Glossary¶

A plain-language reference for the terms used across these docs. On other pages, hover any underlined term to see a short definition without leaving the page. This page is the full list, grouped by topic, with a pointer to where each idea is taught in depth.

New to causal inference? Read the learn series first. This page is a quick reference, not a course.

Core causal ideas¶

causal inference — working out what causes what, so you can predict what an action would do, not just what tends to move with what. See learn: why causality.
correlation (association) — two things tending to move together, with no claim that one causes the other.
confounder — a common cause sitting behind both the treatment and the outcome, which makes them move together and fakes an effect. See learn: why causality.
back-door path — a non-causal route from treatment to outcome that runs through a common cause and lets association leak through. See identification.
back-door adjustment — removing confounding by conditioning on (holding fixed) the variables that block every back-door path.
collider — a node that two arrows point into (X → Z ← Y); a shared effect. A collider blocks a path until you condition on it, which then opens it. See learn: good and bad controls.
fork — one variable causing two others; the shape behind a confounder. See learn: good and bad controls.
chain — A causes B causes C; the effect passes through the middle variable (a mediator).
mediator — a variable on the causal path from treatment to outcome that carries part of the effect. See identification.
selection bias — distortion that appears when you only keep rows where some condition held; conditioning on that condition can correlate its causes even when they are unrelated. See graph.
intervention (do(X)) — setting X yourself rather than just observing it. On a graph this cuts the arrows into X. See graph.
observational data — data you collected by watching the world, not by running an experiment.
counterfactual — what would have happened to a unit under the treatment it did not actually get.
Simpson's paradox — a pattern that holds in every subgroup yet flips when you pool the groups. See learn: why causality.
Berkson's paradox — a fake correlation created by looking only at a selected subgroup. See learn: good and bad controls.
explaining away — once you know a shared effect happened, its independent causes start to look dependent.
interference (SUTVA) — one unit's treatment affecting another's outcome (for example, through a shared queue). SUTVA is the assumption that this does not happen.
exclusion restriction — the assumption that an instrument reaches the outcome only through the treatment. See learn: hidden confounding.
positivity (overlap) — every kind of unit appears both treated and untreated, so there is somebody to compare with. See learn: estimating effects.

Identification¶

identification — deciding whether a causal effect can be computed from the data you have, and if so writing the formula for it, before touching the numbers. See identification.
estimand — the formula identification produces: the effect written in terms of quantities you can actually observe. See identification.
adjustment set — the variables you condition on to close every back-door path. See learn: good and bad controls.
minimal adjustment set — the smallest valid adjustment set, so you measure as little as possible.
front-door — identifying a confounded effect through a fully-mediating, unconfounded middle step. See learn: hidden confounding.
instrument (IV) — a variable that moves the treatment but reaches the outcome only through the treatment. See learn: hidden confounding.
null (zero-effect) strategy — the verdict that no directed path runs from treatment to outcome, so the effect is zero by structure.
do-calculus — the rule system that decides whether any single-graph effect is identifiable and writes the formula. See identification.
ID / IDC algorithm — the complete procedure (Shpitser-Pearl) that implements do-calculus; IDC is its version for a conditional effect.
functional — ergodic's typed estimand object: an algebra of conditional-probability terms (Prob, Product, Marginal, Ratio).
hedge — the structure that proves an effect is not identifiable (the witness ID returns when no formula exists).
bow — a treatment with both a direct effect and hidden confounding on the same pair; the classic effect you cannot identify.
generalized adjustment criterion — the version of back-door adjustment that holds across every graph in an equivalence class, not just one.
amenability — a class is amenable when every possibly-causal path out of the treatment starts with a visible edge, so one adjustment set works for all its members.
visible edge — a directed edge certified to hide no confounder behind it.
possibly causal path / possible ancestor — a path (or reachability) that could be causal in some member of an equivalence class.
IDA — identify an effect across every member of a class and report the set of answers, rather than a single number.
mediation (NDE / NIE / CDE) — splitting a total effect into its direct part, its part through a mediator (indirect), and the direct effect with the mediator held fixed. See identification.
cross-world quantity — a counterfactual that compares two hypothetical worlds at once, so no single experiment can check it.
recanting witness — a post-treatment variable affecting both mediator and outcome, which blocks the natural mediation effects.

