Capability catalog
Find a model semantic or causal analysis by the job it performs.
Browse Darkstar's probabilistic models and causal methods by the problem they solve. Every card explains the approach in plain language and links to background reading.
Probabilistic models
Choose a model for the structure in your problem.
These models cover static, temporal, causal, relational, decision, and uncertain systems. Start with the description, then use the model guides to compare questions, assumptions, and limits.
Bayesian Network (BN) (opens background reference in a new tab)
Represents dependencies between discrete variables using an acyclic graph and conditional probability tables.
Linear Gaussian Causal Model (opens background reference in a new tab)
Represents linear causal relationships between numerical variables with Gaussian disturbances.
Dynamic Bayesian Network (DBN) (opens background reference in a new tab)
Represents discrete variables over time using dependencies within each step and from the preceding step.
Hidden Markov Model (HMM) (opens background reference in a new tab)
Represents a hidden discrete state that changes over time and produces observable measurements.
Gaussian Dynamic Bayesian Network (DBN) (opens background reference in a new tab)
Represents evolving numerical variables through linear Gaussian dependencies within and across time steps.
Kalman State-Space Model (opens background reference in a new tab)
Represents a continuous hidden state with linear Gaussian transitions and noisy observations.
Conditional Linear Gaussian Model (CLG) (opens background reference in a new tab)
Represents mixed discrete and continuous variables by letting discrete states select linear Gaussian relationships.
Factor Graph (opens background reference in a new tab)
Represents a joint distribution as a product of factors over subsets of discrete variables.
Markov Random Field (MRF) (opens background reference in a new tab)
Represents dependencies among discrete variables through an undirected graph and local factors.
Temporal Conditional Linear Gaussian Model (CLG) (opens background reference in a new tab)
Represents mixed discrete and continuous processes using conditional linear Gaussian relationships repeated over time.
Latent Gaussian Causal Model (opens background reference in a new tab)
Represents linear Gaussian causal systems with correlated disturbances that account for unobserved shared causes.
Partially Observable Markov Decision Process (POMDP) (opens background reference in a new tab)
Represents sequential decisions where the true state is hidden and actions depend on beliefs formed from observations.
Markov Decision Process (MDP) (opens background reference in a new tab)
Represents sequential decisions where the current state is fully observed and actions affect future states and rewards.
Continuous-Time Bayesian Network (CTBN) (opens background reference in a new tab)
Represents discrete variables that change at conditional transition rates in continuous time.
Sum-Product Probabilistic Circuit (opens background reference in a new tab)
Represents a probability distribution through weighted sums and products arranged for tractable inference.
Decision Analysis Network (DAN) (opens background reference in a new tab)
Represents chance events, decisions, utilities, and the information available when each decision is made.
Gaussian Process Regression (GPR) (opens background reference in a new tab)
Represents uncertainty about a continuous function using a covariance kernel and observed input-output pairs.
Lauritzen–Wermuth–Frydenberg Chain Graph (LWF) (opens background reference in a new tab)
Represents discrete dependencies using directed and undirected edges under the Lauritzen–Wermuth–Frydenberg interpretation.
Functional Structural Causal Model (SCM) (opens background reference in a new tab)
Represents each variable as an explicit function of its causes and exogenous noise.
Credal Network (opens background reference in a new tab)
Represents imprecise probabilities through sets of distributions, yielding lower and upper probability bounds.
Influence Diagram with Perfect Recall (ID) (opens background reference in a new tab)
Represents sequential decisions where each decision retains all earlier observations and decisions.
Limited-Memory Influence Diagram (LIMID) (opens background reference in a new tab)
Represents sequential decisions with explicit restrictions on the information each decision can use.
Markov Influence Diagram (MID) (opens background reference in a new tab)
Represents finite-horizon decision problems using state transitions, actions, and utilities in a graphical model.
Probabilistic Relational Model / Object-Oriented Bayesian Network (PRM/OOBN) (opens background reference in a new tab)
Represents finite systems of related objects with reusable probabilistic structure for their classes and attributes.
Probabilistic Logic Program (PLP) (opens background reference in a new tab)
Represents uncertainty using probabilistic facts and deterministic rules over a finite set of objects.
