Higher Criticism Research Articles

Differential correlates of criticism versus emotional overinvolvement towards patients with schizophrenia living in halfway houses or with their families

PurposeThis study systematically searched for differential correlates of criticism vs. emotional overinvolvement (EOI) towards patients with schizophrenia in families and halfway houses, which have only incidentally been reported in previous research. Identified patterns were compared across settings.MethodsWe included 40 inpatients with schizophrenia living in halfway houses and 40 outpatients living with their families and recorded the expressed emotion (EE) of 22 psychiatric nurses or 56 parents, respectively, through Five Minutes Speech Samples. Each nurse rated 1–12 inpatients and each inpatient was rated by 2–5 nurses. Each outpatient was rated by one or both parents. As EE ratings had a multilevel structure, weighted Spearman correlations of criticism and EOI with various patient- and caregiver-related characteristics were calculated and compared with Meng’s z-test.ResultsCriticism was weakly negatively correlated with EOI in nurses but negligibly in parents. Distinct patterns of significant differential correlates arose across settings. Outpatients’ aggressive behavior and parents’ related burden were mainly associated with higher criticism. Inpatients’ symptoms (agitation/aggression, negative and other psychotic symptoms) and nurses’ burnout (Depersonalization) were mainly associated with lower EOI. Inpatients’ perceived criticism and outpatients’ previous suicide attempts were equally associated with higher criticism and lower EOI (mirror correlations). Finally, various inpatient attributes (older age, chronicity, unemployment and smoking) triggered higher EOI only. Inpatients’ age, psychopathology (esp. agitation/aggression and negative symptoms) and perceived criticism survived adjustment for multiple comparisons.ConclusionOur findings suggest setting-specific pathogenetic pathways of criticism and EOI and might help customize psychoeducational interventions to staff and families.

Functional connectivity of cognition-related brain networks in adults with fetal alcohol syndrome

BackgroundFetal alcohol syndrome (FAS) can result in cognitive dysfunction. Cognitive functions affected are subserved by few functional brain networks. Functional connectivity (FC) in these networks can be assessed with resting-state functional MRI (rs-fMRI). Alterations of FC have been reported in children and adolescents prenatally exposed to alcohol. Previous reports varied substantially regarding the exact nature of findings. The purpose of this study was to assess FC of cognition-related networks in young adults with FAS.MethodsCross-sectional rs-fMRI study in participants with FAS (n = 39, age: 20.9 ± 3.4 years) and healthy participants without prenatal alcohol exposure (n = 44, age: 22.2 ± 3.4 years). FC was calculated as correlation between cortical regions in ten cognition-related sub-networks. Subsequent modelling of overall FC was based on linear models comparing FC between FAS and controls. Results were subjected to a hierarchical statistical testing approach, first determining whether there is any alteration of FC in FAS in the full cognitive connectome, subsequently resolving these findings to the level of either FC within each network or between networks based on the Higher Criticism (HC) approach for detecting rare and weak effects in high-dimensional data. Finally, group differences in single connections were assessed using conventional multiple-comparison correction. In an additional exploratory analysis, dynamic FC states were assessed.ResultsComparing FAS participants with controls, we observed altered FC of cognition-related brain regions globally, within 7 out of 10 networks, and between networks employing the HC statistic. This was most obvious in attention-related network components. Findings also spanned across subcomponents of the fronto-parietal control and default mode networks. None of the single FC alterations within these networks yielded statistical significance in the conventional high-resolution analysis. The exploratory time-resolved FC analysis did not show significant group differences of dynamic FC states.ConclusionsFC in cognition-related networks was altered in adults with FAS. Effects were widely distributed across networks, potentially reflecting the diversity of cognitive deficits in FAS. However, no altered single connections could be determined in the most detailed analysis level. Findings were pronounced in networks in line with attentional deficits previously reported.

