open data, open code, open papers (open access), and open reviews (open evaluation). A practical guide to the first three of these is provided by Gorgolewski & Poldrack (PP2016). In this open review, I suggest a major revision in which the authors add treatment of the essential fourth pillar: open review. Image: The Porch of the Caryatids (Porch of the Maidens) of the ancient Greek temple Erechtheion on the north side of the Acropolis of Athens.


Open science is a major buzz word. Is all the talk about it just hype? Or is there a substantial vision that has a chance of becoming a reality? Many of us feel that science can be made more efficient, more reliable, and more creative through a more open flow of information within the scientific community and beyond. The internet provides the technological basis for implementing open science. However, making real progress with this positive vision requires us to reinvent much of our culture and technology. We should not expect this to be easy or quick. It might take a decade or two. However, the arguments for openness are compelling and open science will prevail eventually.

The major barriers to progress are not technological, but psychological, cultural, and political: individual habits, institutional inertia, unhealthy incentives, and vested interests. The biggest challenge is the fact that the present way of doing science does work (albeit suboptimally) and our vision for open science has not merely not yet been implemented, but has yet to be fully conceived. We will need to find ways to gradually evolve our individual workflows and our scientific culture.

Gorgolewski & Poldrack (PP2016) offer a brief practical guide to open science for researchers in brain imaging. I was expecting a commentary reiterating the arguments for open science most of us have heard before. However, the paper instead makes good on its promise to provide a practical guide for brain imaging and it contains many pointers that I will share with my lab and likely refer to in the future.

The paper discusses open data, open code, and open publications – describing tools and standards that can help make science more transparent and efficient. My main criticism is that it leaves out what I think of as a fourth essential pillar of open science: open peer review. Below I first summarise some of the main points and pointers to resources that I took from the paper. Along the way, I add some further points overlooked in the paper that I feel deserve consideration. In the final section, I address the fourth pillar: open review. In the spirit of a practical guide, I suggest what each of us can easily do now to help open up the review process.


1 Open data

  • Open-data papers more cited, more correct: If data for a paper are published, the community can reanalyse the data to confirm results and to address additional questions. Papers with open data are cited more (Piwowar et al. 2007, Piwowar & Vision 2013) and tend to make more correct use of statistics (Wicherts et al. 2011).
  • Participant consent: Deidentified data can be freely shared without consent from the participants in the US. However, rules differ in other countries. Ideally, participants should consent to their data being shared. Template text for consent forms is offered by the authors.
  • Data description: The Brain Imaging Data Structure (BIDS) (Gorgolewski et al. 2015) provides a standard (evolved from the authors’ OpenfMRI project; Poldrack et al. 2013) for file naming and folder organisation, using file formats such as NifTI, TSV and JSON.
  • Field-specific brain-imaging data repositories: Two repositories accept brain imaging data from any researcher: FCP/INDI (for resting state fMRI only) and OpenfMRI (for any datasets that includes MRI data).
  • Field-general repositories: Field-specific repositories like those mentioned help standardise sharing for particular types of data. If the formats offered are not appropriate for the data to be shared, field-general repositories, including FigShare, Dryad, or DataVerse can be used.
  • Data papers: A data paper is a paper that focusses on the description of a particular data set that is publicly accessible. This helps create incentives for ambitious data acquisitions and to enable researchers to specialise in data acquisition. Journals publishing data papers include: Scientific Data, Gigascience, Data in Brief, F1000Research, Neuroinformatics, and Frontiers in Neuroscience.
  • Processed-data sharing: It can be useful to share intermediate or final results of data analysis. With the initial (and often somewhat more standardised) steps of data processing out of the way, processed data are often much smaller in volume and more immediately amenable to further analyses by others. Statistical brain-imaging maps can be shared via the authors’ website.