Graphs, marks, and equivalence classes¶

causal graph — a diagram with one node per variable and an arrow for each direct cause. See concepts.
DAG — a directed acyclic graph: one-way arrows, no loops; a fully known causal model. See concepts.
ADMG — a graph that adds two-headed arrows for hidden common causes. See learn: hidden confounding.
CPDAG — what constraint-based discovery returns: arrows where the data decides direction, dashes where several DAGs fit equally well. See concepts.
MAG — a graph type that handles hidden confounders and selection bias together. See concepts.
PAG — what FCI returns: a whole class of MAGs, with circle marks where the class cannot decide an endpoint. See concepts.
mixed graph — ergodic's single object whose edges carry a mark on each end, which lets it represent all the kinds above. See graph.
mark (tail / arrowhead / circle) — the symbol on an edge end: no-arrow, arrow, or unknown. See concepts.
glyph — the string spelling of an edge, like A -> B or A <-> B.
bidirected edge (<->) — an edge meaning two variables share a hidden common cause.
undirected edge (--) — an edge where adjacency is known but direction is not.
skeleton — a graph's adjacencies (who is connected to whom) with all arrow directions stripped off. See discovery.
v-structure — a collider whose two parents are not adjacent (X → Z ← Y with no X-Y edge); the fingerprint that discovery can orient from data.
unshielded triple — three nodes in a line A-B-C where A and C are not adjacent.
Markov equivalence class — the set of graphs that imply the same independences, so the data alone cannot tell them apart.
face (kind) — which graph type a result presents as: dag, cpdag, pag, or mixed. The "mixed face" means the result could not be certified as a valid member of a named class, often because knowledge (not data) oriented some edges. See discovery.
cpdag_valid / pag_valid — a 1.0 / 0.0 flag for whether a discovered graph is a valid CPDAG or PAG.
d-separation / m-separation — the graph rule for whether two variables are independent given a conditioning set (m-separation extends it to graphs with bidirected edges). See graph.
conditioning set — the variables you hold fixed when asking an independence question.
latent (hidden) node — a real cause that was never measured, so it is not a column in the data. See learn: hidden confounding.
latent projection — building the MAG or ADMG over just the observed variables, after projecting out the latents.
Meek rules — the deterministic rules that orient further edges in a CPDAG after the colliders are found.
FCI rules (Zhang's ten rules) — the orientation rules that complete a PAG, including the rules for selection bias.
almost-directed cycle — a loop that would become a directed cycle if a bidirected edge were read as directed; forbidden in a MAG.
ancestral graph / maximality — the conditions a MAG must satisfy; maximality means every non-adjacent pair can be separated by some set.

Estimation¶

estimation — plugging data into an estimand to get a number with its uncertainty. See inference.
EffectEstimate — ergodic's result object: a point with a standard error, draws, or a posterior, behind one interface.
estimator (strategy) — the object encoding how to turn an estimand into a number (for example, AIPW or DML).
learner — the swappable predict model (a scikit-learn-style fit/predict object) plugged into an estimator's slots. See inference.
nuisance model — a helper model the estimator needs (the outcome model, the treatment model) but does not itself report as the answer. See inference.
propensity (score) — the modeled probability of getting the treatment given the covariates, written P(treatment | covariates). See learn: estimating effects.
g-formula (outcome regression) — model the outcome, predict each unit with and without treatment, and average the gap.
IPW (inverse-probability weighting) — reweight units by one over their treatment probability, to mimic a randomized comparison.
AIPW (doubly robust) — combine an outcome model and a treatment model; the estimate is right if either model is right, and it comes with an exact standard error. The default. See inference.
doubly robust — the property that an estimator stays correct if at least one of its two models is correct.
DML (double machine learning) — a cross-fit estimator built to use flexible machine-learning models for its nuisances while keeping valid error bars; handles binary or continuous treatment. See learn: estimating effects.
meta-learner (S / T / X / R / DR-learner) — recipes for estimating per-unit (CATE) effects from standard predictive models.
CATE — the conditional average treatment effect: the effect as a function of who the unit is, instead of one average. See learn: heterogeneous effects.
influence function — a formula for how much each data point pulls on the estimate; its spread gives the standard error without resampling.
Neyman-orthogonality — an estimator built so that small errors in the nuisance models cancel to first order, which is what lets flexible models keep valid inference.
cross-fitting (out-of-fold) — fit the nuisance models on one slice of the data and score them on another, so flexible models cannot bias the estimate. See learn: estimating effects.
2SLS / Wald / PLIV — instrumental-variable estimators: two-stage least squares, the simplest ratio form, and the flexible orthogonal version.
ATE / ATT / LATE — the average effect over everyone / over the units actually treated / for the compliers an instrument moves.
standard error — how much the estimate would wobble if you reran the study. See learn: estimating effects.
confidence interval — a range of effect values compatible with the data; the 95% claim is about the procedure across repeats, not this one interval.
unbiased — an estimate centered on the true value on average, even if any single run is noisy.
posterior / credible interval — a Bayesian result: a full distribution over the estimate, and the interval that holds it with a stated probability.
Bayesian bootstrap — reweighting rows with random (Dirichlet) weights to carry sampling uncertainty into a posterior.
refutation (placebo test) — re-running the whole pipeline with the treatment deliberately broken (for example, scrambled); a trustworthy estimate should then collapse to about zero. See case studies.
balance table / standardized mean difference — a side-by-side of confounder averages in the treated versus untreated groups; the gap divided by the spread is a unit-free measure of imbalance. See case study: birthweight.