Accurate and Ultra-Efficient p-Value Calculation for Higher Criticism Tests

In modern data science, higher criticism (HC) method is effective for detecting rare and weak signals. The computation, however, has long been an issue when the number of p-values combined (K) and/or the number of repeated HC tests (N) are large. Some computing methods have been developed, but they all have significant shortcomings, especially when a stringent significance level is required. In this article, we propose an accurate and highly efficient computing strategy for four variations of HC. Specifically, we propose an unbiased cross-entropy-based importance sampling method ( IS C E ) to benchmark all existing computing methods, and develop a modified SetTest method (MST) that resolves numerical issues of the existing SetTest approach. We further develop an ultra-fast approach (UFI) combining pre-calculated statistical tables and cubic spline interpolation. Finally, following extensive simulations, we provide a computing strategy integrating MST, UFI, and other existing methods with R package “HCp” for virtually any K and small p-values ( ∼ 10 − 20 ). The method is applied to a COVID-19 disease surveillance example for spatio-temporal outbreak detection from case numbers of 804 days in 3342 counties in the United States. Results confirm viability of the computing strategy for large-scale inferences. Supplementary materials for this article are available online.

Melville's Wisdom: Religion, Skepticism, and Literature in Nineteenth-Century America by Damien B. Schlarb

Reviewed by: Melville's Wisdom: Religion, Skepticism, and Literature in Nineteenth-Century America by Damien B. Schlarb Ariel Silver Damien B. Schlarb Melville's Wisdom: Religion, Skepticism, and Literature in Nineteenth-Century America Oxford: Oxford University Press, 2021. xiv + 252 pp. In his reading of the Book of Genesis in The Beginning of Wisdom (2003), Leon Kass is guided by philosophia, the love and pursuit of wisdom. He quickly acknowledges that scripture is not often read in this manner, especially by scholars of the Bible, whose training in higher criticism has led them to focus more on textual sources and the "sensibilities and prejudices of an ancient people" (2). These source critics read the Bible much as do literary critics—as literature more than as an aid to wisdom. Melville was neither a biblical scholar nor a literary critic, but in his elegant new book, Melville's Wisdom, Damien Schlarb contends that Melville seeks to demonstrate through his literary work that the Hebrew Bible can be read in a "reflective and philosophic spirit" (Kass, Leon R. The Beginning of Wisdom: Reading Genesis. Chicago: University of Chicago Press, 2003, p. 2) and that this manner of reading is modeled on the wisdom literature found within the biblical text. In his effort to recover the language and ethics of biblical wisdom, Schlarb asserts that Melville charts a course between the "Scylla of epistemological deadlock and the Charybdis of moral relativism" (20), leading him to theological as well as cultural insight. Literature begins to function as a new form of exegesis, which Melville deploys to try to deeply understand both the biblical text and the religious culture emerging in the midst of modern life. This spirit of philosophia animates Melville, and leads him, through the wisdom literature of the Bible, to what Schlarb calls the "hermeneutics of contemplation" (19). Like Ahab circling the leviathan, drawing ever closer, numerous scholars have sought to apprehend the acute nature of Melville's relationship to the Bible. This search began in earnest after World War II with the publication of Melville's Use of the Bible (Nathalia Wright, 1949) and Melville's Quarrel with God (Lawrance Thompson, 1952), works devoted to the ways in which Melville read biblical prose and poetry. Later works attended more to the religious, political, and cultural milieu informing Melville's biblical interpretations. The [End Page 108] more recent religious turn in literary studies has deepened this search and made it both more incisive and more expansive. In Melville's Bibles (2008), Ilana Pardes seeks to bring together these two previous strains of scholarship on Melville and the Bible: his reading of biblical texts and his reading of cultural contexts through his literary oeuvre. Melville's Bibles focuses principally on Moby-Dick, as does Jonathan A. Cook's Inscrutable Malice (2012). Where Pardes sets biblical texts and characters in Moby-Dick in conversation with multiple modes of biblical exegesis in antebellum America, Cook focuses more on the moral and religious questions which animate Melville's engagement with biblical sources. Melville's interrogation of theodicy—the attempt to reconcile divine justice with the presence of evil—leads him directly to Job. The omnipresence of Job in Moby-Dick points to Melville's interest in biblical wisdom, a genre that informs not only Job, but also Proverbs and Ecclesiastes. In Melville's Wisdom, Schlarb expands beyond Job and Moby-Dick to uncover the ways in which Melville works out his epistemology of skeptical devotion through the body of wisdom literature. At a time when the emerging modern world sought to both affirm and displace religious culture and the language of scripture, Melville discovered in the wisdom texts of the Hebrew Bible a contemplative approach that could lead to syncretic knowledge apart from either the dogma of religion or science. Having discovered that both superstition and empiricism are irredeemable, Melville looks instead for an approach that can respond to his inexhaustible call for inquiry and introspection. Wisdom, grounded in experience and reflection, transcends explanatory systems to arrive at its own moral vector: ambiguity and multiplicity. As Schlarb explains in his discussion on the Book of Job: "What remains in the wake of religious and scientific fervor...