Probabilistic Soft Logic / Hinge-Loss Markov Random Field (PSL/HL-MRF) (opens background reference in a new tab)
Represents soft truth values through weighted logical rules expressed as hinge-loss potentials and hard constraints.
Linear-Chain Conditional Random Field (CRF) (opens background reference in a new tab)
Represents the probability of a label sequence given observed features and dependencies between adjacent labels.
Gaussian Markov Random Field (GMRF) (opens background reference in a new tab)
Represents a latent Gaussian field through sparse conditional dependencies and an observation model.
Switching Linear Dynamical System (SLDS) (opens background reference in a new tab)
Represents a continuous state whose linear Gaussian dynamics change according to a discrete regime.
Nonlinear Non-Gaussian State-Space Model (opens background reference in a new tab)
Represents hidden states and observations with nonlinear mechanisms and noise that need not be Gaussian.
Andersson–Madigan–Perlman Chain Graph (AMP) (opens background reference in a new tab)
Represents discrete dependencies using directed and undirected edges under the Andersson–Madigan–Perlman interpretation.
Causal analysis
Start with the causal task, then inspect the method identity.
A method name does not establish identification. Data, estimand, design assumptions, diagnostics, and sensitivity checks remain part of the analysis.
Effect estimation 14
G-Computation (opens background reference in a new tab)
Estimates average outcomes under each treatment by averaging predictions from an outcome model.
Inverse Probability Weighting (IPW) (opens background reference in a new tab)
Estimates a treatment effect by weighting observations according to the inverse probability of their received treatment.
Inverse Probability of Censoring Weighting (IPCW) (opens background reference in a new tab)
Adjusts treatment-effect estimation for observation or censoring probabilities using inverse weights.
Augmented Inverse Probability Weighting (AIPW) (opens background reference in a new tab)
Combines outcome predictions with treatment-probability weights to estimate an average treatment effect.
Targeted Maximum Likelihood Estimation (TMLE) (opens background reference in a new tab)
Updates an initial outcome model toward a targeted estimate of the average effect of a binary treatment.
Treatment-Effect Generalized Method of Moments (GMM) (opens background reference in a new tab)
Estimates a treatment effect by solving declared regression-adjustment or weighting moment conditions.
Sample-Selection Adjustment (opens background reference in a new tab)
Estimates an average treatment effect while adjusting for the process that determines which outcomes are observed.
Partially Linear Regression Double Machine Learning (PLR DML) (opens background reference in a new tab)
Estimates a treatment coefficient after removing covariate-driven variation from treatment and outcome.
Logistic Partially Linear Regression (Logistic PLR) (opens background reference in a new tab)
Estimates a marginal treatment contrast for a binary outcome with flexible adjustment for covariates.
Interactive Regression Model (IRM) (opens background reference in a new tab)
Estimates average treatment effects using separate outcome relationships for treated and untreated observations.
Average Potential Outcome (APO) (opens background reference in a new tab)
Estimates the population mean outcome that would occur under a specified treatment.
Multiple-Treatment Average Potential Outcomes (APO) (opens background reference in a new tab)
Estimates the mean potential outcome for each treatment in a declared set of treatment options.
Nonparametric Double Machine Learning (DML) (opens background reference in a new tab)
Estimates a flexible treatment-effect function using orthogonalized outcome and treatment information.
Staggered-Adoption Group-Time Effects (opens background reference in a new tab)
Estimates separate treatment effects for groups that begin treatment at different times.
Design and identification 14
Tabular Front-Door Adjustment (opens background reference in a new tab)
Estimates a total causal effect through a measured mediator when the front-door identification conditions hold.
Linear Two-Stage Least Squares (2SLS) (opens background reference in a new tab)
Estimates a linear treatment effect using an instrument to isolate treatment variation.
Partially Linear Instrumental Variables (PLIV) (opens background reference in a new tab)
Estimates a treatment coefficient with an instrument while allowing flexible adjustment for observed covariates.
Interactive Instrumental Variable Model (IIVM) (opens background reference in a new tab)
Estimates a complier treatment effect with a binary instrument and treatment using flexible outcome and assignment models.
External Out-of-Fold Predictions (OOF) (opens background reference in a new tab)
Validates externally supplied nuisance predictions and fold assignments for use in cross-fitted causal estimation.