Discovery¶

causal discovery (structure learning) — learning the graph's edges from data instead of drawing them by hand. See discovery.
constraint-based — discovery that orients edges by testing which variables are conditionally independent (PC, FCI).
score-based — discovery that searches for the graph that maximizes a fit score (GES, BOSS, GRaSP).
conditional independence (CI) test — a statistical test of whether X and Y are independent once you hold a set Z fixed.
oracle — an object you query for independence answers: either the data-bound test, or a known graph used as ground truth.
separating set (sepset) — the conditioning set that makes two variables independent; the reason an edge between them is removed.
decomposable / score-equivalent — a score that is a sum of one local term per node (decomposable) and that scores graphs in the same class equally (score-equivalent).
PC — the classic constraint-based algorithm: build the skeleton, find colliders, propagate with Meek rules; returns a CPDAG. See discovery.
FCI / RFCI — discovery that tolerates hidden confounders and returns a PAG; RFCI is the faster relaxation.
MMPC / MMHC — a max-min independence screen that returns just a skeleton; MMHC adds a score search inside it.
GES — Greedy Equivalence Search: add edges then remove them, searching over equivalence classes; returns a CPDAG.
HillClimb / tabu — steepest-ascent search over DAGs with a short memory of recent moves to avoid cycling.
A* — an exact search for the single best-scoring DAG.
BOSS / GRaSP — order-based searches that rearrange a variable ordering; fast and, in tests, as good as the exact optimum.
DirectLiNGAM — discovery for linear data with non-Gaussian noise, which can orient edges a CPDAG would leave undecided.
glasso (graphical lasso) — a sparse estimate of the inverse covariance matrix whose nonzero entries form a skeleton.
PCMCI — time-series discovery on a lagged frame; the result is a window graph with one node per variable per lag. See discovery.
window graph — a discovered time-series graph whose nodes are variables at lags, like X[t-1].
contemporaneous edge — a same-time-step edge, which has no time order to help orient it.
Granger causality — a forecasting test (do X's past values improve predicting Y); it is confounding-blind, so ergodic returns it as a table, not a graph.
BIC / BDeu / EBIC — penalized-fit scores used to compare graphs (Gaussian, Bayesian-discrete, and the criterion that picks the lasso penalty).
bootstrap (stability) — rerun a method on resampled rows to see which edges keep showing up; a confidence signal, not a posterior.

