dataesr/scientific-paragraphs-categorization huggingface dataset:
In terms of Zmix, recall that in the simulation studies, the algorithm was able to identify a component with a very small weight of π k = 0. 01 in 35% of replicates when n = 100, and 70% of replicates when n = 200; it is frequently able to identify well separated univariate Gaussian components when these are represented by as few as two or three observations in a sample. From these observations, there appears to be some evidence that the Galaxy dataset may not originate from a Gaussian mixture. If this distribution is Gaussian, a larger number of observations is required for Zmix to estimate a more complex configuration, or some restrictions must be placed.
The value of τ can be adjusted easily in the R implementation of Zmix. This behaviour is observed in the results of the Galaxy case study, where only two components are found by Zmix. It may be more reasonable to weaken the bounds on the variance of the means for this dataset to reflect our existing knowledge that the observations do come from many small, separate sections of space. Repeating the analysis with τ = 0. 01 results in a posterior with a 100% probability of three non-empty components, placing the two small clusters in each tail in separate groups (results not shown). The tempering algorithm (PPT) which is incorporated in Zmix allows for an exchange of information between the many potential overfitted posteriors, from fully merged configurations with many identical components to the sparsest configuration, where components either differ by at least one parameter or are empty.
One must also ensure that Zswitch is only applied to a posterior containing no identical (merged) components. We present Zmix and Zswitch as part of an R package called Zmix, which is available on Github at github. com/zoevanhavre/Zmix. Zmix includes all methods and functions described in this paper for overfitting univariate Gaussian mixtures, with the intention of providing a straightforward Bayesian tool for modelling and order estimation of the most common type of mixtures. This paper presents a comprehensive solution to estimating Gaussian mixtures with an unknown number of components, dealing with three general problems which inhibit accurate estimation. The issue of non-identifiability induced by overfitting is cast as an order estimation tool using recent theory on the effect of the prior on the weights of an overfitted Bayesian mixture model.
MCMC mixing difficulties common to mixtures are greatly amplified by this prior, and this is resolved by Prior Parallel Tempering which ensures full posterior exploration by travelling through all possible configurations of the posterior. This is analogous to parallel tempering but uses a much simpler acceptance ratio formulation. Finally, Zswitch provides a straightforward and complete relabelling algorithm which is adaptable to a wide range of models, allowing the results of an MCMC sampler on mixture data to be interpreted with no extra modelling effort on the part of the analyst. Parameter summaries for each model estimated by Zmix, for each simulation. Parameter summaries are included for n = 100 and n = 200 for all non-empty components for Sim 1 to 4. 95% Bayesian credible intervals are included for all estimates.
K0 defines the number of non-empty groups in the configuration considered in that row, and is annotated by an asterisk when this is correct. The parameter estimates corresponding to this configuration which contain the true value are similarly identified with an asterisk. (PDF) S1 File. R Code. Script file (format. r) containing instructions for downloading and installing the Zmix package, obtaining the simulations and case studies, and repeating the analysis performed in the paper. (R).
Boxplot of the number of non-empty groups for each chain. For n = 100 and n = 200, the distribution of the number of alive (non-empty) groups in each chain of the tempering is plotted across all 50,000 iterations minus a burn in of 5,000. The value of the hyperparameter of the weights α of each chain is included in red. (EPS) S3 Fig. Sim 4, Boxplot of the number of non-empty groups for each chain. For n = 100 and n = 200, the distribution of the number of alive (non-empty) groups in each chain of the tempering is plotted across all 50,000 iterations minus a burn in of 5,000. The value of the hyperparameter of the weights α of each chain is included in red. ' (EPS) S4 Fig. Sim 1 (n = 100): Results of Zmix and Zswitch. From upper left to lower right: the posterior parameter densities of all parameters from estimated groups, the posterior probability of allocations for each observation for each component, and a density plot of the data over the densities of 10,000 predicted datasets of the same size from the posterior.
