Heavy-tailed prior distributions for sequence count data: removing the noise and preserving large differences

Anqi Zhu, Joseph G. Ibrahim, Michael I. Love · Bioinformatics · 2018 · statistics · 10.1093/bioinformatics/bty895 · record zhu2018-heavy-tailed-prior-distributions-f
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Other fields define these differently the same word, defined another way in another discipline
library size 2 fields · variance 2 fields

Tags on this paper

Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 8 concept tags on this paper, all 8 are grounded in a quoted sentence. All carry the tagger's gloss of what the term means in this paper, which is not something the article can license.
logarithmic fold change pseudocounts shrinkage estimator Cauchy prior local false sign rate Laplace approximation empirical Bayes maximum a posteriori library size maximum likelihood variance posterior SD system-or-tool-building
Method, as described: empirical Bayes with an adaptive Cauchy prior, fitted by approximate posterior estimation, evaluated against filtering, Normal priors and other shrinkage estimators

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relation to other workclaim_relationshow this paper stands to another: agrees, contradicts, extends, qualifies
claim typeclaim_typethe shape of the claim: existence, mechanism, method, critique, prediction, null
conceptconceptsan idea the paper works with, quoted where the paper uses it
content tagcontent_tagsa finding, definition, quantity, statistic or variable named in the paper
contributioncontributionwhat the paper claims to add
controlcontrolsan experiment run to eliminate a rival explanation
limitationlimitationswhat the paper says its evidence cannot support
mechanismmechanismshow the reported effect is said to come about
methodmethodhow the paper produced its evidence
object of studyobject_of_studywhat the paper is about — the thing it investigates
phenomenonphenomenonthe effect or regularity under study
research questionresearch_questionthe question the paper sets itself
sensesensesa distinct use of a term, quoted where the paper fixes it

The paper

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Every tag on this page

claim_relations 3 · claim_type 1 · concepts 8 · content_tags 15 · contribution 1 · controls 6 · limitations 6 · mechanisms 5 · method 1 · object_of_study 1 · phenomenon 1 · research_question 1 · senses 3

This record holds no relations between concepts. A layer is empty when the tagger recorded nothing in it — which is not the same as the paper having nothing to record.