Sharp Regression Discontinuity Design (RDD) (opens background reference in a new tab)
Estimates a local treatment effect at a cutoff that deterministically assigns treatment.
Fuzzy Regression Discontinuity Design (RDD) (opens background reference in a new tab)
Estimates a local complier effect where crossing a cutoff changes the probability of treatment.
Covariate-Adjusted Regression Discontinuity Design (RDD) (opens background reference in a new tab)
Estimates a local cutoff effect while adjusting for observed covariates.
Instrumental Forest (opens background reference in a new tab)
Estimates heterogeneous treatment effects from instrument-induced treatment variation.
Selection-Diagram Data Fusion (opens background reference in a new tab)
Combines data sources to identify an effect under declared graphical assumptions about population differences.
Linear Proximal Causal Effect (opens background reference in a new tab)
Estimates a treatment effect through linear bridge functions using observed proxies for unmeasured confounders.
Intervention Calculus with an Absent Directed Acyclic Graph (IDA) (opens background reference in a new tab)
Evaluates possible causal effects across graphs consistent with a partially specified causal structure.
Generalized Covariate Adjustment (opens background reference in a new tab)
Checks which covariate sets identify a causal effect under the graph's adjustment criterion.
Partially Linear Instrumental Variables Weak-Instrument Check (PLIV) (opens background reference in a new tab)
Assesses whether the instrument supplies enough treatment variation for the declared partially linear analysis.
Longitudinal and panel designs 16
Panel Partially Linear Regression (Panel PLR) (opens background reference in a new tab)
Estimates a treatment coefficient in panel data while adjusting for covariates and the declared panel structure.
Two-Group, Two-Period Difference-in-Differences (DiD) (opens background reference in a new tab)
Estimates the effect on a treated group by comparing its before-and-after change with a control group.
Panel Difference-in-Differences (DiD) (opens background reference in a new tab)
Estimates treatment effects from repeated observations of the same units before and after treatment.
Repeated Cross-Section Difference-in-Differences (DiD) (opens background reference in a new tab)
Estimates treatment effects from before-and-after population samples that need not contain the same individuals.
Two-Way Fixed Effects (TWFE) (opens background reference in a new tab)
Estimates a declared panel treatment coefficient after accounting for unit and time fixed effects.
Event Study (opens background reference in a new tab)
Estimates a sequence of treatment effects indexed by time before or after treatment begins.
Two-Stage Difference-in-Differences (DiD) (opens background reference in a new tab)
Estimates a treatment effect in a second stage after removing untreated outcome patterns in a first stage.
Local-Projection Difference-in-Differences (DiD) (opens background reference in a new tab)
Estimates treatment responses at separate time horizons using local-projection comparisons.
Synthetic Control (opens background reference in a new tab)
Estimates an intervention effect by comparing a treated unit with a weighted combination of untreated donor units.
Synthetic Difference-in-Differences (SDiD) (opens background reference in a new tab)
Estimates a panel treatment effect using unit and time weights to improve treated-control comparability.
Low-Rank Panel Counterfactuals (opens background reference in a new tab)
Estimates untreated outcomes by completing a low-rank panel and compares them with observed treated outcomes.
Segmented Interrupted Time Series (ITS) (opens background reference in a new tab)
Estimates changes in outcome level and trend at a declared intervention time.
Comparative Interrupted Time Series (ITS) (opens background reference in a new tab)
Estimates an intervention effect by comparing changes in a treated time series with a control series.
Bayesian Structural Time-Series Causal Impact (BSTS) (opens background reference in a new tab)
Estimates intervention impact by comparing observations with a posterior forecast of the untreated time series.
Geographic Lift (opens background reference in a new tab)
Estimates incremental outcomes across treated and comparison regions under a declared geographic study design.
Synthetic Control Diagnostics (opens background reference in a new tab)
Assesses synthetic-control credibility with donor placebo comparisons and leave-one-out checks.
Heterogeneous effects 19
Doubly Robust Conditional Average Treatment Effect (DR-CATE) (opens background reference in a new tab)
Estimates how treatment effects vary with observed characteristics using cross-fitted outcome and propensity predictions.