2 Open code

  • Code sharing for transparency and reuse: Data-analysis details are complex in brain imaging, often specific to a particular study, and seldom fully defined in the methods section. Sharing code is the only realistic way of fully defining how the data have been analysed and enabling others to check the correctness of the code and effects of adjustments. In addition, the code can be used as a starting point for the development of further analyses.
  • Your code is good enough to share: A barrier to sharing is the perception among authors that their code might not be good enough. It might be incompletely documented, suboptimal, or even contain errors. Until the field finds ways to incentivise greater investment in code development and documentation for sharing, it is important to lower the barriers to sharing. Sharing imperfect code is preferable to not sharing code (Barnes 2010).
  • Sharing does not imply provision of user support: Sharing one’s code does not imply that one will be available to provide support to users. Websites like org can help users ask and answer questions independently (or with only occasional involvement) of the authors.
  • Version Control System (VCS) essential to code sharing: VCS software enables maintenance of complex code bases with multiple programmers and versions, including the ability to merge independent developments, revert to previous versions when a change causes errors, and to share code among collaborators or publicly. An excellent, freely accessible, widely used, web-based VCS platform is com, introduced in Blischak et al. (2016).
  • Literate programming combines code and results and text narrative: Scripted automatic analyses have the advantage of automaticity and reproducibility (Cusack et al. 2014), compared to point-and-click analysis in an application with a graphical user interface. However, the latter enables more interactive interrogation of the data. Literate programming (Knuth 1992) attempts to make coding more interactive and provides a full and integrated record of the code, results, and text explanations. This provides a fully computationally transparent presentation of results, makes the code accessible to oneself later in time, and to collaborators and third parties, with whom literate programs can be shared (e.g. via GitHub). Software supporting this includes: Jupyter (for R, Python and Julia), R Markdown (for R) and matlabweb (for MATLAB).


3 Open papers

  • Open notebook science: Open science is about enhancing the bandwidth and reducing the latency in our communication network. This means sharing more and at earlier stages, not only our data and code, but ultimately also our day-to-day incremental progress. This is called open notebook science and has been explored, by Cameron Neylon and Michael Nielson among others. Gorgolewski & Poldrack don’t comment on this beautiful vision for an entirely different workflow and culture at all. Perhaps open notebook science is too far in the future? However, some are already practicing it. Surely, we should start exploring it in theory and considering what aspects of open notebook science we can integrate into our workflow. It would be great to have some pointers to practices and tools that help us move in this direction.
  • The scientific paper remains a critical component of scientific communication: Data and code sharing are essential, but will not replace communication through permanently citable scientific papers that link (increasingly accessible) data through analyses to novel insights and relate these insights to the literature.
  • Papers should simultaneously achieve clarity and transparency: The conceptual clarity of the argument leading to an insight is often at a tension with the transparency of all the methodological details. Ideally, a paper will achieve both clarity and transparency, providing multiple levels of description: a main narrative that abstracts from the details, more detailed descriptions in the methods section, additional detail in the supplementary information, and full detail in the links to the open data and code, which together enable exact reproduction of the results in the figures. This is an ideal to aspire to. I wonder if any paper in our field has fully achieved it. If there is one, it should surely be cited.
  • Open access: Papers need to be openly accessible, so their insights can have the greatest positive impact on science and society. This is really a no brainer. The internet has greatly lowered the cost of publication, but the publishing industry has found ways to charge higher prices through a combination of paywalls and unreasonable open-access charges. I would add that every journal contains unique content, so the publishing industry runs hundreds of thousands of little monopolies – safe from competition. Many funding bodies require that studies they funded be published with open access. We need political initiatives that simply require all publicly funded research to be publicly accessible. In addition, we need publicly funded publication platforms that provide cost-effective alternatives to private publishing companies for editorial boards that run journals. Many journals are currently run by scientists whose salaries are funded by academic institutions and the public, but whose editorial work contributes to the profits of private publishers. In historical retrospect, future generations will marvel at the genius of an industry that managed for decades to employ a community without payment, take the fruits of their labour, and sell them back to that very community at exorbitant prices – or perhaps they will just note the idiocy of that community for playing along with this racket.
  • Preprint servers provide open access for free: Preprint servers like bioRxiv and arXiv host papers before and after peer review. Publishing each paper on a preprint server ensures immediate and permanent open access.
  • Preprints have digital object identifiers (DOIs) and are citable: Unlike blog posts and other more fleeting forms of publication, preprints can thus be cited with assurance of permanent accessibility. In my lab, we cite preprints we believe to be of high quality even before peer review.
  • Preprint posting enables community feedback and can help establish precedence: If a paper is accessible before it is finalised the community can respond to it and help catch errors and improve the final version. In addition, it can help the authors establish the precedence of their work. I would add that this potential advantage will be weighed against the risk of getting scooped by a competitor who benefits from the preprint and is first to publish a peer-reviewed journal version. Incentives are shifting and will encourage earlier and earlier posting. In my lab, we typically post at the time of initial submission. At this point getting scooped is unlikely, and the benefits of getting earlier feedback, catching errors, and bringing the work to the attention of the community outweighs any risks of early posting.
  • Almost all journals support the posting of preprints: Although this is not widely known in the brain imaging and neuroscience communities, almost all major journals (including Nature, Science, Nature Neuroscience and most others) have preprint policies supportive of posting preprints. Gorgolewski & Poldrack note that they “are not aware of any neuroscience journals that do not allow authors to deposit preprints before submission, although some journals such as Neuron and Current Biology consider each submission independently and thus one should contact the editor prior to submission.” I would add that this reflects the fact that preprints are also advantageous to journals: They help catch errors and get the reception process and citation of the paper going earlier, boosting citations in the two-year window that matters for a journal’s impact factor.


