Describe
Working knowledge
Notes for reasoning with data.
A connected, illustrated statistics curriculum: start with a scientific question, follow the decision guide, and move from study design to defensible inference, prediction, and bioimage analysis.
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Explore how the ideas connect.
Each point is a note. Lines reveal shared concepts; larger points are highly connected foundations. Drag the field, scroll to zoom, hover to inspect, or select a note to open it.
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FoundationsStudy designModelsBayesianTime & survivalImaging
Adaptive decision guide
Tell me about the question and the data.
Answer one question at a time. The guide checks design, sample size, dependence, outcome type and assumptions before suggesting concepts or tests.
Step 1
Start hereWhat do you need to learn from the data?
Compare
Do groups or conditions differ?
Associate
Do two measurements vary together?
Count
Are outcomes categorical or frequency based?
Predict
How well does a model perform?
Infer
How uncertain is an estimate?
Design
Can the study answer the question?
Model
How does an outcome depend on predictors?
Update
What does the evidence make plausible?
Follow
Are observations ordered in time?
Cause
What would an intervention change?
Image
What is the biological unit?
278 notes
14 min read
A/B testing from design to analysis
A reference-level guide to a/b testing from design to analysis: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Accelerated failure-time models
A reference-level guide to accelerated failure-time models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Alpha-spending functions
A reference-level guide to alpha-spending functions: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Always-valid p-values and e-values
A reference-level guide to always-valid p-values and e-values: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
ANCOVA: adjusted group comparisons
A reference-level guide to ancova: adjusted group comparisons: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
p, np, c, and u charts
A reference-level guide to p, np, c, and u charts: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Beta regression for proportions
A reference-level guide to beta regression for proportions: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Bland–Altman agreement analysis
A reference-level guide to bland–altman agreement analysis: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Bonferroni and Šidák corrections
A reference-level guide to bonferroni and šidák corrections: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Calibration, traceability, and uncertainty budgets
A reference-level guide to calibration, traceability, and uncertainty budgets: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Statistical change-point detection
A reference-level guide to statistical change-point detection: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Competing risks and cumulative incidence
A reference-level guide to competing risks and cumulative incidence: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Completeness and ancillary statistics
A reference-level guide to completeness and ancillary statistics: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Compositional data and log-ratio models
A reference-level guide to compositional data and log-ratio models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Conditional probability and independence
A reference-level guide to conditional probability and independence: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Crossover designs, period, and carryover
A reference-level guide to crossover designs, period, and carryover: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
CUSUM control charts
A reference-level guide to cusum control charts: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Delta method and asymptotic normality
A reference-level guide to delta method and asymptotic normality: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Diagnostic-test meta-analysis
A reference-level guide to diagnostic-test meta-analysis: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Doubly robust estimation
A reference-level guide to doubly robust estimation: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Dunn rank-based post-hoc testing
A reference-level guide to dunn rank-based post-hoc testing: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Equivalence studies and TOST
A reference-level guide to equivalence studies and tost: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
EWMA control charts
A reference-level guide to ewma control charts: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Expectation, variance, and covariance
A reference-level guide to expectation, variance, and covariance: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
ETS and exponential-smoothing models
A reference-level guide to ets and exponential-smoothing models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Fine–Gray subdistribution hazards
A reference-level guide to fine–gray subdistribution hazards: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Fisher information and the Cramér–Rao bound
A reference-level guide to fisher information and the cramér–rao bound: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Fixed- and random-effects meta-analysis
A reference-level guide to fixed- and random-effects meta-analysis: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Rolling-origin forecast evaluation
A reference-level guide to rolling-origin forecast evaluation: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Forest plots and meta-regression
A reference-level guide to forest plots and meta-regression: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Fourier and wavelet time-frequency analysis
A reference-level guide to fourier and wavelet time-frequency analysis: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Fractional factorial designs and aliasing
A reference-level guide to fractional factorial designs and aliasing: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Full factorial designs and interactions
A reference-level guide to full factorial designs and interactions: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
8 min read
Gauge R&R: is your measurement noisier than what you're measuring?