The Sidney Sperry/Heber Snell Debates: Critical Biblical Scholarship and Mormon Tradition

The Sidney Sperry/Heber Snell Debates: Critical Biblical Scholarship and Mormon Tradition

Evangelicals and the Philosophy of Science: The Victoria Institute, 1865-1939, by Stuart Mathieson

Reviewed by: Evangelicals and the Philosophy of Science: The Victoria Institute, 1865–1939 by Stuart Mathieson Martin Hewitt (bio) Evangelicals and the Philosophy of Science: The Victoria Institute, 1865–1939, by Stuart Mathieson; pp. xi + 171. Abingdon and New York: Routledge, 2020, £96.00, $160.00, $41.60 ebook. It is probably too much to say that we urgently needed a full-length study of the Victoria Institute. The brainchild of an obscure civil servant with some dubious ideas about Newtonian physics, a defensive organization out of step with all but a marginalized evangelical fringe, and largely ridiculed by the establishment, its scholarly neglect is understandable. And yet this organization—which appropriated Queen Victoria's name, has survived from 1865 to the present day, and which, at its nineteenth-century peak, could claim more than a thousand members across the UK and beyond (including some prominent scientists and religious writers), and which published a substantial volume of annual Transactions (1867–1957)—certainly deserves more attention than it has hitherto attracted. After all, a proper historical understanding should encompass the losers as well as the winners. Stuart Mathieson's Evangelicals and the Philosophy of Science: The Victoria Institute, 1865–1939 partly rectifies this neglect, but remains something of a missed opportunity. Bookending his analysis with an account of the Institute's establishment and early years, then turning to its twentieth-century decline and reorientation, Mathieson explores four broad areas: natural theology, the higher criticism, geology and deep time, and Darwinism. This approach effectively brings out some consistent themes: evolutionary skepticism and a certain biblical literalism, of course, but also and perhaps most significantly the persistent attempt to deploy a version of Baconian inductivism as a methodological prophylactic to so-called speculative deductive science and the -isms that followed in its wake, not least materialism and atheism. But his reliance on the serial discussion of a small selection of the papers presented and the discussions that followed produces a rather narrow and bloodless account of the institution's significance. There is too much summary and not enough synthesis here. To be fair, Evangelicals and the Philosophy of Science does not disguise its limited ambitions, claiming only to "investigate the debates around religion and science at the influential Victoria Institute" (i). And in the absence of any institutional archive before 1909, heavy reliance on the published Transactions is understandable. But the internalist focus leaves little opportunity for exploring the influence of the Institute. The book might have examined not only how the Institute was treated by outsiders, but also the place it [End Page 347] occupied within the broader activities of its leading participants. Other sources could have been consulted but are surprisingly underused. Despite one reference to the papers of George Gabriel Stokes, who was president of the Institute from 1885 to 1903, his surviving correspondence with the Institute's secretaries is not exploited. And although the Institute shares the general fate of nineteenth-century intellectual associations in that newspaper coverage concentrated almost exclusively on the content of papers presented, there are scattered descriptions of the Institute's meetings that would have enriched Mathieson's account. C. M. Davies's portrayal in Heterodox London (1874), for example, reveals that the papers were preprinted and handed to members at the door as well as circulated for comment by correspondence, a feature which merits more attention. lyttelton Stewart Forbes Winslow's Recollections of Forty Years (1910), moreover, portrays cadaverous men with long white hair braving the elements to hear anti-Darwinian diatribes, thus reinforcing one of the Institute's fundamental characteristics: its membership, as well as being predominantly Anglican, was significantly skewed by age. In the Ph.D. thesis on which the book is very closely based, Mathieson provides an illuminating study of the sociology of the Institute's membership and leadership that is, inexplicably, omitted here. As Mathieson emphasizes, the travel and evolution of ideas matter. But this necessarily involves the networks of texts, people, and institutions in which these ideas are produced and disseminated. A few of the dramatis personae of the Institute's history are fleshed out, including James Reddie and F. W. H. Petrie, its two Victorian secretaries, and its...