4 Open reviews

The fourth pillar of open science is the open evaluation (OE, i.e. open peer review and rating) of scientific papers. This pillar is entirely overlooked in the present version of the Gorgolewski & Poldrack’s commentary. However, peer review is an essential component of communication in science. Peer review is the process by which we prioritise the literature, guiding each field’s attention, and steering scientific progress. Like other components of science, peer review is currently compromised by a lack of transparency, by inefficiency of information flow, and by unhealthy incentives. The movement for opening the peer review process is growing.

In traditional peer review, we judge anonymously, making inherently subjective decisions that decide about the publication of our competitors’ work, under a cloak of secrecy and without ever having to answer for our judgments. It is easy to see that this does not provide ideal incentives for objectivity and constructive criticism. We’ve inherited secret peer review from the pre-internet age (when perhaps it made sense). Now we need to overcome this dysfunctional system. However, we’ve grown used to it and may be somewhat comfortable with it.

Transparent review means (1) that reviews are public communications and (2) that many of them are signed by their authors. Anonymous reviewing must remain an option, to enable scientists to avoid social consequences of negative judgments in certain scenarios. However, if our judgment is sound and constructively communicated, we should be able to stand by it. Just like in other domains, transparency is the antidote to corruption. Self-serving arguments won’t fly in open reviewing, and even less so when the review is signed. Signing adds weight to a review. The reviewer’s reputation is on the line, creating a strong incentive to be objective, to avoid any impression of self-serving judgment, and to attempt to be on the right side of history in one’s judgment of another scientist’s work. Signing also enables the reviewer to take credit for the hard work of reviewing.

The arguments for OE and a synopsis of 18 visions for how OE might be implemented are given in Kriegeskorte, Walther & Deca (2012). As for other components of open science, the primary obstacles to more open practices are not technological, but psychological, cultural, and political. Important journals like eLife and those of the PLoS family are experimenting with steps toward opening the review process. New journals including, the Winnower, ScienceOpen, and F1000 Research already rely on postpublication peer review.

We don’t have to wait for journals to lead us. We have all the tools to reinvent the culture of peer review. The question is whether we can handle the challenges this poses. Here, in the spirit of Gorgolewki & Poldrack’s practical guide, are some ways that we can make progress toward OE now by doing things a little differently.