Binary-Treatment Causal Forest (opens background reference in a new tab)
Estimates how the effect of a binary treatment varies across observations using an ensemble of causal trees.
Double Machine Learning Orthogonal Forest (DML) (opens background reference in a new tab)
Estimates local treatment effects with forest weights and orthogonalized outcome and treatment models.
Doubly Robust Orthogonal Forest (DR) (opens background reference in a new tab)
Estimates local treatment effects with forest weights and doubly robust outcome and propensity adjustments.
Causal Forest with Double Machine Learning (DML) (opens background reference in a new tab)
Estimates heterogeneous treatment effects with an honest forest fitted to residualized treatment and outcome information.
Doubly Robust Forest (DR) (opens background reference in a new tab)
Estimates heterogeneous treatment effects by fitting a forest to doubly robust effect targets.
Single-Model Meta-Learner (S-Learner) (opens background reference in a new tab)
Estimates conditional treatment effects by comparing predictions from one outcome model with treatment as an input.
Two-Model Meta-Learner (T-Learner) (opens background reference in a new tab)
Estimates conditional treatment effects by comparing separate treated and untreated outcome models.
Imputed-Effect Meta-Learner (X-Learner) (opens background reference in a new tab)
Estimates conditional treatment effects by combining effect models fitted to imputed treatment contrasts.
Residual-Loss Meta-Learner (R-Learner) (opens background reference in a new tab)
Estimates conditional treatment effects by minimizing a loss based on residualized outcomes and treatments.
Uplift Tree (opens background reference in a new tab)
Partitions observations into groups with different incremental responses to treatment.
Uplift Forest (opens background reference in a new tab)
Combines multiple uplift trees to score how incremental treatment responses vary across observations.
Causal Tree (opens background reference in a new tab)
Estimates treatment effects within subgroups while separating tree construction from effect estimation.
Multiple-Treatment Causal Forest (opens background reference in a new tab)
Estimates heterogeneous treatment contrasts across multiple treatment arms using a causal forest.
Restricted Mean Survival Time Forest (RMST) (opens background reference in a new tab)
Estimates heterogeneous treatment effects on expected survival time up to a specified horizon.
Survival Probability Forest (opens background reference in a new tab)
Estimates heterogeneous treatment effects on the probability of surviving beyond a specified time.
Continuous-Treatment Partial-Effect Forest (opens background reference in a new tab)
Estimates how a continuous treatment locally changes the outcome across different covariate profiles.
Conditional-Effect Result Evaluation (opens background reference in a new tab)
Evaluates a previously fitted conditional-effect result for declared observations and treatment contrasts.
Policy Tree or Forest (opens background reference in a new tab)
Evaluates treatment decisions learned as a tree or forest of rules based on observed characteristics.
Distributional, dose, and transport effects 7
Potential-Outcome Quantiles (opens background reference in a new tab)
Estimates quantiles of the outcome distribution under each declared treatment.
Quantile Treatment Effects (QTE) (opens background reference in a new tab)
Compares treatment-specific outcome quantiles across a declared probability grid.
Conditional Distribution Treatment Effects (CDTE) (opens background reference in a new tab)
Compares treatment-specific outcome distribution probabilities at declared thresholds and covariate profiles.
Dose-Response Curve (opens background reference in a new tab)
Estimates how the mean outcome changes across a declared grid of treatment doses.
Generalized Propensity Score Dose Response (GPS) (opens background reference in a new tab)
Estimates a dose-response curve while adjusting for the conditional distribution of a continuous treatment.
Stochastic Intervention (opens background reference in a new tab)
Estimates the mean outcome under a treatment policy that assigns treatments probabilistically.
Transported Treatment Effect (opens background reference in a new tab)
Estimates a treatment effect for a target population using information from a different source population.
Diagnostics and sensitivity 11
Placebo Treatment Check (opens background reference in a new tab)
Tests whether replacing the treatment with a placebo assignment produces an unexpected estimated effect.
Random Common-Cause Check (opens background reference in a new tab)
Checks how an effect estimate changes after adding a randomly generated candidate confounder.
Unobserved-Confounder Sensitivity (opens background reference in a new tab)
Traces how an estimated effect changes across declared strengths of unmeasured confounding.
