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Network Cross-Validation for Determining the Number of Communities in Network Data
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 241-251 |
| Abstrak | : | The stochastic block model (SBM) and its variants have been a popular tool for analyzing large network data with community structures. In this article, we develop an efficient network cross-validation (NCV) approach to determine the number of communities, as well as to choose between the regular stochastic block model and the degree corrected block model (DCBM). The proposed NCV method is based on a block-wise node-pair splitting technique, combined with an integrated step of community recovery using sub-blocks of the adjacency matrix. We prove that the probability of under-selection vanishes as the number of nodes increases, under mild conditions satisfied by a wide range of popular community recovery algorithms. The solid performance of our method is also demonstrated in extensive simulations and two data examples. Supplementary materials for this article are available online. |
A Qualitative Metasynthesis of Teaching Mathematics for Social Justice in Action: Pitfalls and Promises of Practice
| Pengarang | : | Frances K. Harper |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 3) |
| Halaman | : | 268-310 |
| Abstrak | : | Mathematics classrooms are increasingly becoming sites for investigating social (in)justice, but research on teaching mathematics for social justice remains limited to individual case studies. This article reports on a metasynthesis of 35 qualitative reports of social justice mathematics enactments in diverse classroom contexts. Critical race theory serves as a guiding framework for analyzing possibilities and limitations of these enactments to address racial inequities in mathematics education. Findings from this metasynthesis reveal that addressing race in social justice mathematics explorations provided opportunities for centering the voices of people of Color and critiquing liberal views that camouflage subtle forms of racism and involved substantial and authentic mathematical work. Promising practices and implications for future research are identified based on this synthesis. |
Exact p-Values for Network Interference
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 230-240 |
| Abstrak | : | We study the calculation of exact p-values for a large class of nonsharp null hypotheses about treatment effects in a setting with data from experiments involving members of a single connected network. The class includes null hypotheses that limit the effect of one unit’s treatment status on another according to the distance between units, for example, the hypothesis might specify that the treatment status of immediate neighbors has no effect, or that units more than two edges away have no effect. We also consider hypotheses concerning the validity of sparsification of a network (e.g., based on the strength of ties) and hypotheses restricting heterogeneity in peer effects (so that, e.g., only the number or fraction treated among neighboring units matters). Our general approach is to define an artificial experiment, such that the null hypothesis that was not sharp for the original experiment is sharp for the artificial experiment, and such that the randomization analysis for the artificial experiment is validated by the design of the original experiment. |
Two Undergraduate Students Reinvention of the Multiplication Principle
| Pengarang | : | Elise Lockwood and Branwen Purdy |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 3) |
| Halaman | : | 225-267 |
| Abstrak | : | The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration, serving as an effective tool for solving counting problems and underlying many key combinatorial formulas. In this study, the authors used guided reinvention to investigate 2 undergraduate students' reasoning about the MP, and they sought to answer the following research questions: How do students come to understand and make sense of the MP? Specifically, while a pair of students reinvented a statement of the MP, how did they attend to and reason about key mathematical features of the MP? The students participated in a paired 8-session teaching experiment during which they progressed from a nascent to a sophisticated statement of the MP. Two key mathematical features emerged for the students through this process, including independence and distinct composite outcomes, and we discuss ways in which these ideas informed the students' reinvention of the statement. In addition, we present potential implications and directions for future research. |
Martingale Difference Divergence Matrix and Its Application to Dimension Reduction for Stationary Multivariate Time Series
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 216-229 |
| Abstrak | : | In this article, we introduce a new methodology to perform dimension reduction for a stationary multivariate time series. Our method is motivated by the consideration of optimal prediction and focuses on the reduction of the effective dimension in conditional mean of time series given the past information. In particular, we seek a contemporaneous linear transformation such that the transformed time series has two parts with one part being conditionally mean independent of the past. To achieve this goal, we first propose the so-called martingale difference divergence matrix (MDDM), which can quantify the conditional mean independence of V ∈ Rp given U ∈ Rq and also encodes the number and form of linear combinations of V that are conditional mean independent of U. Our dimension reduction procedure is based on eigen-decomposition of the cumulative martingale difference divergence matrix, which is an extension of MDDM to the time series context. Interestingly, there is a static factor model representation for our dimension reduction framework and it has subtle difference from the existing static factor model used in the time series literature. Some theory is also provided about the rate of convergence of eigenvalue and eigenvector of the sample cumulative MDDM in the fixed-dimensional setting. Favorable finite sample performance is demonstrated via simulations and real data illustrations in comparison with some existing methods. Supplementary materials for this article are available online. |
Theoretical Framing as Justifying