  • Sign peer reviews you author: Signing our reviews is a major step out of the dark ages of peer review. It’s easier said than done. How can we be as critical as we sometimes have to be and stand by our judgment? We can focus first on the strengths of a paper, then communicate all our critical arguments in a constructive manner. Some people feel that we must sign either all or none of our reviews. I think that position is unwise. It discourages beginning to sign and thus de facto cements the status quo. In addition, there are cases where the option to remain anonymous is needed, and as long as this option exists we cannot enforce signing anyway. What we can do is take anonymous comments with a grain of salt and give greater credence to signed reviews. It is better to sign sometimes than never. When I started to sign my reviews, I initially reserved the right to anonymity for myself. After all this was a unilateral act of openness; most of my peers do not sign their reviews. However, after a while, I decided to sign all of my reviews, including negative ones.
  • Openly review papers that have preprints: When we read important papers as preprints, let’s consider reviewing them openly. This can simultaneously serve our own and our collective thought process: an open notebook distilling the meaning of a paper, why its claims might or might not be reliable, how it relates to the literature, and what future steps it suggests. I use a blog. Alternatively or additionally, we can use PubMed Commons or PubPeer.
  • Make the reviews you write for journals open: When we are invited to do a review, we can check if the paper has been posted as a preprint. If not, we can contact the authors, asking them to consider posting. At the time of initial submission, the benefits tend to outweigh the risks of posting, so many authors will be open to this. Preprint posting is essential to open review. If a preprint is available, we can openly review it immediately and make the same review available to the journal to contribute to their decision process.
  • Reinvent peer review: What is an open review? For example, what is this thing you’re reading? A blog post? A peer review? Open notes on the essential points I would like to remember from the paper with my own ideas interwoven? All of the above. Ideally, an open review helps the reviewer, the authors, and the community think – by explaining the meaning of a paper in the context of the literature, judging the reliability of its claims, and suggesting future improvements. As we begin to review openly, we are reinventing peer review and the evaluation of scientific papers.
  • Invent peer rating: Eventually we will need quantitative measures evaluating papers. These should not be based on buzz and usage statistics, but reflect the careful judgement of peers who are experts in the field, have considered the paper in detail, and ideally stand by their judgment. Quantitative judgments can be captured in ratings. Multidimensional peer ratings can be used to build a plurality of paper evaluation functions (Kriegeskorte 2012) that prioritise the literature from different perspectives. We need to invent suitable rating systems. For primary research papers, I use single-digit ratings on multiple scales including reliability, importance, and novelty, using capital letters to indicate the scale in the following format: [R7I5].


Errors are normal

As we open our science and share more of it with the community, we run the risk of revealing more of our errors. From an idealistic perspective that’s a good thing, enabling us learn more efficiently as individuals and as a community. However, in the current game of high-impact biomedical science there is an implicit pretense that major errors are unlikely. This is the reason why, in the rare case that a major error is revealed despite our lack of transparent practices, the current culture requires that everyone act surprised and the author be humiliated. Open science will teach us to drop these pretenses. We need to learn to own our mistakes (Marder 2015) and to be protective of others when errors are revealed. Opening science is an exciting creative challenge at many levels. It’s about reinventing our culture to optimise our collective cognitive process. What could be more important or glamorous?


Additional suggestions for improvements in revision

  • A major relevant development regarding open science in the brain imaging community is the OHBM’s Committee on Best Practices in Data Analysis and Sharing (COBIDAS), of which author Russ Poldrack and I are members. COBIDAS is attempting to define recommended practices for the neuroimaging community and has begun a broad dialogue with the community of researchers (see weblink above). It would be good to explain how COBIDAS fits in with the other developments.
  • About a third of the cited papers are by the authors. This illustrates their substantial contribution and expertise in this field. I found all these papers worthy of citation in this context. However, I wonder if other groups that have made important contributions to this field should be more broadly cited. I haven’t followed this literature closely enough to give specific suggestions, but perhaps it’s worth considering whether references should be added to important work by others.
  • As for the papers, the authors are directly involved in most of the cited web resources OpenfMRI, NeuroVault, This is absolutely wonderful, and it might just be that there is not much else out there. Perhaps readers of this open review can leave pointers in the comments in case they are aware of other relevant resources. I would share these with the authors, so they can consider whether to include them in revision.
  • Can the practical pointers be distilled into a table or figure that summarises the essentials? This would be a useful thing to print out and post next to our screens.
  • “more than fair” -> “only fair”