How Gauge R&R separates real differences between specimens from noise introduced by repeated measurement, operators, or instruments — and how to read the %GRR number honestly.
14 min read
Games–Howell post-hoc comparisons
A reference-level guide to games–howell post-hoc comparisons: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Generalized estimating equations
A reference-level guide to generalized estimating equations: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Generalized linear mixed models
A reference-level guide to generalized linear mixed models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Group-sequential designs
A reference-level guide to group-sequential designs: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Heterogeneity: Q, I², and tau²
A reference-level guide to heterogeneity: q, i², and tau²: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Hidden Markov models
A reference-level guide to hidden markov models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Hierarchical Bayesian models
A reference-level guide to hierarchical bayesian models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Holm, Hommel, and Hochberg procedures
A reference-level guide to holm, hommel, and hochberg procedures: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Huber and Tukey loss functions
A reference-level guide to huber and tukey loss functions: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Hurdle models
A reference-level guide to hurdle models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Instrumental variables and two-stage least squares
A reference-level guide to instrumental variables and two-stage least squares: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Intraclass correlation coefficients
A reference-level guide to intraclass correlation coefficients: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Inverse-probability weighting
A reference-level guide to inverse-probability weighting: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Joint, marginal, and conditional distributions
A reference-level guide to joint, marginal, and conditional distributions: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Kriging and Gaussian processes
A reference-level guide to kriging and gaussian processes: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Latin-square and split-plot designs
A reference-level guide to latin-square and split-plot designs: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Least-median and least-trimmed squares
A reference-level guide to least-median and least-trimmed squares: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Likelihood-ratio, score, and Wald tests
A reference-level guide to likelihood-ratio, score, and wald tests: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Limits of detection and quantification
A reference-level guide to limits of detection and quantification: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
M-estimation and robust regression
A reference-level guide to m-estimation and robust regression: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
MANCOVA with covariate adjustment
A reference-level guide to mancova with covariate adjustment: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
MANOVA for multiple outcomes
A reference-level guide to manova for multiple outcomes: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Marked point patterns
A reference-level guide to marked point patterns: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Maximum-likelihood properties
A reference-level guide to maximum-likelihood properties: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Causal mediation analysis
A reference-level guide to causal mediation analysis: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Method-of-moments estimation
A reference-level guide to method-of-moments estimation: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Mixed between-within ANOVA
A reference-level guide to mixed between-within anova: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Almost-sure, probability, and distributional convergence
A reference-level guide to almost-sure, probability, and distributional convergence: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Moment-generating and characteristic functions
A reference-level guide to moment-generating and characteristic functions: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Multi-state and illness-death models
A reference-level guide to multi-state and illness-death models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Multinomial logistic regression
A reference-level guide to multinomial logistic regression: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Multivariate SPC and Hotelling T²
A reference-level guide to multivariate spc and hotelling t²: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Nested and crossed multilevel structures
A reference-level guide to nested and crossed multilevel structures: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Network meta-analysis
A reference-level guide to network meta-analysis: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Non-inferiority designs
A reference-level guide to non-inferiority designs: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Ordinal logistic regression
A reference-level guide to ordinal logistic regression: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Partial pooling and shrinkage
A reference-level guide to partial pooling and shrinkage: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Permutation ANOVA and PERMANOVA
A reference-level guide to permutation anova and permanova: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Planned contrasts and orthogonality
A reference-level guide to planned contrasts and orthogonality: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Spatial point processes
A reference-level guide to spatial point processes: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Poisson and Cox point processes
A reference-level guide to poisson and cox point processes: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Power for equivalence, survival, and repeated measures
A reference-level guide to power for equivalence, survival, and repeated measures: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Power for factorial and cluster-randomized designs
A reference-level guide to power for factorial and cluster-randomized designs: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Process capability: Cp and Cpk
A reference-level guide to process capability: cp and cpk: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Publication bias and funnel plots
