Link taxonomy uncertainty explorer

Start here — what this is, what it assumes, and how to use it

What this is: an interactive guide to the Bayesian framework of Contextual evidence for categorising interactions and guiding their discovery. The taxonomy assigns each candidate link to one of eight categories from three pieces of evidence — the model prediction Y, the local observation O_l, and the replicate observation O_r. That assignment is deterministic, but every source is error-prone, so it carries uncertainty. The framework therefore treats the true category C as unknown and returns a posterior P(C | E) over the eight.

Scope: the three tabs below the setup cards are alternative versions of the framework, one shown at a time. The simple version takes binary evidence, one symmetric error rate per source, a uniform prior, and independent errors. Extension: many replicates relaxes two of those: the replicate evidence keeps its full quantitative count n, and the local axis can err at a different rate in each direction. Extension: informed priors replaces the uniform prior with ecological belief about the species pair, regionally (π_r) and at the site (π_l). Throughout, the rates start at ε_Y = 0.2, ε_l = 0.3, ε_r = 0.1, ρ = 0.15 and f = 0.05, chosen to show the behaviour of the framework rather than to describe any particular system, and each is adjustable with the sliders.

How to use: pick a category on the taxonomy tree. Its error-free signature z_c = (1, 0, 1) becomes the observed evidence E, and the confidence in that label is (1−ε_Y)(1−ε_l)(1−ε_r).

Try this: pick possibly missing — predicted and seen elsewhere, but not here. Open Error rates and push ε_l up: confidence in the label falls and recurrent takes the difference, because the more local sampling misses, the likelier the link was simply overlooked. Then switch to Extension and watch confidence climb as replicates accumulate — and stop at κ.

Mapping observations to truth — understanding the error rates

Each arrow runs from a quantity to the one it is trying to recover, and carries the error rate of that recovery. The green diagonal is what we actually want: how well the model we have, Y, recovers the ground truth. It is never measured directly — but composing the top and right edges gives it. Move the three rates — δ is 1 − accuracy, the number cross-validation reports — and watch the diagonal: it brightens as the model closes on the truth. These sliders are local to this panel and change nothing else on the page.

δ model vs observations

ε_l miss rate

f false detection

80.0%apparent accuracy — what CV says

69.5%real accuracy — against the truth

–of Y against the ground truth

Pick a link category — click any leaf

Each leaf carries its signature z_c = (Ŷ, L_l, L_r): predicted · realised here · realisable in the replicates — the evidence it would produce if no source erred

Category prior (base rates) — uniform by default; edit to break the symmetry

A uniform prior treats all eight categories as equally probable before any evidence arrives, so confidence in the chosen label depends only on the error rates — not on which category it is. Making some categories more probable than others would make the posterior no longer equal to the likelihood. Weights are relative, rescaled to sum to 1 (shown as %).

Error rates ε_d

ε_Y model error0.20

how often the prediction would change had the model been fitted to the ground truth — not the error cross-validation reports

ε_l local error0.30

the miss rate: the probability that a link realised where we sampled goes unrecorded in O_l

ε_r replicate error0.10

the probability that a realisable link is recorded in none of the replicates

ε_Y and ε_l drive all versions below. ε_r belongs to the simple version only: the extension replaces it with ρ and f, and lets the local axis err at a different rate in each direction.

Posterior P(C | E) over the eight categories

possibly missing (no mismatch) 1 mismatched source 2 mismatched 3 mismatched

Key quantities — for the chosen category

–

Confidence in possibly missing — the posterior probability P(C = possibly missing | E) that the label is correct.

–

φ — feasibility confidence — a lower bound on the probability that the link is feasible, whichever exact label is right.

–

κ — maximum contextual confidence — under these symmetric rates, (1−ε_Y)(1−ε_l): the most that within-system replication alone can deliver.

