Model Projections in Model Space: A Geometric Interpretation of the AIC Allows Estimating the Distance Between Truth and Approximating Models

Ponciano, José Miguel; Taper, Mark L.

doi:10.3389/fevo.2019.00413

Cited by 9 publications

(19 citation statements)

References 43 publications

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“…If the test fails to reject, it only tells that the researcher does not have sufficient sample size or specified inappropriate effect size. Model comparison via consistent information criteria like the Bayesian Information Criterion (BIC) used here, coupled with process simulations, can and do remedy these problems [ 66 , 67 ].…”

Section: Resultsmentioning

confidence: 99%

Convergent evolution of diverse Bacillus anthracis outbreak strains toward altered surface oligosaccharides that modulate anthrax pathogenesis

et al. 2020

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Bacillus anthracis, a spore-forming gram-positive bacterium, causes anthrax. The external surface of the exosporium is coated with glycosylated proteins. The sugar additions are capped with the unique monosaccharide anthrose. The West African Group (WAG) B. anthracis have mutations rendering them anthrose deficient. Through genome sequencing, we identified 2 different large chromosomal deletions within the anthrose biosynthetic operon of B. anthracis strains from Chile and Poland. In silico analysis identified an anthrose-deficient strain in the anthrax outbreak among European heroin users. Anthrose-deficient strains are no longer restricted to West Africa so the role of anthrose in physiology and pathogenesis was investigated in B. anthracis Sterne. Loss of anthrose delayed spore germination and enhanced sporulation. Spores without anthrose were phagocytized at higher rates than spores with anthrose, indicating that anthrose may serve an antiphagocytic function on the spore surface. The anthrose mutant had half the LD50 and decreased time to death (TTD) of wild type and complement B. anthracis Sterne in the A/J mouse model. Following infection, anthrose mutant bacteria were more abundant in the spleen, indicating enhanced dissemination of Sterne anthrose mutant. At low sample sizes in the A/J mouse model, the mortality of ΔantC-infected mice challenged by intranasal or subcutaneous routes was 20% greater than wild type. Competitive index (CI) studies indicated that spores without anthrose disseminated to organs more extensively than a complemented mutant. Death process modeling using mouse mortality dynamics suggested that larger sample sizes would lead to significantly higher deaths in anthrose-negative infected animals. The model was tested by infecting Galleria mellonella with spores and confirmed the anthrose mutant was significantly more lethal. Vaccination studies in the A/J mouse model showed that the human vaccine protected against high-dose challenges of the nonencapsulated Sterne-based anthrose mutant. This work begins to identify the physiologic and pathogenic consequences of convergent anthrose mutations in B. anthracis.

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Section: Resultsmentioning

confidence: 99%

Convergent evolution of diverse Bacillus anthracis outbreak strains toward altered surface oligosaccharides that modulate anthrax pathogenesis

et al. 2020

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“…After obtaining the consensus sequences of assembly programs, we reconstructed NMDS plots of sequences for examining relative locations against the reference. According to Ponciano and Taper (2019), we can obtain reliable estimates of the generating (true) model by plotting candidate models in a distance space with NMDS methods. A critical difference from Ponciano and Taper ( 2019) is that we do not have parametric generating functions for reconstructing contigs from the reference, and we cannot apply estimating methods for neg-cross and neg-selfentropies.…”

Section: Consensus Sequencementioning

confidence: 99%

“…A critical difference from Ponciano and Taper ( 2019) is that we do not have parametric generating functions for reconstructing contigs from the reference, and we cannot apply estimating methods for neg-cross and neg-selfentropies. But if we can assume that h 2 = 0 in Equation 9 (Ponciano and Taper, 2019), we can estimate the true reference location as the origin (0,0) in the reconstructed NMDS spaces.…”

Section: Consensus Sequencementioning

confidence: 99%

“…In our preliminary examination, a general NMDS method applicable for sequence data (nmds, Taguchi and Oono, 2005) could not converge to a common spatial configuration. Dr. Mark L. Taper kindly recommended using mds function in smacof library (https://cran.r-project.org/web/packages/ smacof/vignettes/smacof.pdf) for NMDS plottings, based on his experience in Ponciano and Taper (2019), compared to other NMDS functions available in R. Different NMDS functions adopt different stress functions being minimized. We checked that 2D NMDS plots created with metaMDS function in vegan library (https://www.rdocumentation.org/packages/vegan/versions/2.…”

Section: Consensus Sequencementioning

confidence: 99%

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The Evidential Statistics of Genetic Assembly: Bootstrapping a Reference Sequence

Toquenaga

Gagné

2021

Front. Ecol. Evol.