A panel of plots is included for each candidate model found by Zmix. (EPS) S5 Fig. Sim 1 (n = 200): Results of Zmix and Zswitch. From upper left to lower right: the posterior parameter densities of all parameters from estimated groups, the posterior probability of allocations for each observation for each component, and a density plot of the data over the densities of 10,000 predicted datasets of the same size from the posterior. (EPS) S6 Fig. Sim 3 (n = 100): Results of Zmix and Zswitch. From upper left to lower right: the posterior parameter densities of all parameters from estimated groups, the posterior probability of allocations for each observation for each component, and a density plot of the data over the densities of 10,000 predicted datasets of the same size from the posterior. A panel of plots is included for each candidate model found by Zmix.
(EPS) S7 Fig. Sim 3 (n = 200): Results of Zmix and Zswitch. From upper left to lower right: the posterior parameter densities of all parameters from estimated groups, the posterior probability of allocations for each observation for each component, and a density plot of the data over the densities of 10,000 predicted datasets of the same size from the posterior. (EPS) S8 Fig. Sim 4 (n = 100): Results of Zmix and Zswitch. From upper left to lower right: the posterior parameter densities of all parameters from estimated groups, the posterior probability of allocations for each observation for each component, and a density plot of the data over the densities of 10,000 predicted datasets of the same size from the posterior. A panel of plots is included for each candidate model found by Zmix. (EPS) S9 Fig.
S2 Fig. Sim 3 , 3 Boxplot of the number of non-empty groups for each chain. For n = 100 and n = 200, the distribution of the number of alive (non-empty) groups in each chain of the tempering is plotted across all 50,000 iterations minus a burn in of 5,000. The value of the hyperparameter of the weights α of each chain is included in red. (EPS) S3 Fig. Sim 4, Boxplot of the number of non-empty groups for each chain. For n = 100 and n = 200, the distribution of the number of alive (non-empty) groups in each chain of the tempering is plotted across all 50,000 iterations minus a burn in of 5,000. The value of the hyperparameter of the weights α of each chain is included in red. ' (EPS) S4 Fig. Sim 1 (n = 100): Results of Zmix and Zswitch. From upper left to lower right: the posterior parameter densities of all parameters from estimated groups, the posterior probability of allocations for each observation for each component, and a density plot of the data over the densities of 10,000 predicted datasets of the same size from the posterior.
Acknowledgements. We would like to thank the anonymous reviewers for careful reading and pointing out some gaps in an earlier version of the paper. Most of this work was conducted when G. I. , Y. Q. and M. S. were at the  Centre for Quantum Technologies (CQT) in Singapore , and partially funded by the  Singapore Ministry of Education  and the  National Research Foundation , also through the  Tier 3 Grant  " Random numbers from quantum processes " ( MOE2012-T3-1-009 ). Research partially supported by the  European Commission IST   STREP  project  Quantum Algorithms (QALGO )  600700 , by the  French ANR Blanc program  under contract  ANR-12-BS02-005  ( RDAM  project), by the  Hungarian Scientific Research Fund (OTKA) , and by the  Hausdorff grant   EXC59-1/2.
e. , accounting for changes in explanatory variables; and (5) high-dimensional data, i. e. , analyzing complex and multidimensional data such as neuroimaging, genomic information, or database linkages. For some topics in the checklist (Fig. 1 ), substantial controversy remains regarding optimal analytic approaches, especially when considering both bias and variance of the methods. In many cases, although the potential for bias is clear, it has not been established that this bias is substantial in real data. The guidelines in Fig. 1  are intended as a first step toward improved evaluation and reporting of methodological challenges in dementia research, to support a move toward field-wide consensus on best practices, and identifying the highest priority areas for methodological innovations.