| Pengarang | : | Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer, and James Hiebert |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 3) |
| Halaman | : | 218-224 |
| Abstrak | : | In our March editorial (Cai et al., 2019), we discussed the nature of significant research questions in mathematics education. We asserted that the choice of a suitable theoretical framework is critical to establishing the significance of a research question. In this editorial, we continue our series on high-quality research in mathematics education by elaborating on how a well-constructed theoretical framework strengthens a research study and the reporting of research for publication. In particular, we describe how the theoretical framework provides a connecting thread that ties together all of the parts of a research report into a coherent whole. Specifically, the theoretical framework should help (a) make the case for the purpose of a study and shape the literature review; (b) justify the study design and methods; and (c) focus and guide the reporting, interpretation, and discussion of results and their implications. |
Minimax Optimal Procedures for Locally Private Estimation
| Pengarang | : | John C. Duchi |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 182-215 |
| Abstrak | : | Working under a model of privacy in which data remain private even from the statistician, we study the tradeoff between privacy guarantees and the risk of the resulting statistical estimators. We develop private versions of classical information-theoretical bounds, in particular those due to Le Cam, Fano, and Assouad. These inequalities allow for a precise characterization of statistical rates under local privacy constraints and the development of provably (minimax) optimal estimation procedures. We provide a treatment of several canonical families of problems: mean estimation and median estimation, generalized linear models, and nonparametric density estimation. For all of these families, we provide lower and upper bounds that match up to constant factors, and exhibit new (optimal) privacy-preserving mechanisms and computationally efficient estimators that achieve the bounds. Additionally, we present a variety of experimental results for estimation problems involving sensitive data, including salaries, censored blog posts and articles, and drug abuse; these experiments demonstrate the importance of deriving optimal procedures. Supplementary materials for this article are available online. |
Mission CO2ntrol: A Statistical Scientist's Role in Remote Sensing of Atmospheric Carbon Dioxide
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 152-181 |
| Abstrak | : | Too much carbon dioxide (CO2) in the atmosphere is a threat to long-term sustainability of Earth's ecosystem. Atmospheric CO2 is a leading greenhouse gas that has increased to levels not seen since the middle Pliocene (approximately 3.6 million years ago). One of the US National Aeronautics Space Administration's (NASA) remote sensing missions is the Orbiting Carbon Observatory-2, whose principal science objective is to estimate the global geographic distribution of CO2 sources and sinks at Earth's surface, through time. This starts with raw radiances (Level 1), moves on to retrievals of the atmospheric state (Level 2), from which maps of gap-filled and de-noised geophysical variables and their uncertainties are made (Level 3). With the aid of a model of transport in the atmosphere, CO2 fluxes (Level 4) can be obtained from Level 2 data directly or possibly through Level 3. Decisions about how to mitigate or manage CO2 could be thought of as Level 5. Hierarchical statistical modeling is used to qualify and quantify the uncertainties at each level. Supplementary materials for this article are available online. |
Posing Significant Research Questions
| Pengarang | : | Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer, and James Hiebert |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 2) |
| Halaman | : | 114-120 |
| Abstrak | : | In 2002, the National Research Council (NRC) released Scientific Research in Education, a report that proposed six principles to serve as guidelines for all scientific inquiry in education. The first of these principles was to “pose significant questions that can be investigated empirically” (p. 3). The report argued that the significance of a question could be established on a foundation of existing theoretical, methodological, and empirical work. However, it is not always clear what counts as a significant question in educational research or where such questions come from. Moreover, our analysis of the reviews for manuscripts submitted to JRME1 suggests that some practical, specific guidance could help researchers develop a significant question or make the case for the significance of a research question when preparing reports of research for publication. |
A Bayesian Approach for Estimating Dynamic Functional Network Connectivity in fMRI Data
| Pengarang | : | Ryan Warnick |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 134-151 |
| Abstrak | : | Dynamic functional connectivity, that is, the study of how interactions among brain regions change dynamically over the course of an fMRI experiment, has recently received wide interest in the neuroimaging literature. Current approaches for studying dynamic connectivity often rely on ad hoc approaches for inference, with the fMRI time courses segmented by a sequence of sliding windows. We propose a principled Bayesian approach to dynamic functional connectivity, which is based on the estimation of time varying networks. Our method utilizes a hidden Markov model for classification of latent cognitive states, achieving estimation of the networks in an integrated framework that borrows strength over the entire time course of the experiment. Furthermore, we assume that the graph structures, which define the connectivity states at each time point, are related within a super-graph, to encourage the selection of the same edges among related graphs. We apply our method to simulated task -based fMRI data, where we show how our approach allows the decoupling of the task-related activations and the functional connectivity states. We also analyze data from an fMRI sensorimotor task experiment on an individual healthy subject and obtain results that support the role of particular anatomical regions in modulating interaction between executive control and attention networks. |