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The reference sequences play an essential role in genome assembly, like type specimens in taxonomy. Those references are also samples obtained at some time and location with a specific method. How can we evaluate or discriminate uncertainties of the reference itself and assembly methods? Here we bootstrapped 50 random read data sets from a small circular genome of a Escherichia coli bacteriophage, phiX174, and tried to reconstruct the reference with 14 free assembly programs. Nine out of 14 assembly programs were capable of circular genome reconstruction. Unicycler correctly reconstructed the reference for 44 out of 50 data sets, but each reconstructed contig of the failed six data sets had minor defects. The other assembly software could reconstruct the reference with minor defects. The defect regions differed among the assembly programs, and the defect locations were far from randomly distributed in the reference genome. All contigs of Trinity included one, but Minia had two perfect copies other than an imperfect reference copy. The centroid of contigs for assembly programs except Unicycler differed from the reference with 75bases at most. Nonmetric multidimensional scaling (NMDS) plots of the centroids indicated that even the reference sequence was located slightly off from the estimated location of the true reference. We propose that the combination of bootstrapping a reference, making consensus contigs as centroids in an edit distance, and NMDS plotting will provide an evidential statistic way of genetic assembly for non-fragmented base sequences.

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“…Then the strength of evidence for θ 2 vs. θ 1 is given by the likelihood ratio LR(θ 2 , θ 1 ) = L(θ 2 ; y (n) ) L(θ 1 ; y (n) ) with values larger than 1 implying θ 2 is better supported than θ 1 and vice versa. Strength of evidence can be seen to be a comparison of the divergence between the true model and the two competing hypotheses (Lele, 2004;Taper and Lele, 2004;Dennis et al, 2019;Ponciano and Taper, 2019). The law of the likelihood corresponds to using the Kullback-Leibler divergence but other measures, such as the Hellinger divergence, Jeffrey's divergence, etc.…”

Section: The Law Of the Likelihoodmentioning

confidence: 99%

How Should We Quantify Uncertainty in Statistical Inference?

Lele

2020

Front. Ecol. Evol.

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An inferential statement is any statement about the parameters, form of the underlying process or future outcomes. An inferential statement, that provides an approximation to the truth, becomes "statistical" only when there is a measure of uncertainty associated with it. The uncertainty of an inferential statement is generally quantified in terms of probability of the strength of approximation to the truth. This is what we term "inferential uncertainty." Answer to this question has significant implications in statistical decision making where inferential uncertainty is combined with loss functions for predicted outcomes to compute the risk associated with the decision. The Classical and the Evidential paradigms use aleatory (frequency based) probability for quantifying uncertainty whereas the Bayesian approach utilizes epistemic (belief based) probability. To compute aleatory uncertainty, one needs to answer the question: which experiment is being repeated, hypothetically or otherwise? whereas computing epistemic uncertainty requires: What is the prior belief? Deciding which type of uncertainty is appropriate for scientific inference has been a contentious issue and without proper resolution because it has been commonly formulated in terms of statements about parameters, that are statistical constructs, not observables. Common to these approaches is the desire to understand the data generating mechanism. Whether one follows the Frequentist or the Bayesian approach inferential statements concerning prediction are aleatory in nature and are practically ascertainable. We consider the desirable characteristics for quantification of uncertainty as: (1) Parameterization and data transformation invariance, (2) correct predictive coverage, (3) uncertainty that depends only on the data at hand and the hypothesized data generating mechanism, and (4) diagnostics for model misspecification and guidance for correction. We examine the Classical, Bayesian and Evidential approaches in the light of these characteristics. Unfortunately, none of these inferential approaches possesses all of our desiderata although the Evidential approach seems to come closest. Choosing an inferential approach, thus, involves choosing between either specifying the hypothetical experiment that will be repeated or equivalently a sampling distribution of the estimator or a prior distribution on the model space or an evidence function.

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Model Projections in Model Space: A Geometric Interpretation of the AIC Allows Estimating the Distance Between Truth and Approximating Models

Cited by 9 publications

References 43 publications

Convergent evolution of diverse Bacillus anthracis outbreak strains toward altered surface oligosaccharides that modulate anthrax pathogenesis

Convergent evolution of diverse Bacillus anthracis outbreak strains toward altered surface oligosaccharides that modulate anthrax pathogenesis

The Evidential Statistics of Genetic Assembly: Bootstrapping a Reference Sequence

How Should We Quantify Uncertainty in Statistical Inference?

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