A reference-level guide to publication bias and funnel plots: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Quantile regression
A reference-level guide to quantile regression: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Random slopes and crossed random effects
A reference-level guide to random slopes and crossed random effects: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Random variables and transformations
A reference-level guide to random variables and transformations: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
RANSAC regression
A reference-level guide to ransac regression: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Recurrent-event survival models
A reference-level guide to recurrent-event survival models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Regression-discontinuity designs
A reference-level guide to regression-discontinuity designs: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Repeatability and reproducibility studies
A reference-level guide to repeatability and reproducibility studies: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Repeated-measures ANOVA
A reference-level guide to repeated-measures anova: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Response-surface methodology
A reference-level guide to response-surface methodology: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Robust covariance and Mahalanobis distance
A reference-level guide to robust covariance and mahalanobis distance: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Sandwich and cluster-robust standard errors
A reference-level guide to sandwich and cluster-robust standard errors: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Scheffé simultaneous contrasts
A reference-level guide to scheffé simultaneous contrasts: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Clinical sensitivity, specificity, and predictive values
A reference-level guide to clinical sensitivity, specificity, and predictive values: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Sequential probability-ratio tests
A reference-level guide to sequential probability-ratio tests: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Shewhart control charts
A reference-level guide to shewhart control charts: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Sigma-algebras, events, and probability spaces
A reference-level guide to sigma-algebras, events, and probability spaces: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Simultaneous confidence intervals and bands
A reference-level guide to simultaneous confidence intervals and bands: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Spatial autocorrelation and Moran’s I
A reference-level guide to spatial autocorrelation and moran’s i: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Spatial scan statistics and cluster detection
A reference-level guide to spatial scan statistics and cluster detection: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Spectral density and the periodogram
A reference-level guide to spectral density and the periodogram: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
State-space models and Kalman filtering
A reference-level guide to state-space models and kalman filtering: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Stratified Cox models
A reference-level guide to stratified cox models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Sufficiency and the factorization theorem
A reference-level guide to sufficiency and the factorization theorem: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Synthetic-control methods
A reference-level guide to synthetic-control methods: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Statistical workflow for systematic reviews
A reference-level guide to statistical workflow for systematic reviews: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Target-trial emulation
A reference-level guide to target-trial emulation: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Time-varying covariates in Cox models
A reference-level guide to time-varying covariates in cox models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Two-way factorial ANOVA
A reference-level guide to two-way factorial anova: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Variance components and intraclass correlation
A reference-level guide to variance components and intraclass correlation: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Variograms and spatial covariance
A reference-level guide to variograms and spatial covariance: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Vector autoregression
A reference-level guide to vector autoregression: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Zero-inflated negative-binomial models
A reference-level guide to zero-inflated negative-binomial models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
14 min read
Zero-inflated Poisson models
A reference-level guide to zero-inflated poisson models: theory, assumptions, diagnostics, worked bioimaging analysis, exercises, and reporting.
6 min read
AlexNet: the result that ended the debate about deep learning
How a convolutional network trained on two GPUs cut ImageNet error by a margin large enough to reset computer vision, and why every microscopy segmentation model on this site descends from it.
6 min read
ARIMA models
Model autoregressive dependence, differencing, and lagged shocks for univariate forecasting and residual analysis.
6 min read
Batch effects and harmonization
Separate biological differences from acquisition-day, instrument, staining, or processing shifts without erasing real biology.
6 min read
Bayes factors and Bayesian model comparison
Compare marginal evidence carefully, recognising sensitivity to prior scale and the distinction from posterior predictive quality.
6 min read
Bayes theorem for statistical inference
Update prior plausibility with data evidence and distinguish posterior probability from a p-value.
6 min read
Bias, variance, and mean-squared error
Decompose estimation error into systematic displacement and sampling variability.
6 min read
Blinding, preregistration, and analysis plans
Reduce conscious and unconscious analytic flexibility by separating confirmatory decisions from observed results.
6 min read
CARE: trading photons for computation
How a network trained on paired noisy/clean images turned denoising into something learnable — recovering usable data from far fewer photons than direct acquisition needs.
6 min read
Causal directed acyclic graphs
Encode assumed causal structure to identify confounders, mediators, colliders, and defensible adjustment sets.