I have the following relationships with the authors.

relationship number of authors
acquainted 2
collaborated on committee 1
collaborated on scientific project 0



Barnes N (2010) Publish your computer code: it is good enough. Nature. 467: 753. doi: 10.1038/467753a

Blischak JD, Davenport ER, Wilson G. (2016) A Quick Introduction to Version Control with Git and GitHub. PLoS Comput Biol. 12: e1004668. doi: 10.1371/journal.pcbi.1004668

Cusack R, Vicente-Grabovetsky A, Mitchell DJ, Wild CJ, Auer T, Linke AC, et al. (2014) Automatic analysis (aa): efficient neuroimaging workflows and parallel processing using Matlab and XML. Front Neuroinform. 2014;8: 90. doi: 10.3389/fninf.2014.00090

Gorgolewski KJ, Auer T, Calhoun VD, Cameron Craddock R, Das S, Duff EP, et al. (2015) The Brain Imaging Data Structure: a standard for organizing and describing outputs of neuroimaging experiments [Internet]. bioRxiv. 2015. p. 034561. doi: 10.1101/034561

Gorgolewski KJ, Varoquaux G, Rivera G, Schwarz Y, Ghosh SS, Maumet C, et al. (2015) a webbased repository for collecting and sharing unthresholded statistical maps of the human brain. Front Neuroinform. Frontiers. 9. doi: 10.3389/fninf.2015.00008

Knuth DE (1992) Literate programming. CSLI Lecture Notes, Stanford, CA: Center for the Study of Language and Information (CSLI).

Kriegeskorte N, Walther A, Deca D (2012) An emerging consensus for open evaluation: 18 visions for the future of scientific publishing Front. Comput. Neurosci

Kriegeskorte N (2012) Open evaluation: a vision for entirely transparent post-publication peer review and rating for science. Front. Comput. Neurosci., 17

Marder E (2015) Living Science: Owning your mistakes DOI: eLife 2015;4:e11628

Piwowar HA, Day RS, Fridsma DB (2007) Sharing detailed research data is associated with increased citation rate. PLoS One. 2007;2: e308. doi: 10.1371/journal.pone.0000308

Piwowar HA, Vision TJ (2013) Data reuse and the open data citation advantage. PeerJ. 1: e175. doi: 10.7717/peerj.175

Poldrack RA, Barch DM, Mitchell JP, Wager TD, Wagner AD, Devlin JT, et al. (2013) Toward open sharing of taskbased fMRI data: the OpenfMRI project. Front Neuroinform. 2013;7: 1–12. doi: 10.3389/fninf.2013.00012

Wicherts JM, Bakker M, Molenaar D (2011) Willingness to Share Research Data Is Related to the Strength of the Evidence and the Quality of Reporting of Statistical Results. Tractenberg RE, editor. PLoS One. 6: e26828. doi: 10.1371/journal.pone.0026828









Pattern-component modelling disentangles the code and the noise in representational similarity analysis


This paper proposes an interesting and potentially important extension to representational similarity analysis (RSA), which promises unbiased estimates of response-pattern similarities and more compelling comparisons of representations between different brain regions.

RSA consists in the analysis of the similarity structure of the representations of different stimuli (or mental states associated with different tasks) in a region of interest (ROI). To this end, the similarity of regional response patterns elicited by the different stimuli is estimated, typically by using their linear correlation coefficient across voxels (or neurons or recording sites in electrophysiology). It is often desirable to be able to compare these pattern similarities between different regions. For example, we would like to be able to address whether stimuli A and B elicit more highly correlated response patterns in region 1 or region 2. However, such comparisons are problematic, because the pattern correlations depend on fMRI noise (which might be different between the regions), voxel selection (e.g. selecting additional noisy voxels will reduce the pattern correlation), and unspecific pattern components (e.g. a strong shared component between all stimuli will increase the pattern correlation, with the high correlation not specific to the particular pair of stimuli).