Panel and quasi-experimental designs¶

panel data — the same units observed over the same time periods. See panel designs.
difference-in-differences (DiD) — subtract the comparison group's before-and-after change from the treated group's, to cancel both fixed differences and the shared calendar. See learn: quasi-experiments.
parallel trends — the DiD assumption: without the treatment, the two groups' outcomes would have moved up and down together (they can sit at different heights). See panel designs.
staggered adoption (cohort) — units that adopt the treatment at different dates, in groups.
group-time ATT (Callaway-Sant'Anna) — for staggered adoption, one small DiD per cohort and period, averaged together with cohort-size weights.
TWFE (two-way fixed effects) — a regression with unit and time dummies; it can be biased when adoption is staggered and the effect changes over time.
Goodman-Bacon decomposition — the result showing TWFE is a weighted mix of small comparisons, with weights that can go negative.
event study — one DiD estimate per distance from adoption (event time), tracing the effect over time and checking for pre-trends.
synthetic control — build a weighted blend of untreated "donor" units that tracks the treated unit before treatment; the gap afterward is the effect. See learn: quasi-experiments.
donor pool — the untreated units available to blend into a synthetic control.
placebo permutation — refit the method pretending each donor was the treated one, then rank the real unit's gap among them for a p-value.
RMSPE — root-mean-square prediction error; for synthetic control, how closely the blend tracked the treated unit before treatment.
interrupted time series (ITS) — for one series with a dated change and no comparison group, fit the level and slope before and after the break.
Newey-West (HAC) — standard errors that stay valid when a single series' errors are correlated over time.
Design record — the plain-words statement of a design's untestable assumptions; the panel-side counterpart of an Identification.

Process intelligence¶

event log — the native process record: one row per event, with a case id, an activity, and a timestamp. See process intelligence.
case / activity / timestamp — the thing flowing through the process, the step that happened, and when it happened.
process map (directly-follows graph, DFG) — counts of how often one activity directly follows another, with the time gaps; the first picture any process tool draws. See process intelligence.
variant — one distinct activity sequence; cases are grouped by it.
lifecycle (start / complete) — two stamps per step that let you split waiting time from working (service) time.
case_table — flattens a log to one row per case (treatment, outcome, covariates measured before the treatment moment) for the causal tools.
landmark — the fixed moment in a case's life where features are measured and the treatment is assessed.
post-treatment leakage — letting information from after the treatment into the adjustment set, which biases the estimate.
kpi_panel — aggregates a log into a panel (or time series) of per-period KPIs, ready for the panel designs.
process tree — a structured model of a process built from seq / xor / par / loop operators, with each activity a leaf. See process intelligence.
seq / xor / par / loop / TAU — run children in order / pick exactly one / interleave / repeat, plus TAU, a silent step that does nothing visible.
inductive miner — the algorithm that recovers a process tree by repeatedly cutting the directly-follows graph; its noise knob drops rare arcs.
workflow net (Petri net) — the executable form of a process tree. Tokens sit in places and flow through transitions (the steps); a marking is the current arrangement of tokens, and a transition fires to move them. See process intelligence.
soundness (is_sound) — the check that every run can finish, no run leaves a token stranded, and every step is reachable on some path.
conformance — measuring how well a log's real traces fit a model. See process intelligence.
token replay — push each trace through the net and count the tokens it had to invent or leave behind; a fast, forgiving fitness score.
optimal alignment — walk a trace and the model together and name each disagreement: a sync move (agree), a model move (a step the trace skipped), or a log move (an extra event).
decision point — an xor split read causally: the branch a case took becomes the treatment, and features from before the split are the covariates.
decision_table — one row per case for a single split, with the timing discipline built in, ready to estimate the effect of the branch.
PositivityReport / overlap_share — a per-branch coverage check and its warning flag, so you know when a comparison rests on too little data.

ergodic objects and entry points¶

MixedGraph (and dag, admg, cpdag, pag, mixed) — the one graph object and the typed builders that construct and validate it. See graph.
DomainKnowledge — the immutable set of hard prior constraints (tiers, required and forbidden edges, roots, sinks) that discovery and inference read. See domain knowledge.
tiers — a layering of variables by order in time; a later tier cannot cause an earlier one.
Dataset (and tabular, timeseries, panel, hts, event_log) — the typed data family; the shape picks which algorithms apply. See data.
Schema — the per-column type record (continuous, categorical, ordinal, datetime, excluded; binary is derived).
identify_effect / Identification — the call that turns a graph into an estimand, and the record it returns (identifiable, strategy, estimand).
estimate_effect — the call that takes a graph, data, a treatment, and an outcome, and returns an EffectEstimate. See inference.
discover / bootstrap — the discovery entry point and the resampling-stability wrapper. See discovery.
refute_effect — the entry point for refutation checks (placebo treatment and friends).