6 min read
Cellpose: segmentation that generalises because it doesn't assume a shape
Why predicting a flow field toward each object's centre, instead of a mask directly, let one trained model segment cell types it had never seen — without retraining.
6 min read
CLIP: learning to see from what images are captioned, not labelled
How pairing images with their naturally occurring text turned classification into a similarity search, and why that's the conceptual ancestor of every open-vocabulary vision tool since.
6 min read
How to interpret confidence intervals
Use confidence intervals as procedure-based ranges of compatible parameter values, not posterior probabilities.
6 min read
Confounding, mediation, and collider bias
Distinguish variables that open biasing paths from those that close them or lie on the causal pathway.
6 min read
Cox proportional-hazards regression
Relate covariates to instantaneous event rates without specifying the baseline hazard.
6 min read
Credible intervals and highest-density intervals
Summarise posterior uncertainty with direct probability statements while preserving skew or multimodality when important.
6 min read
Cross-validation without data leakage
Estimate generalisation by keeping preprocessing, tuning, and correlated groups inside correctly separated folds.
6 min read
Van Valen et al.: CNNs learn live-cell tracking from ~100 annotated cells
One of the earliest demonstrations that a small amount of manual annotation was enough to train a CNN that out-tracked classical live-cell segmentation methods — the work that grew into DeepCell.
6 min read
Difference-in-differences
Estimate differential before-after change under a defensible parallel-trends assumption.
6 min read
DINOv2: features learned with no labels at all
How a self-supervised training recipe produced general-purpose visual features that match supervised pretraining — the exact constraint most scientific imaging labs work under: plenty of images, almost no annotation.
6 min read
DINOv3: fixing the feature drift that blocked longer self-supervised training
Why dense patch-level features used to degrade over very long self-supervised training runs, and how Gram anchoring fixed it well enough to be the first SSL model to beat weakly-supervised alternatives broadly.
6 min read
Estimands and estimators
Define the exact scientific quantity of interest before choosing a test or model.
7 min read
Generalized linear models: when your outcome isn't a bell curve
Ordinary linear regression assumes continuous, symmetric, constant-variance noise. GLMs swap in a distribution and link function that actually match counts, binary outcomes, or skewed intensities.
6 min read
Image-level versus cell-level inference
Match the inferential unit to treatment assignment and biological replication rather than the number of segmented objects.
6 min read
Kaplan-Meier curves and the log-rank test
Estimate survival functions under censoring and compare groups across event times.
6 min read
Law of large numbers
Understand why averages stabilise with increasing independent observations and why dependence can defeat the intuition.
6 min read
Likelihood and log-likelihood
View observed data as evidence for competing parameter values and understand maximum-likelihood estimation.
6 min read
Logistic regression
Model binary-outcome probabilities through log odds and interpret coefficients on odds or probability scales.
6 min read
Longitudinal growth curves
Model individual trajectories, irregular timing, and between-unit variability rather than collapsing each series prematurely.
6 min read
Mask R-CNN: instance segmentation as detection plus one branch
How adding a single mask-prediction branch onto an existing object detector turned 'find the objects' into 'find and precisely outline every object' — and the alignment fix that made small-object masks accurate.
7 min read
Measurement error propagation: your final number is a chain of estimates
Every derived measurement carries the uncertainty of everything that fed into it — calibration, segmentation, background. Propagation is how you compute the combined uncertainty instead of ignoring it.
6 min read
MCAR, MAR, and MNAR missing data
Identify why values are missing before choosing complete-case analysis, imputation, or sensitivity analysis.
7 min read
Mixed-effects models: letting every group have its own baseline
How random effects let a model respect that cells nested in wells nested in experiments aren't independent, without throwing away the structure by averaging it all flat.
6 min read
Multicollinearity and variance inflation
Understand unstable coefficients caused by strongly correlated predictors and use domain-guided feature reduction.
6 min read
Multiple imputation
Propagate uncertainty from plausible missing values instead of replacing each missing entry once.