High-dimensional data The proliferation of data sources and emergence of high-dimensional data could powerfully accelerate dementia research but only if harnessed effectively  [66]. Administrative databases, omics data, brain imaging data (magnetic resonance imaging and positron emission tomography), biomarker panels assessing gene expression, and metabolic pathways, among many others, present both new challenges and opportunities (Supplementary Appendix 5). New technologies will provide information on numerous biomarkers, which may help us distinguish more specific dementia phenotypes, but we need strong measurement tools to better take advantage of these data. Challenges in the statistical analyses of high-dimensional data are numerous (Table  5 ), even when the number of observations is much larger than typically available in research cohorts.
Big data do not necessarily resolve the familiar internal and external validity challenges in epidemiologic studies and may in some situations exacerbate challenges with measurement validity and selection bias. For example, dementia is known to be substantially underrepresented in many US administrative databases, due to underdiagnosis. Underdiagnosis rates may differ by demographic or other background variables  [67]. A provocative and unexpected finding was recently reported from a UK administrative database (UK Clinical Practice Research Datalink) with almost 2 million individuals ages ≥40 years, accruing over 45,000 incident dementia cases  [68] : obese people carried a third lower risk of developing dementia than their normal weight peers. The huge sample provided very precise effect estimates but also entailed numerous tradeoffs that may have introduced biases, such as limited confounder control based on variables recorded in the database and potential for misclassification of the outcome  [69].
Recent worldwide efforts to merge data from multiple dementia cohorts are generating unique and promising databases: the European Medical Information Framework-AD, a partnership of academics, pharmaceutical companies, and medical informatics specialists focuses on the identification of preclinical biomarkers of AD. Despite huge sample sizes, results will be useful only if it is possible to derive harmonized measures of exposure, biomarkers, and outcomes. Coordinating such efforts is a major challenge  [66]. The Integrated Analysis of Longitudinal Studies of Aging collaboration focuses on data harmonization and reproducibility of research from international longitudinal studies focused on aging and health-related change in cognition, health, and well-being  [70]. High-dimensional data analysis generates multiple statistical comparisons/tests potentially addressed by various statistical corrections (family-wise error and false discovery).
Acknowledgments Role of the funding source: The MELODEM initiative has been supported by the  "Fondation Plan Alzheimer. "J. W. was supported by  NIEHS  grant  R21ES020404  and  Alzheimer's Association  grant  NIRG-12-242395. M. C. P. was supported by  NIA  grant  T32 AG027668. A. L. G. was supported by  NIA  grant  R03AG045494. S. M. H. was supported by  NIA  grants  P01AG043362  and  R01AG026453. M. M. G. was supported by  NIA  grant  R21 AG034385.
Acknowledgements We would like to thank  Chris Beem ,  Davide Gaiotto ,  Simone Giombi ,  Igor Klebanov ,  Marco Meineri ,  Toine Van Proeyen ,  Silviu Pufu ,  Slava Rychkov ,  Balt van Rees , and  Alessandro Vichi  for useful discussions. The work of NB is supported in part by the starting grant  BOF/STG/14/032  from  KU Leuven , by the  COST Action   MP1210  The  String Theory Universe , and by the  European Science Foundation Holograv Network. The research of DM was supported by  Perimeter Institute for Theoretical Physics. Research at  Perimeter Institute  is supported by the  Government of Canada through Industry Canada  and by the  Province of Ontario  through the  Ministry of Research and Innovation. During this work MFP was supported by a  Marie Curie Intra-European Fellowship  of the  European Community's 7th Framework Programme  under contract number  PIEF-GA-2013-623606  and by  US DOE- grant  DE-SC0010010.
Acknowledgements UF wants to thank the  Alfried Krupp Wissenschaftskolleg in Greifswald , where he spent the summer term 2014 as research fellow, and where part of this research of carried out. AS is grateful to  CNRS  and the  Département de mathématiques de Besançon  for the hospitality in autumn 2014. We all thank  Michael Schürmann  for several useful discussions. Finally we are very grateful to the anonymous referee for a very careful reading of our manuscript and several useful remarks.