facettagfieldconf.whose words
object_of_studythe logarithmic fold change between conditions in RNA-seq, and what to do when the estimate of it is dominated by noise
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object_of_studythe paper's words
research_questionhow to shrink unreliable effect-size estimates without losing the genes whose large effects are real
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research_questionthe paper's words
contributiona heavy-tailed Cauchy prior that removes the need for filter thresholds and pseudocounts, with lower bias than earlier shrinkage estimators
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contributionthe paper's words
claim_typemethod
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claim_typethe paper's words
phenomenonmaximum-likelihood effect sizes that blow up when counts are low, producing large estimates that are not differences
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phenomenonthe paper's words
methodsystem-or-tool-building
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methodthe paper's words
mechanismsthe estimate is unreliable exactly where the counts are small, so the maximum likelihood LFC has high variance and produces `large estimates not representative of true differences` - the noise appears as a big effect, not as a small one
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mechanisms[0]0.95the tagger's words
mechanismsa heavy tail on the prior is what lets shrinkage be aggressive near zero and gentle far from it: the Cauchy pulls in the noise-driven estimates while leaving genuinely large fold changes where they are
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mechanisms[1]0.95the tagger's words
mechanismsswapping a Normal prior for a Cauchy gives heavy tails, so small effects are still shrunk while genuinely large ones survive - shrinkage without flattening
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mechanisms[2]0.95the tagger's words
mechanismsthe prior's scale is fitted by subtracting each estimate's own error variance from its squared value, so the prior learns how much of the observed spread is real
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mechanisms[3]0.95the tagger's words
mechanismsthe scale is set from a Normal assumption even though the prior itself is Cauchy - the two roles come apart and the authors say the mismatch works in practice
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mechanisms[4]0.9the tagger's words
limitationsEVERY STANDARD CORRECTION TRADES ONE ERROR FOR THE OPPOSITE ONE: `filtering or application of Normal priors each can have drawbacks, either leading to loss of genes with sufficient signal, or overly aggressive shrinkage of true, large LFCs`
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limitations[0]0.95the tagger's words
limitationsand the second-order cost is stated: filtering loses genes with real differences, and `pseudocounts provide a limited solution that must be adapted per dataset` - a correction re-tuned per dataset is a free parameter wearing a method's name
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limitations[1]0.95the tagger's words
limitationschoosing the filter is named as an act of judgement rather than a setting: `Setting the threshold requires careful consideration of which genes may be lost`
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limitations[2]0.95the tagger's words
limitationsif most genes move in the same direction the global normalisation breaks down - and the paper says this defeats EVERY method under comparison, not only theirs
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limitations[3]0.95the tagger's words
limitationsthat failure is detectable, and the paper names the diagnostics rather than leaving it as a caveat
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limitations[4]0.95the tagger's words
limitationswhere the maximum likelihood estimates are not supplied the prior scale falls back to a fixed value rather than being fitted
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limitations[5]0.9the tagger's words
controlsthe method is compared against BOTH failure modes rather than against one baseline - filtering, which loses genes, and Normal priors, which over-shrink
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eliminates: a new estimator that beats the over-shrinking baseline by under-shrinking, or the reverse; the two-sided comparison is what makes 'lower bias while still reducing variance' a claim rather than a trade · outcome: held
controls[0]0.95the tagger's words
controlswhether the correction needs a per-dataset parameter
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eliminates: a method whose performance is really the analyst's tuning - the proposed prior 'avoids the use of filter thresholds or pseudocounts' entirely · outcome: held
controls[1]0.95the tagger's words
controlswhether the approach is tied to the negative-binomial likelihood it was developed on
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eliminates: a method that works because of one distributional assumption - apeglm 'accepts arbitrary likelihoods, as long as additional parameters are pre-specified' · outcome: held
controls[2]0.95the tagger's words
controlstesting robustness when the assumption of a unimodal symmetric distribution of effects is violated
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eliminates: the possibility that the method only works when its own prior assumption happens to hold · outcome: held
controls[3]0.95the tagger's words
controlsquantifying the effect of substituting estimated standard errors where the derivation requires known ones, specifically at very low counts
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eliminates: the possibility that the borrowed estimator breaks exactly where the data are weakest · outcome: held
controls[4]0.95the tagger's words
controlstrying an alternative posterior approximation by integrating over a fine grid instead of the Laplace method
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eliminates: the possibility that the chosen approximation was adopted without a competitor · outcome: failed
controls[5]0.95the tagger's words
conceptslogarithmic fold change
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concepts[0]0.95the paper's words
conceptspseudocounts
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also in: pseudocounts
concepts[1]0.95the paper's words
conceptsshrinkage estimator
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concepts[2]0.95the paper's words
conceptsCauchy prior
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also in: Cauchy prior
concepts[3]0.95the paper's words
conceptslocal false sign rate
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concepts[4]0.95the paper's words
conceptsLaplace approximation
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concepts[5]0.95the paper's words
conceptsempirical Bayes
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concepts[6]0.95the paper's words
conceptsmaximum a posteriori
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concepts[7]0.9the paper's words
senseslogarithmic fold change - AS ESTIMATED, NOT AS DEFINED. The definition is a ratio of average expression between conditions; the estimate at low counts is `large ... not representative of true differences`. THE SAME SYMBOL NAMES A QUANTITY AND A NUMBER THAT DOES NOT MEASURE IT
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senses[0]0.95the tagger's words
sensesshrinkage - the family of corrections, and this paper's point is that the family members fail in OPPOSITE directions: a filter loses true signal, a Normal prior flattens true large effects. WHICH ERROR YOU GET IS A CHOICE, AND USUALLY AN UNEXAMINED ONE
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senses[1]0.95the tagger's words
sensespseudocount - a correction that `must be adapted per dataset`. The paper's remedy is to remove the parameter rather than to tune it, which is the same move a field makes when it replaces an inferred name with a measured one
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
senses[2]0.95the tagger's words
claim_relationscritiques → count filtering as practised in edgeR and limma-voom, which removes genes before analysis and can lose those with sufficient signal
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claim_relations[0]0.95the tagger's words
claim_relationscritiques → DESeq2's adaptive Normal prior, which shrinks true large fold changes too aggressively
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claim_relations[1]0.95the tagger's words
claim_relationsextends → the empirical Bayes shrinkage tradition itself - the method is offered as a replacement for the prior, not for the framework
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claim_relations[2]0.95the tagger's words
content_tagsfiltering loses genes with sufficient signal, while Normal priors over-shrink true large LFCs
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content_tags.findings[0]0.95the tagger's words
content_tagspseudocounts provide only a limited solution that must be adapted to each dataset
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content_tags.findings[1]0.95the tagger's words
content_tagssetting the filter threshold requires careful thought about which genes may be lost
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content_tags.findings[2]0.95the tagger's words
content_tagsat low or highly variable counts the maximum-likelihood LFC has high variance, giving large estimates not representative of true differences
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content_tags.findings[3]0.95the tagger's words
content_tagsthe proposed heavy-tailed Cauchy prior avoids filter thresholds and pseudocounts
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content_tags.findings[4]0.95the tagger's words
content_tagsthe Laplace approximation was consistently more accurate than numerical integration over a grid
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content_tags.findings[5]0.95the tagger's words
content_tagsthe resulting scale estimate is only slightly biased even at very low counts
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content_tags.findings[6]0.95the tagger's words
content_tagsshrinkage improves the ranking of genes by effect size relative to methods that do not shrink at all
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content_tags.findings[7]0.95the tagger's words
content_tagsthe difference between conditions, defined as the log ratio of average expression levels
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content_tags.definitions[0]0.95the tagger's words
content_tagsthe local false sign rate given as a two-case posterior probability keyed on the sign of the MAP estimate
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content_tags.definitions[1]0.95the tagger's words
content_tagsmaximum likelihood
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content_tags.statistics[0]0.95the tagger's words
content_tagsvariance
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also in: variance
content_tags.statistics[1]0.95the tagger's words
content_tagsposterior SD
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also in: posterior SD
content_tags.statistics[2]0.85the tagger's words
content_tagslibrary size
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also in: library size
content_tags.variables[0]0.95the tagger's words
content_tagsruntimes for the pipeline on a ten-thousand-gene simulation - dispersion and MLE fitting, Normal-prior shrinkage, Cauchy-prior shrinkage, and MAP-only
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content_tags.quantities[0]0.95the tagger's words

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