Higher criticism to compare two large frequency tables, with sensitivity to possible rare and weak differences

We adapt Higher Criticism (HC) to the comparison of two frequency tables which may—or may not—exhibit moderate differences between the tables in some unknown, relatively small subset out of a large number of categories. Our analysis of the power of the proposed HC test quantifies the rarity and size of assumed differences and applies moderate deviations-analysis to determine the asymptotic powerfulness/powerlessness of our proposed HC procedure. Our analysis considers the null hypothesis of no difference in underlying generative model against a rare/weak perturbation alternative, in which the frequencies of N1−β out of the N categories are perturbed by r(logN)/2n in the Hellinger distance; here, n is the size of each sample. Our proposed Higher Criticism (HC) test for this setting uses P-values obtained from N exact binomial tests. We characterize the asymptotic performance of the HC-based test in terms of the sparsity parameter β and the perturbation intensity parameter r. Specifically, we derive a region in the (β,r)-plane where the test asymptotically has maximal power, while having asymptotically no power outside this region. Our analysis distinguishes between cases in which the counts in both tables are low, versus cases in which counts are high, corresponding to the cases of sparse and dense frequency tables. The phase transition curve of HC in the high-counts regime matches formally the curve delivered by HC in a two-sample normal means model.

Higher criticism for discriminating word-frequency tables and authorship attribution

We adapt the Higher Criticism (HC) goodness-of-fit test to measure the closeness between word-frequency tables. We apply this measure to authorship attribution challenges, where the goal is to identify the author of a document using other documents whose authorship is known. The method is simple yet performs well without handcrafting and tuning; reporting accuracy at the state of the art level in various current challenges. As an inherent side effect, the HC calculation identifies a subset of discriminating words. In practice, the identified words have low variance across documents belonging to a corpus of homogeneous authorship. We conclude that in comparing the similarity of a new document and a corpus of a single author, HC is mostly affected by words characteristic of the author and is relatively unaffected by topic structure.

The Victorian Cult of Shakespeare: Bardology in the Nineteenth Century

The Victorian Cult of Shakespeare: Bardology in the Nineteenth Century

Modern Western Critical Discourse on Seerah Sources

Seerah of the Prophet falls mainly under Orientalist studies evolving from an early skeptical normative to revisionism, higher criticism, biblical literary criticism and Hagarism. This perpetual change of Western academic methodology seems to indicate their fragile and non-traditional academic approach. The Orientalists like Goldziher and Schacht have been able to transform skeptical theories considerably to the extent ‘revisionist’ theories have emerged. In this paper, a critical review of modern Western critique has been discussed while conjecturing about its lacunas at the same time.

Copernicus, his Latin style and comments to Commentariolus

A methodology of historical or higher criticism and of stylometry/stylochronometry known from Biblical and literary studies is applied to the examination of Nicolaus Copernicus’s writings. In particular, his early work Commentariolus is compared at the level of the Latin language with his later ones (Meditata, Letter against Werner and De revolutionibus) as well as the texts of some other authors. A number of striking stylistic dissimilarities between these works have been identified and interpreted in the light of stylometry/stylochronometry, historical criticism and the history of Copernican research. The conducted research allowed to draw some plausible conclusions about the Sitz im Leben (historical context), the dating of Commentariolus and related matters.

In the Christian Archives: Sacrifice, the Higher Criticism, and the History of Religion

Much recent scholarship has shown just how indebted the secular sciences of religion were to the Protestant world from which they grew. Yet this “Protestant world” is typically described schematically, as if Protestantism offered a coherent worldview or even a consistent set of doctrines. A different picture emerges if we deepen our historical horizon, and explore the reflexes, aspirations, and norms that have found a home in the Christian (in this case, Protestant) theological imagination. This “Christian archive” was a heterogeneous place, with room for many things that we would now call secular or even profane. Protestant reform in fact began by condemning this heterogeneity, insisting that much of what the church had come to see was sacred was, at best, only and all too human. Yet centuries of conflict in Europe over the truth of Christianity only pluralized this archive further. The nineteenth-century history of religion grew less out of “Protestantism,” in other words, than out of the sedimented mixture of theological, historical, philological, and anthropological materials inherited from these earlier moments. It was, moreover, also an intellectual project that discovered new uses for these materials and thereby opened new horizons of humanistic inquiry. This article makes this argument with reference to sacrifice—a theological challenge for Christian thinkers from the outset of the tradition, but especially for Protestants; a magnet for diverse historical, anthropological, and theological reflections; and a productive zone of inquiry for the nineteenth-century German philosophers, philologians, and “higher critics” of the Hebrew Bible who together helped create the modern history of religion.