Pattern-component modelling yields estimates of the similarity of representational patterns that are not systematically distorted by noise and common components. Representational pattern similarity is measured here by the correlation across measurement channels (e.g. fMRI voxels) and is plotted as a function of the noise level (horizontal axes) for different amplitudes (shades of gray) of a common pattern component shared by both representational patterns. Figure from Diedrichsen et al. (2011).

When representational dissimilarities (or, equivalently similarities) are estimated from estimates of response patterns in a multidimensional space, the dissimilarity estimates are positively (or the similarity estimates negatively) biased. This is because the inevitable noise affecting the pattern estimates will typically increase the apparent distance between any two patterns (the probability of a decrease of the distance due to noise is 0.5 in 1 dimension and drops rapidly as dimensionality increases).

Instead of estimating the distances from pattern estimates, the authors therefore propose to estimate the distances from a covariance component model that captures the pattern variances and covariances across space. The approach requires that each stimulus (or, more generally, each experimental condition) has been repeated multiple times to yield multiple pattern estimates. Whereas simple RSA would consider the average pattern for each stimulus, the authors’ approach models the original trial-by-voxel matrix Y as a linear combination of a set of stimulus-related patterns U (thought to underlie the observed patterns) and  noise, and estimates the covariance structure of the patterns. The noise E is assumed to be independent between trials, but there is no assumption of independence of the noise between voxels. This is important because fMRI error time series from voxels closeby within a region are known to be correlated.

This is an original and potentially important contribution. The core mathematical model appears well developed. The demonstration of the advantages of the method is compellingly demonstrated based on simulated data. The paper is well written. However, it requires a number of improvements to ensure that it successfully communicates its important message. (1) The authors should more clearly explain the assumptions their pattern-covariance modelling approach relies upon. (2) The authors should add a section explaining the practical application of the approach (3) A number of clarifications and didactical improvements, notably to the presentation of the analysis of the real fMRI data, would be desirable. These three major points are explained in detail below.

[This is my original secret peer review of Diedrichsen et al. (2011). Most of the suggestions for improvements were addressed in revision and are no longer relevant.]


(1) Assumptions and consequences of violations

The advantages of pattern-covariance modeling are well explained. However, the assumptions of this approach should be more clearly communicated, perhaps in a separate section.

  • Does the validity of the approach depend on assumptions about the probability densities of the response amplitudes? Are there any other assumptions about the nature of the response patterns?
  • What are the effects of violations of the assumptions? Please give examples of cases where the assumptions are violated and describe the expected effects on the analysis.
  • As long as statistical inference is performed at the level of the variability across subjects or by using randomisation testing, results might be robust to certain violations. Please clarify if and when this is the case.


(2) Practical application of the new approach

Please add a section explaining how to apply this method to fMRI data, addressing the following questions:

  • Do the authors plan to make matlab code available for the new method? If so, it would be good to state this in the paper.
  • Is there a function that takes the regional data matrix Y, the design matrix Z (including effects of no interest) and perhaps a predictor selection vector for selecting effects of interest as input and returns the corrected correlation (and perhaps Euclidean) distance matrix?
  • Does the method only work with slow event-related designs (with approximately independent trial estimates)?
  • Can we use the method on rapid-event-related designs where we do not have separate single-trial estimates (because single-trial responses overlap in time and multiple trials of the same condition must be estimated together for stability)?
  • What if we have only one pattern estimate per condition, because our design is condition-rich (e.g. 96 conditions as in Kriegeskorte et al. 2008) and rapid-event related?
  • More generally, what are the requirements and limitations of the proposed approach?