6 min read
Multiple linear regression
Estimate partial associations while controlling specified covariates and avoiding causal overinterpretation.
7 min read
Evaluating object detection: matching, not just counting
Why detection and counting metrics live or die on the matching rule between predictions and ground truth — and how duplicate detections and missed objects distort the count.
6 min read
Poisson and negative-binomial regression
Model event counts with exposure offsets and handle overdispersion when variance exceeds the Poisson mean.
6 min read
Polynomial regression and splines
Model smooth nonlinear relationships without forcing a single straight-line effect.
6 min read
Population, sample, parameter, and statistic
Separate the population target from the observed sample and the unknown parameter from its calculated estimate.
6 min read
Posterior predictive checks
Evaluate whether replicated data from a fitted Bayesian model resemble important features of the observations.
7 min read
Power analysis: how many independent replicates do you actually need?
Statistical power is the probability of detecting a real effect of a given size. Sample-size planning runs that logic backward, before data collection, using a realistic estimate of noise.
6 min read
Prediction intervals
Distinguish uncertainty in a mean response from uncertainty for a new individual observation.
6 min read
Priors and prior-predictive checks
Encode plausible parameter scales and test their implications before observing the study outcome.
6 min read
Propensity scores and covariate balance
Use treatment-assignment probabilities for matching or weighting while checking overlap and balance rather than predictive accuracy.
6 min read
Pseudoreplication and the experimental unit
Avoid treating nested technical observations as independent biological evidence.
6 min read
Randomization, blocking, and allocation concealment
Use random allocation and blocking to balance nuisance variables without leaking future assignments.
6 min read
Regression diagnostics
Check residual form, variance, independence, leverage, and influence before trusting coefficients or predictions.
6 min read
Ridge, lasso, and elastic-net regularization
Control prediction variance and feature selection using penalties tuned entirely within training data.
6 min read
Repeated-measures analysis
Account for within-subject correlation when the same unit is observed under several times or conditions.
6 min read
SAM 2: keeping a mask's identity across a video
How a streaming-memory architecture let promptable segmentation extend from single images to video, tracking an object's identity through occlusion and motion in real time.
6 min read
SAM 3: segmenting by concept, not by click
How moving from single-instance prompts to open-vocabulary concept prompts let one phrase or example image segment every matching object in a scene at once.
6 min read
Sampling distributions and standard error
Understand how an estimate would vary over repeated samples and why standard error is not sample standard deviation.
6 min read
Random, stratified, cluster, and systematic sampling
Choose a sampling scheme that represents the population while respecting natural clusters and acquisition constraints.
6 min read
µSAM: closing the gap between SAM and real microscopy images
SAM was trained on natural photographs and performs noticeably worse on fluorescence and electron microscopy out of the box. µSAM fine-tunes it for exactly those modalities and ships it as a usable napari tool.
7 min read
Segment Anything (SAM): segmentation you can prompt instead of retrain
How SAM turned segmentation into a promptable task, why its billion-mask training set exists, and why that idea mattered enough to spawn a whole branch of microscopy-specific models.
6 min read
Selection bias and representativeness
Recognise when inclusion, exclusion, survival, or visibility mechanisms distort the analysed sample.
6 min read
Simple linear regression
Estimate a linear conditional mean, quantify slope uncertainty, and inspect whether the line is an adequate summary.
6 min read
Stable Diffusion: generative image modelling on one consumer GPU
How training a diffusion model in a compressed latent space, and releasing the weights openly, made large-scale generative image modelling broadly accessible for the first time.
6 min read
StarDist: segmenting nuclei by predicting their shape directly
Why representing each nucleus as a star-convex polygon sidestepped the touching-object problem that plain pixel classification struggles with — and where that shape assumption breaks down.
6 min read
Stationarity, trends, and differencing
Separate systematic trends and changing variance from stable temporal fluctuations before fitting stationary models.
6 min read
Statistical versus practical significance
Separate evidence against a null hypothesis from the magnitude and usefulness of an effect.
6 min read
Survival data and censoring
Represent time-to-event outcomes when some units have not experienced the event by the end of observation.