Likelihood breakdown — every cell updates with the sliders

Category	signature z_c	mismatched sources	model (Y)	local (l)	replicate (r)	P(E\|C)	P(C\|E)

Cumulative replicate evidence — the posterior when the count n is retained

ρ realisation rate0.15

the probability that a link is realised in a given place. ρ > 0 is what L_r = 1 means

f false-detection rate0.05

the probability that a link that is not there is recorded anyway, through misidentification or contamination

The posterior over all eight categories under the scenario you picked, so the eight lines sum to 1 at every R. The eight fall into four pairs, one per cell of the confusion matrix: the two members of a pair share Y and O_l and differ only on O_r, so colour marks the pair and line style the replicate bit — solid observed elsewhere, dashed not. The chosen category and its replicate counterpart are one such pair, drawn bold with markers. The full count n is retained throughout, which is what lets confidence accumulate: had the count been collapsed to the single bit O_r = 1[n ≥ 1], the same replicates would push confidence the other way, towards half of κ. Switch the scenario to see the mirror image. Note that the local axis is directional here: a link that is there is missed at ε_l, and one that is not there is recorded at f. That is what makes κ larger than the (1−ε_Y)(1−ε_l) of the simple version.

Effort to confidence — how many replicates? — the same curves read as a design question

Instead of asking "how confident am I after R replicates?", we can ask: "how many replicates of consistent evidence do I need to reach a confidence target?" That count is R*. The two lines are the chosen category and its replicate counterpart — the two halves of one confusion cell (same Y and O_l, opposite O_r). One is corroborated by detections (it keeps being seen elsewhere), the other by absences (it keeps not being seen). Pick any category on the tree to re-pair; ρ and f are shared with the panel above, and the count n is retained throughout.

target confidence50%

absolute posterior confidence to reach. It must lie strictly below the maximum contextual confidence κ = –, which no amount of replication can beat, so the slider stops there

ρ realisation rate0.15

the same slider as in the panel above; move either and both follow

f false-detection rate0.05

the same slider as in the panel above; move either and both follow

–

possibly missing — R* replicates to the target, at – bits/replicate.

–

phantom — R* replicates to the target, at – bits/replicate.

–

effort gap — how much more sampling the absence-corroborated category needs than the detection-corroborated one. The contrast between ρ and f vanishes at f = p₁ = –, beyond which both R* are infinite.

The two lines are one pair, so they share a colour with the plot above and differ only in style: solid is the category observed elsewhere, dashed the one that is not. Both rise with consistent replicates toward the shared maximum contextual confidence κ — here the y axis is scaled so that κ is the top of the plot, so a line reaching the top edge has extracted everything replicates can give. The y values are real confidences, and so is the target: the orange line sits at the absolute confidence you asked for, and each R* dot marks where a curve crosses it. The target must lie strictly below κ, since replicates buy only speed towards the maximum that ε_Y, ε_l and f impose; raising it requires a better model or a complementary local method. A category and its counterpart differ only in the replicate term, so their log-odds grow linearly in R, but at very different rates: a detection is rare under either hypothesis and so is surprising, whereas an empty replicate is what both mostly predict. The detection-corroborated line is therefore steeper and the absence-corroborated one lags. R* depends on ρ only through its contrast with f: if f = 0 the factor p₁^R cancels and confidence sits at κ from the first replicate, while as f approaches p₁ R* climbs and then becomes infinite, a detection then being evidence for a false detection. Replicates are worth taking only while they are cleaner than the link is rare.

How confident are we that this is a possibly missing link?

Pick a link category — click any leaf

Category prior (base rates) — uniform by default; edit to break the symmetry

Error rates ε_d

Posterior P(C | E) over the eight categories

Key quantities — for the chosen category

Likelihood breakdown — every cell updates with the sliders

Cumulative replicate evidence — the posterior when the count n is retained

Effort to confidence — how many replicates? — the same curves read as a design question

Which source explains the evidence? — an informed prior on the two ecological truths

How confident are we that this is a possibly missing link?

Pick a link category — click any leaf i

Category prior (base rates) — uniform by default; edit to break the symmetry i

Error rates εd i

Posterior P(C | E) over the eight categories i

Key quantities — for the chosen category

Likelihood breakdown i — every cell updates with the sliders

Cumulative replicate evidence i — the posterior when the count n is retained

Effort to confidence — how many replicates? i — the same curves read as a design question

Which source explains the evidence? i — an informed prior on the two ecological truths

Pick a link category — click any leaf

Category prior (base rates) — uniform by default; edit to break the symmetry

Error rates ε_d

Posterior P(C | E) over the eight categories

Likelihood breakdown — every cell updates with the sliders

Cumulative replicate evidence — the posterior when the count n is retained

Effort to confidence — how many replicates? — the same curves read as a design question

Which source explains the evidence? — an informed prior on the two ecological truths