(3) Particular clarifications and didactical improvements

In classical multivariate regression, we get an estimate of the error of a spatial response pattern estimate as a multinormal (characterised by a scaled version of the voxel-by-voxel covariance matrix of the residuals, where the scaling factor reflects the amount of averaging for the case of binary nonoverlapping predictors, and, more generally, the sums of squares and products of the design matrix). Couldn’t this multinormal model of the variability of each condition-related pattern estimate be used to get an unbiased estimate of the correlation of each pair of pattern estimates? If so, would this approach be inferior or superior to the proposed method, and why?

  1. 7: What exactly are the ‘simplifying assumptions’ that allow a to be estimated independently of G by averaging the trial response patterns within conditions?

“The corrected estimate from the covariance-component model is unbiased over a large range of parameter settings.” What are the limits of this range? Is the estimate formally unbiased or just approximately so?

Can question a) “Does the region encode information about the finger in the movement and/or stimulation condition?” be addressed with the traditional and the proposed RSA method? It seems that that would necessitate estimating the replicability of patterns elicited by moving the same finger (and similarly for sensation). It is a typical and important neuroscientific question, so please consider addressing in the framework of RSA (not just in terms of a possible classifier analysis as in the current draft).

Across different runs, pattern correlations are usually found to be much lower (e.g. Misaki et al. 2010). This phenomenon requires further investigation. The authors suggest error correlations among trials closeby in time within a run as the cause. However, I suspect that such error correlations, though clearly present, might not be the major cause of this. Other causes include scanner drifts and greater head-motion-related disalignment (due to greater separation in time), which can cause distortions, that head-motion-correction cannot undo. It would be good to hear the authors’ assessment of these alternative causes.

The notation u_beta[c,1,…4], where c is an element of {1,2} is confusing to me. Shouldn’t it be u_beta[c,d], where c is an element of {1,2}, and d is an element of {1,2,3,4}?

Eq. 8 requires more unpacking. Perhaps a figure with the vertical and horizontal dimensions marked (“task effects: movement vs sensation”, “individual finger effects: (1) movement, (2) sensation”) and arrows pointing from conceptual labels (“shared pattern between all movement trials”, “shared pattern between all sensation trials”, etc.) to the variance components could serve this function.

Figures 1-4 are great.

Figures 6 and 7: This comparison between traditional RSA and the proposed method is not completely successful. Figure 6 the traditional approach is very comprehensible. Figure 7 is cryptic (partly due to lack of meaningful labeling of the vertical axes). Moreover, the relationship between the traditional and the proposed approach to RSA remains unclear (or anyway difficult to grasp at a glance). I suggest adding a figure that compares traditional RSA and the proposed method side by side. The top row should show the correlation matrices (sample correlation versus unbiased estimates from covariance component model). The next three rows should address the three questions raised in the text: “a) Does the region encode information about the finger in the movement and/or stimulation condition? b) Are the patterns evoked by movement of a given finger similar to the patterns evoked by stimulation of the same finger? c) Is this similarity greater in one region than another?” Results from the traditional and the proposed RSA should be shown for each question to demonstrate how the results appear in both approaches and where the traditional approach falls short.




In Eq. 8, u_beta[1,2] should read u_beta[1,1], I think.

“The decomposition method offers an elegant way to control for all these possible influences on the size of the correlation coefficients. In addition to noise (ε), condition ( , ), and finger ( , ) effects (Eq. 7), we also added a run effect.” Should say Eq. 8, I think.

Does U stand for ‘(u)nderlying patters’ and a for spatial-average (a)ctivation? It would help to make this explicit.

Figure 6 : Please label the vertical axes (intuitive and clear conceptual label). Please mark all significant effects. Please add a colorbar (grayscale code for correlation). Legend: “(D) These correlations” Which correlations exactly? (Averaged across sense and move now?)

Figure 7: The vertical axes need to be intuitively labeled. The reader should not have to decode mathematical symbols from the legend to understand the meaning of the bar graphs. Even after a careful read of the legend (and after spending quite a bit of time on the paper), the neuroscientific findings are not easy to grasp here. As a result, the present version of this figure will leave readers preferring traditional RSA (Figure 6) as it at least can be interpreted without much effort. Please label gray and white (“sense” and “move”) bars as in Figure 6.