6 min read
Autocorrelation: why adjacent time points aren't independent evidence
Nearby observations in a time series tend to resemble each other, which quietly shrinks the amount of independent information a long series actually contains.
6 min read
Transformers: the architecture that made attention the whole model
How replacing recurrence with self-attention unlocked full parallelism during training, and why nearly every model later on this timeline is built on this one mechanism.
6 min read
Type I and Type II errors: the two ways a test can be wrong
A hypothesis test can fail in exactly two directions — a false alarm or a missed detection — and the same trade-off from detection theory applies directly.
7 min read
U-Net: the architecture built for too little data
Why the encoder-decoder-with-skip-connections shape became the default starting point for biomedical segmentation, and how it was designed specifically around having very few annotated images.
7 min read
The t-test: comparing means with uncertainty
A practical guide to one-sample, paired, and independent t-tests, their assumptions, and responsible interpretation.
6 min read
What makes a statistical method parametric?
Understanding parameters, distributional models, assumptions, and why parametric does not simply mean normal.
6 min read
Non-parametric tests: what they do and do not test
A guide to rank-based methods, permutation tests, distributional assumptions, and interpretation beyond the median myth.
6 min read
The central limit theorem: why averages become predictable
How repeated sampling makes standardized means approach a normal distribution, and where that intuition can fail.
5 min read
Effect sizes and confidence intervals
Moving from binary significance decisions to estimates of magnitude, direction, precision, and scientific relevance.
6 min read
P-values, false positives, and multiple testing
What a p-value means, common misinterpretations, and why image-rich experiments need multiplicity-aware analysis.
9 min read
Descriptive and robust statistics with SciPy
Mean, median, variance, IQR, MAD, skewness, and kurtosis: what each summary measures and when it can mislead.
8 min read
Normality and goodness-of-fit diagnostics
Shapiro–Wilk, D’Agostino–Pearson, Anderson–Darling, Q–Q thinking, and why testing normality is not a checkbox.
9 min read
Correlation: Pearson, Spearman, and Kendall
Linear, monotonic, and concordance-based association, with confidence intervals and microscopy examples.
10 min read
Comparing more than two groups
ANOVA, Welch ANOVA, Kruskal–Wallis, and Friedman tests with assumptions, effect decomposition, and post-hoc cautions.
9 min read
Contingency tables, risk, and exact tests
Chi-square independence, Fisher’s exact test, odds ratios, relative risk, and cell-count case studies.
10 min read
Bootstrap and permutation inference
Resampling distributions, confidence intervals, permutation p-values, exchangeability, and custom image-analysis statistics.
11 min read
Classification metrics from the confusion matrix
Accuracy, balanced accuracy, precision, recall, specificity, F1, MCC, and choosing metrics under class imbalance.
10 min read
ROC AUC and precision–recall curves
Threshold sweeps, ranking performance, average precision, prevalence, and why ROC and PR answer different questions.
9 min read
Probability calibration, log loss, and Brier score
Evaluating whether predicted probabilities mean what they say, with proper scoring rules and reliability diagrams.
11 min read
Regression metrics: MAE, RMSE, R², and deviance
Choosing a loss that matches error costs and outcome distributions, from continuous measurements to count predictions.
11 min read
Segmentation metrics: IoU, Dice, and boundary error
Overlap, class imbalance, object-level failure, and how to evaluate biological segmentation beyond one score.
10 min read
Clustering metrics: silhouette, ARI, and mutual information
Internal versus reference-based cluster evaluation, geometry assumptions, chance correction, and phenotype discovery.
