Dataset Information

ESTIMATION OF A MONOTONE DENSITY IN S-SAMPLE BIASED SAMPLING MODELS.

ABSTRACT: We study the nonparametric estimation of a decreasing density function g 0 in a general s-sample biased sampling model with weight (or bias) functions wi for i = 1, …, s. The determination of the monotone maximum likelihood estimator ?n and its asymptotic distribution, except for the case when s = 1, has been long missing in the literature due to certain non-standard structures of the likelihood function, such as non-separability and a lack of strictly positive second order derivatives of the negative of the log-likelihood function. The existence, uniqueness, self-characterization, consistency of ?n and its asymptotic distribution at a fixed point are established in this article. To overcome the barriers caused by non-standard likelihood structures, for instance, we show the tightness of ?n via a purely analytic argument instead of an intrinsic geometric one and propose an indirect approach to attain the n -rate of convergence of the linear functional ? wi ?n.

SUBMITTER: Chan KCG

PROVIDER: S-EPMC6251412 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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ESTIMATION OF A MONOTONE DENSITY IN S-SAMPLE BIASED SAMPLING MODELS.

Chan Kwun Chuen Gary KCG Ling Hok Kan HK Sit Tony T Yam Sheung Chi Phillip SCP

Annals of statistics 20180817 5

We study the nonparametric estimation of a decreasing density function g 0 in a general s-sample biased sampling model with weight (or bias) functions wi for i = 1, …, s. The determination of the monotone maximum likelihood estimator ĝn and its asymptotic distribution, except for the case when s = 1, has been long missing in the literature due to certain non-standard structures of the likelihood function, such as n ...[more]

PMID: 30479456

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Project description:BackgroundThe internet is a relevant source of health-related information. The huge amount of information available on the internet forces users to engage in an active process of information selection. Previous research conducted in the field of experimental psychology showed that information selection itself may promote the development of erroneous beliefs, even if the information collected does not.ObjectiveThe aim of this study was to assess the relationship between information searching strategy (ie, which cues are used to guide information retrieval) and causal inferences about health while controlling for the effect of additional information features.MethodsWe adapted a standard laboratory task that has previously been used in research on contingency learning to mimic an information searching situation. Participants (N=193) were asked to gather information to determine whether a fictitious drug caused an allergic reaction. They collected individual pieces of evidence in order to support or reject the causal relationship between the two events by inspecting individual cases in which the drug was or was not used or in which the allergic reaction appeared or not. Thus, one group (cause group, n=105) was allowed to sample information based on the potential cause, whereas a second group (effect group, n=88) was allowed to sample information based on the effect. Although participants could select which medical records they wanted to check-cases in which the medicine was used or not (in the cause group) or cases in which the effect appeared or not (in the effect group)-they all received similar evidence that indicated the absence of a causal link between the drug and the reaction. After observing 40 cases, they estimated the drug-allergic reaction causal relationship.ResultsParticipants used different strategies for collecting information. In some cases, participants displayed a biased sampling strategy compatible with positive testing, that is, they required a high proportion of evidence in which the drug was administered (in the cause group) or in which the allergic reaction appeared (in the effect group). Biased strategies produced an overrepresentation of certain pieces of evidence at the detriment of the representation of others, which was associated with the accuracy of causal inferences. Thus, how the information was collected (sampling strategy) demonstrated a significant effect on causal inferences (F1,185=32.53, P<.001, η2p=0.15) suggesting that inferences of the causal relationship between events are related to how the information is gathered.ConclusionsMistaken beliefs about health may arise from accurate pieces of information partially because of the way in which information is collected. Patient or person autonomy in gathering health information through the internet, for instance, may contribute to the development of false beliefs from accurate pieces of information because search strategies can be biased.

Project description:Unlike the core structural elements of a protein like regular secondary structure, template based modeling (TBM) has difficulty with loop regions due to their variability in sequence and structure as well as the sparse sampling from a limited number of homologous templates. We present a novel, knowledge-based method for loop sampling that leverages homologous torsion angle information to estimate a continuous joint backbone dihedral angle density at each loop position. The φ,ψ distributions are estimated via a Dirichlet process mixture of hidden Markov models (DPM-HMM). Models are quickly generated based on samples from these distributions and were enriched using an end-to-end distance filter. The performance of the DPM-HMM method was evaluated against a diverse test set in a leave-one-out approach. Candidates as low as 0.45 Å RMSD and with a worst case of 3.66 Å were produced. For the canonical loops like the immunoglobulin complementarity-determining regions (mean RMSD <2.0 Å), the DPM-HMM method performs as well or better than the best templates, demonstrating that our automated method recaptures these canonical loops without inclusion of any IgG specific terms or manual intervention. In cases with poor or few good templates (mean RMSD >7.0 Å), this sampling method produces a population of loop structures to around 3.66 Å for loops up to 17 residues. In a direct test of sampling to the Loopy algorithm, our method demonstrates the ability to sample nearer native structures for both the canonical CDRH1 and non-canonical CDRH3 loops. Lastly, in the realistic test conditions of the CASP9 experiment, successful application of DPM-HMM for 90 loops from 45 TBM targets shows the general applicability of our sampling method in loop modeling problem. These results demonstrate that our DPM-HMM produces an advantage by consistently sampling near native loop structure. The software used in this analysis is available for download at http://www.stat.tamu.edu/~dahl/software/cortorgles/.

Dataset Information

ESTIMATION OF A MONOTONE DENSITY IN S-SAMPLE BIASED SAMPLING MODELS.

Publications

ESTIMATION OF A MONOTONE DENSITY IN <i>S</i>-SAMPLE BIASED SAMPLING MODELS.

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