BD acknowledges the support of  WCMS  postdoctoral grant. UF was supported by an  ANR  Project  OSQPI  ( ANR-11-BS01-0008 ). AK was partially supported by the  PostDoctoral Fellowship   2012/04/S/ST1/00102  of the Polish National Science Center. AS is partially supported by the  HARMONIA NCN  grant  2012/06/M/ST1/00169.
this paper, we propose to analyze the problem in the Bayesian context. As well as in the deterministic context, the Bayesian Cramér-Rao bound cannot be computed due to the discrete nature of the parameters and the Bayesian Barankin bound (a Bayesian version of the Chapman-Robbins and McAuly-Seidman bounds) neither due to some regularity This work has been partially supported by the iCODE institute, research project of the IDEX Paris-Saclay, by the MAGELLAN project (ANR-14-CE23-0004-01), by the Display-Mastodons project of CNRS and by DGA MRIS.
Acknowledgements OF thanks  M Bershtein  for collaboration on [14], ideas of which were used in this work,  J F Morales ,  E Pomoni  and  R Poghossian  for discussions on their works and related topics. OF also acknowledges the excellent hospitality and financial support of the  Galileo Galilei Institute, University of Florence , and particularly of the  scientific program  " Statistical Mechanics, Integrability and Combinatorics ". RS thanks  G Bonelli  and  A Tanzini  for discussions. All authors thank  B Estienne  and  B LeFloch  for discussions, and the  Institut Henri Poincare, Paris , where this work was completed, for excellent hospitality and financial support. We also thank the referee for pointing out [40] to our attention. VB is supported by the  Russian Science Foundation  under the grant  14-12-01383.
Acknowledgments This work was founded by  CNRS  ( Centre National de la Recherche Scientifique ) via a PEPS (Projets  Exploratoires Premier Soutien) HuMain (Humanités-Mathématiques-sciences de l'Information ) in 2013 and 2014, and by the  RNSC (Réseau national des systèmes complexes) , via the interdisciplinary network MAPS (Modélisation multi-agents appliquée aux phènoménes spatialisés http://maps. hypotheses. org/).
When observational data are used for this purpose, three more sources of bias may arise: confounding, survivorship bias, and selection due to preferential inclusion in surveillance datasets of those who are hospitalized and/or die. We illustrate these biases and caution against causal interpretation of differential CFR among those receiving different interventions in observational datasets. Again, we discuss ways to reduce these biases, particularly by estimating outcomes in smaller but more systematically defined cohorts ascertained before the onset of symptoms, such as those identified by forward contact tracing. Finally, we discuss the circumstances in which these biases may affect non-causal interpretation of risk factors for death among cases.
Therefore, observational estimates of CFR under different treatment conditions may be the only available means to assess the impact of various treatments. However, observational studies conducted in the early phases of an outbreak, when public health authorities are appropriately concentrating on crisis response and not on rigorous study design, are challenging. A common problem is that disease severity of the cases recorded in a surveillance database will differ, perhaps substantially, from that of all cases in the population. This issue has arisen in the present epidemic of Ebola virus disease in West Africa and in many previous outbreaks and epidemics  [4] [5] [6] [7] [8] [9]  and will continue to arise in future ones. Here we outline two biases that may occur when estimating the CFR in a population from a surveillance database, and three more biases that may occur when comparing the CFR between subgroups to estimate the causal effect of medical interventions.
Preferential ascertainment of severe cases For diseases that have a spectrum of clinical presentation, those cases that come to the attention of public health authorities and are entered into surveillance databases will typically be people with the most severe symptoms, who seek medical care, are admitted to hospital, or die. Therefore, the CFR will typically be higher among detected cases than among the entire population of cases, given that the latter may include individuals with mild, subclinical, and (under some definitions of "case") asymptomatic presentations. Laboratory confirmation as an inclusion criterion may reduce this bias if it is able to detect a wider spectrum of presentations, or may exacerbate it if the probability of receiving a laboratory test is higher for more severe cases and/or if test sensitivity is higher for more severe cases.