6 min read
Normal distribution
Normal distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Binomial distribution
Binomial distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Poisson distribution
Poisson distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Negative binomial distribution
Negative binomial distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Geometric distribution
Geometric distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Hypergeometric distribution
Hypergeometric distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Exponential distribution
Exponential distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Gamma distribution
Gamma distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Beta distribution
Beta distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Lognormal distribution
Lognormal distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Weibull distribution
Weibull distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Student t distribution
Student t distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Chi-square distribution
Chi-square distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
F distribution
F distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Uniform distribution
Uniform distribution: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Kernel density estimation
Kernel density estimation: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Empirical cumulative distribution function
Empirical cumulative distribution function: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Quantiles and percentiles
Quantiles and percentiles: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Entropy and information
Entropy and information: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Maximum-likelihood distribution fitting
Maximum-likelihood distribution fitting: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
One-sample t-test
One-sample t-test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Paired t-test
Paired t-test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Welch independent t-test
Welch independent t-test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Wilcoxon signed-rank test
Wilcoxon signed-rank test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Mann–Whitney U test
Mann–Whitney U test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Kruskal–Wallis test
Kruskal–Wallis test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Friedman repeated-measures test
Friedman repeated-measures test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Shapiro–Wilk normality test
Shapiro–Wilk normality test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
D’Agostino–Pearson normality test
D’Agostino–Pearson normality test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Anderson–Darling goodness-of-fit test
Anderson–Darling goodness-of-fit test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
One-sample Kolmogorov–Smirnov test
One-sample Kolmogorov–Smirnov test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Two-sample Kolmogorov–Smirnov test
Two-sample Kolmogorov–Smirnov test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Cramér–von Mises goodness-of-fit test
Cramér–von Mises goodness-of-fit test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Levene and Brown–Forsythe variance tests
Levene and Brown–Forsythe variance tests: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Bartlett variance test
Bartlett variance test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Chi-square goodness-of-fit test
Chi-square goodness-of-fit test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Exact binomial test
Exact binomial test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Poisson means test
Poisson means test: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Tukey honestly significant difference
Tukey honestly significant difference: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Dunnett comparisons against a control
Dunnett comparisons against a control: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Accuracy: the simplest classification metric, and its trap
What accuracy actually measures, why it becomes misleading as classes grow imbalanced, and when it's still the right number to report.
6 min read
Balanced accuracy
Balanced accuracy: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Precision
Precision: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Recall and sensitivity
Recall and sensitivity: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Specificity
Specificity: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
F1 score
F1 score: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
F-beta score
F-beta score: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Jaccard score
Jaccard score: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Matthews correlation coefficient
Matthews correlation coefficient: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Cohen’s kappa
Cohen’s kappa: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Hamming loss
Hamming loss: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Zero-one loss
Zero-one loss: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Top-k accuracy
Top-k accuracy: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Multilabel confusion matrices
Multilabel confusion matrices: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Positive and negative likelihood ratios
Positive and negative likelihood ratios: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Average precision
Average precision: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Binary ROC AUC
Binary ROC AUC: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Log loss
Log loss: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Brier score
Brier score: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Hinge loss
Hinge loss: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Mean absolute error
Mean absolute error: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Mean squared error
Mean squared error: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Root mean squared error
Root mean squared error: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Mean squared logarithmic error
Mean squared logarithmic error: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Root mean squared logarithmic error
Root mean squared logarithmic error: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Mean absolute percentage error
Mean absolute percentage error: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Median absolute error
Median absolute error: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Maximum residual error
Maximum residual error: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Coefficient of determination R²
Coefficient of determination R²: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Explained variance
Explained variance: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Mean Poisson deviance
Mean Poisson deviance: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Mean Gamma deviance
Mean Gamma deviance: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Mean Tweedie deviance
Mean Tweedie deviance: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Pinball loss for quantile regression
Pinball loss for quantile regression: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Silhouette coefficient
Silhouette coefficient: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Davies–Bouldin index
Davies–Bouldin index: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Calinski–Harabasz index
Calinski–Harabasz index: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Adjusted Rand index
Adjusted Rand index: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Adjusted mutual information
Adjusted mutual information: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Homogeneity, completeness, and V-measure
Homogeneity, completeness, and V-measure: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Fowlkes–Mallows index
Fowlkes–Mallows index: theory, interpretation, Python computation, and a scientific-imaging case study.
6 min read
Cosine similarity
Cosine similarity: theory, interpretation, Python computation, and a scientific-imaging case study.
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