Contributions and Criticism of Western Scholars on Islamic inheritance (An Analytical Study)

In this paper, the criticisms and contributions of Western Scholars and their impacts on society have been discussed. To study the civilization‘s heritage, history, language, literature, fine arts, sciences, and sociology, of the people of East, by the westerns, is called Orientalism. In the ancient Arabic dictionary, the term “orientalism” is not present. In Europe, after the Renaissance, to introduce the East in the West, and to point out the expected interests of the West in the East, the Western Scholars performed their duty elegantly. All of the ancient and modern western scholars wrote about the Holy Qur‘an, and almost all of them neglected its present order and tried to determine the order of revelation of Qur’anic verses according to their own mind. Torrey of Yale spent his whole life to find out contradictions in the book of God. Bell of Edinburgh applied the rules of higher criticism on Qur’anic injunctions. Many other orientalists as Arthur Jeffery, A.T.Welch, J.D.Pearson, Montgomery Watt and Karen Armstrong are also written about the Qur’an and biography of the prophet (PBUH). Western scholars also have a great role in denouncing the history of Islam. It is the need of the era to go through their literary efforts to explore their objectives and outcomes. It is also essential to study their struggle to prove about their right and wrong points. At a time, the Orientalists gained popularity among all schools of thought of different religions. This study is necessary and beneficial for all students, teachers and research scholars of every field of life.

Correlates of Expressed Emotion Among Family Members of Individuals Who Sought Treatment for Opioid Use.

Expressed emotion has been robustly associated with negative mental health outcomes. Understanding correlates of expressed emotion by family members of individuals with opioid use disorder is important, as this group faces high levels of stress and can play an important role in their loved ones' treatment. Thus, immediate family members of individuals who sought treatment for opioid problems (N = 195) completed a web-based survey that included measures of expressed emotion, self-stigma, social support, and demographic characteristics. Multiple linear regression analyses were conducted to examine correlates of two types of expressed emotion-criticism and emotional overinvolvement. Results indicated that higher self-stigma and lower social support were significantly associated with higher emotional overinvolvement. Higher self-stigma and having experienced debt related to a family member's opioid use were associated with higher criticism. Thus, self-stigma and financial burden may exacerbate likelihood of expressed emotion, whereas social support may buffer against expressed emotion.

Beyond HC: More sensitive tests for rare/weak alternatives

Higher criticism (HC) is a popular method for large-scale inference problems based on identifying unusually high proportions of small $p$-values. It has been shown to enjoy a lower-order optimality property in a simple normal location mixture model which is shared by the ‘tailor-made’ parametric generalised likelihood ratio test (GLRT) for the same model; however, HC has also been shown to perform well outside this ‘narrow’ model. We develop a higher-order framework for analysing the power of these and similar procedures, which reveals the perhaps unsurprising fact that the GLRT enjoys an edge in power over HC for the normal location mixture model. We also identify a similar parametric mixture model to which HC is similarly ‘tailor-made’ and show that the situation is (at least partly) reversed there. We also show that in the normal location mixture model a procedure based on the empirical moment-generating function enjoys the same local power properties as the GLRT and may be recommended as an easy to implement (and interpret), complementary procedure to HC. Some other practical advice regarding the implementation of these procedures is provided. Finally, we provide some simulation results to help interpret our theoretical findings.

Discrimination, the Model Minority Stereotype, and Peer Relationships Across the High School Years.

Ethnic stereotyping can profoundly influence youth adjustment; however, little work has addressed how the model minority stereotype may affect adolescent social adjustment. This study examined Asian American adolescents' peer relationships over time and how perceived discrimination and model minority stereotyping are associated with positive (support) and negative (criticism) qualities in these relationships. Multi-wave survey data were collected from 175 Asian adolescents in the Southeast over three time points. Participants were 60% female (freshmen Mage = 14.42 years, SD = 0.64 and sophomores Mage = 15.56 years, SD = 0.74). They were 75% US-born and represented various heritage groups (e.g., Hmong, East/Southeast Asian, South Asian). Within-person, year-to-year associations between variables were explored. Criticism from White and other-ethnic peers decreased over time. Discrimination was associated with higher criticism over time, and links between model minority stereotyping and support were found. With White peers, when stereotyping experiences increased, both positive and negative relationship qualities increased. Experiences of stereotyping and discrimination interacted, exacerbating each other with regard to criticism. The discussion compares model minority stereotyping and discrimination, both likely to create strained relationships.