Bias due to delayed reporting of death During an ongoing epidemic, there is a delay between the time someone dies and the time their death is reported. Therefore, at any moment in time, the list of cases includes people who will die and whose death has not yet occurred, or has occurred but not yet been reported. Thus dividing the cumulative number of reported deaths by the cumulative number of reported cases at any moment will underestimate the true CFR. The key determinants of the magnitude of the bias are the epidemic growth rate and the distribution of delays from case-reporting to death-reporting; the longer the delays and the faster the growth rate, the greater the bias. Heuristically, the underestimate will be proportionate to the expansion of the epidemic during the delay between the time a case enters the database to the time the death of that case enters the database (if it occurs).
Possible solutions Preferential ascertainment of severe cases: In an infection with a range of manifestations from relatively mild to highly severe, milder cases are less likely to appear in surveillance databases than more severe ones; therefore, the CFR among ascertained cases will be higher than that among all cases. Spuriously increases estimate of CFR Influenza H1N1pdm  [10] [11] [12] , Influenza H7N9  [6] , Influenza H5N1  [7]  (though this hypothesis has been refuted  [8] ), Middle East Respiratory Syndrome  [4] , Ebola (this article)  [13]  Note: these solutions are listed in approximately the temporal order in which they may be practical, from early in the outbreak to later on; details will depend on the epidemiology of the outbreak. Use sentinel surveillance sites to estimate multipliers between various levels of severity and extrapolate to a larger population  [6].
Apply a competing-risk Kaplan-Meier-like method or a parametric mixture model to the full dataset (biased if the times to death and time to recovery have different distributions)  [24, 25]. Fit the distribution of times to death and to recovery to estimate the true CFR  [10, 11] , or inverse-probability weight deaths using the conditional probability of having survived by w, given that one dies  [21]  (biased if the probability distribution is incorrect). a risk difference (RD), the difference between the CFR in group A and group B. We use the term relative CFR to refer to any of these measures, and call a relative CFR non-null when it differs from 1 (ratio) or 0 (difference). When these biases are present, a relative CFR, different from the null value in group B compared with A does not imply a causal effect of group.
May be in either direction, depending on whether those receiving the intervention have better or worse prognosis. Ebola (this article), H1N1pdm (effect of antiviral treatment on death)  [28] , Influenza H5N1 (effect of antiviral treatment on death)  [29, 30, 31]  In principle, analysis can adjust for prognostic factors that also predict hospitalization via matching, stratification, or multivariable analysis. In practice, such information may be unavailable  [27]. Such adjustments will be more readily made if data are obtained prospectively from a cohort of cases identified before becoming cases. Selection bias occurring because mortality and hospitalization both affect the probability a case will appear in the database  [32] : When inclusion in a database can occur as a result of either of two (or more) factors, the association between these two factors within the database will be biased relative to that in the source population.
For example, if death and hospital admission are both means by which cases are ascertained and enter a database, as may be the case for Ebola datasets, hospitalization will be spuriously associated with death in the dataset even if hospitalization has no causal effect in preventing death. Direction of bias depends on the probabilities of inclusion in the dataset depending on exposure and outcome. Ebola (this article) Without knowledge of how cases came to enter a dataset, the magnitude of this bias cannot be evaluated. Under assumptions about the proportion of cases entering the dataset for various reasons, a sensitivity analysis could be performed to assess the plausibility of assigning any observed protective effect to this bias  [33]. This bias too may be avoided by prospectively following a cohort of individuals who are identified before becoming cases.
However, such information may frequently be limited or unavailable in databases compiled during outbreaks, especially in resource-limited settings. The third source of bias is selection occurring because mortality and hospitalization both affect the probability a case will appear in the database. During an outbreak, many cases may not appear in the database because they are not ascertained or because information about them is not obtainable. In particular, cases who are not hospitalized, and cases who do not die, may be less likely than other cases to appear in the database because they are less likely to come to medical or public health attention. If appearance in a database is the common effect of hospitalization and death, then the association between hospitalization and death among cases in the database may be non-null even if hospitalization and death were independent in the population of all cases.