Data-Subset Stability Check (opens background reference in a new tab)
Checks how an effect estimate changes when the analysis is repeated on subsets of the data.
Bootstrap Stability Check (opens background reference in a new tab)
Assesses variation in an effect estimate by repeatedly resampling the observed data.
Negative-Control Check (opens background reference in a new tab)
Tests a relationship expected to have no causal effect to detect possible bias or model problems.
Rosenbaum Sensitivity Bounds (opens background reference in a new tab)
Bounds the sensitivity of matched-study conclusions to hidden differences in treatment assignment odds.
E-Value Sensitivity (opens background reference in a new tab)
Summarizes the unmeasured-confounding strength needed to explain away a declared risk-ratio effect.
Ordinary Least Squares Partial R-Squared Sensitivity (OLS) (opens background reference in a new tab)
Assesses how omitted-variable relationships with treatment and outcome could change a linear effect estimate.
Treatment Overlap Diagnostics (opens background reference in a new tab)
Checks whether treated and untreated observations have sufficient overlap in their treatment probabilities.
Pre-Treatment Trend Diagnostics (opens background reference in a new tab)
Checks whether differences in outcome trends are evident before treatment begins.
Mediation and pathways 6
Controlled Direct Effect (opens background reference in a new tab)
Measures the treatment effect when the mediator is held at a specified value.
Natural Direct Effect (opens background reference in a new tab)
Measures the treatment effect while the mediator follows its natural value under the reference treatment.
Natural Indirect Effect (opens background reference in a new tab)
Measures the effect transmitted through treatment-induced changes in the mediator.
Total Effect (opens background reference in a new tab)
Measures the combined direct and mediated effect of changing the treatment.
Path-Specific Effect (opens background reference in a new tab)
Measures the treatment effect transmitted along selected causal paths.
Interventional Mediation (opens background reference in a new tab)
Separates direct and indirect effects using interventions on the mediator's distribution.
Policy evaluation and optimization 10
Propensity Score Matching (PSM) (opens background reference in a new tab)
Estimates a treatment effect by comparing treated and untreated observations with similar treatment probabilities.
Propensity Score Subclassification (opens background reference in a new tab)
Estimates an average treatment effect by combining comparisons within groups of similar propensity scores.
Contextual Bandit Policy Value (opens background reference in a new tab)
Estimates the expected reward of a target action policy using contextual logged decisions.
Inverse Propensity Scoring / Self-Normalized Inverse Propensity Scoring (IPS/SNIPS) (opens background reference in a new tab)
Estimates target-policy value by reweighting logged rewards, optionally normalizing the weights.
Doubly Robust Off-Policy Evaluation (DR-OPE) (opens background reference in a new tab)
Estimates target-policy value by combining reward predictions with importance-weighted corrections.
Sequential Doubly Robust Policy Evaluation (DR) (opens background reference in a new tab)
Estimates finite-horizon policy value using reward predictions and sequential importance-weighted corrections.
Fitted Q Evaluation (FQE) (opens background reference in a new tab)
Estimates a target policy's value by repeatedly fitting its expected future reward function.
Structural Policy Replay (opens background reference in a new tab)
Evaluates a target policy within a structural model while reusing the same exogenous randomness across policy comparisons.
Dynamic Treatment Regime (DTR) (opens background reference in a new tab)
Evaluates a sequence of treatment rules that adapt to an individual's observed history.
Finite-Horizon Policy Optimization (opens background reference in a new tab)
Selects a policy using a conservative estimate of its value over a declared finite horizon.
Bayesian causal profiles 4
Bayesian Causal Generalized Linear Model (GLM) (opens background reference in a new tab)
Estimates a posterior treatment contrast with a Bayesian linear or generalized linear outcome model.
Hierarchical Bayesian Treatment Effects (opens background reference in a new tab)
Estimates population and group treatment effects with partial pooling across groups.
Bayesian Additive Regression Trees for Causal Effects (BART) (opens background reference in a new tab)
Estimates nonlinear conditional treatment effects with a posterior ensemble of regression trees.
Gaussian Process Causal Surface (GP) (opens background reference in a new tab)
Estimates a smooth treatment-effect surface with posterior uncertainty using a Gaussian process.