Diagonally Dominant Principal Component Analysis

We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the “diagonally dominant principal component analysis (DD-PCA).” DD-PCA is an effective tool for designing statistical methods for strongly correlated data. We showcase the use of DD-PCA in two statistical problems: covariance matrix estimation and global detection in multiple testing. Using the output of DD-PCA, we propose a new estimator for estimating a large covariance matrix with factor structure. Thanks to a nice property of diagonally dominant matrices, this estimator enjoys the advantage of simultaneous good estimation of the covariance matrix and the precision matrix (by a plain inversion). A plug-in of this estimator to linear discriminant analysis and portfolio optimization yields appealing performance in real data. We also propose two new tests for testing the global null hypothesis in multiple testing when the z-scores have a factor covariance structure. Both tests first use DD-PCA to adjust the individual p-values and then plug in the adjusted p-values to the higher criticism (HC) test. These new tests significantly improve over the HC test and compare favorably with other existing tests. For computation of DD-PCA, we propose an iterative projection algorithm and an ADMM algorithm. Supplementary materials for this article are available online.

Distributions and Power of Optimal Signal-Detection Statistics in Finite Case

For detecting weak and sparse signals by a set of n input p-values, the Higher Criticism (HC) type statistics, the BerkJones (B-J) type statistics, and the phi-divergence statistics have the equivalent asymptotic optimality as n goes to infinity. However, they can have significantly different performance in practical data analysis, where n is always finite and even very small. To address this problem in a broader context, this paper introduces a general family of goodness-of-fit statistics, called the gGOF, which unifies a broad signal-detection statistics including these optimal ones. Efficient and accurate analytical calculations for the distributions of the gGOF statistics are provided under arbitrary i.i.d. continuous models of the null and the alternative hypotheses. Based on that, a systematic power study reveals that in finite case, the number of signals is often more relevant than the signal proportion. The HC and the reverse HC have advantages for relatively sparser and denser signals, respectively, while the B-J is more robust. A general framework is given to apply the gGOF into data analysis based on the generalized linear models. An application to the SNP-set based genome-wide association study (GWAS) for Crohn's disease shows that these optimal statistics have a good potential for detecting novel disease genes with weak SNP effects. The calculations have been implemented into an R package SetTest and published on the CRAN.

Efficient Nonprofiling 2nd-Order Power Analysis on Masked Devices Utilizing Multiple Leakage Points

2nd-order attacks utilize power values at two leakage points to break cryptographic systems protected by 1st-order random masking. Without profiling, the attacker do not know the exact location of the two leakage points. Standard 2nd-order attacks with an exhaustive search over two windows of size $n_w$nw has computational complexity $\mathcal {O}(n_w^2)$O(nw2) and does not scale well with the window size $n_w$nw. We propose to apply a decision-combination attack, the majority vote (MV) attack, to combine 2nd order attacks at multiple candidate pairs of leakage points selected through two filters. The first filter pre-process the power traces with Fast Fourier Transformation (FFT) techniques and reduce the complexity to $\mathcal {O}(n_w\log _2(n_w))$O(nwlog2(nw)). The second filter use an advanced statistical feature selection procedure, Higher Criticism (HC), to select leakage candidates that improve the effectiveness of decision-combination MV attack and other leakage-combination attacks. We derive theoretical success conditions of MV attacks as well as the typical maximum attack and a leakage-combination sum attack. The theoretical conditions are confirmed through performance comparisons of the attacks on synthetic data sets and on two real data sets, an FPGA implementation and a software implementation of masked AES. The proposed FF-HC-MV attack is data-adaptive, working well in all data sets.

Detection of sparse mixtures: higher criticism and scan statistic

We consider the problem of detecting a sparse mixture as studied by Ingster (1997) and Donoho and Jin (2004). We consider a wide array of base distributions. In particular, we study the situation when the base distribution has polynomial tails, a situation that has not received much attention in the literature. Perhaps surprisingly, we find that in the context of such a power-law distribution, the higher criticism does not achieve the detection boundary. However, the scan statistic does.