Mathematics & Statistics
Cost-benefit Analysis
Cost-benefit analysis compares incremental consequences of alternatives against a defined baseline and horizon
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Mathematics & Statistics
Distributions (Understanding Shape)
Distributional shape describes how values are spread, including center, dispersion, skew, tails, and possible modes
Quantitative ModelsMathematics & Statistics
Economies of Scale
Economies of scale mean declining long-run average cost as output expands under the relevant production and input conditions
Quantitative ModelsMathematics & Statistics
Expected Value
Expected value is the probability-weighted average of outcomes when the expectation exists
Quantitative ModelsMathematics & Statistics
False Positives and False Negatives
False positives flag an absent condition, and false negatives miss a present condition
Quantitative ModelsMathematics & Statistics
Fat Tails
Fat-tail analysis examines distributions that assign relatively substantial probability to extreme outcomes
Quantitative ModelsMathematics & Statistics
Fermi Estimation
Fermi estimation builds an approximate answer from a defensible decomposition, rough component estimates, and consistent units
Quantitative ModelsMathematics & Statistics
Finite Time Singularity
A finite-time singularity occurs when a model's solution becomes unbounded as time approaches a finite point
Quantitative ModelsMathematics & Statistics
Granularity of Probability Estimates
Probability granularity is the resolution at which probabilities are expressed
Quantitative ModelsMathematics & Statistics
Inflection Point
A mathematical inflection point is a point where a curve changes concavity
Quantitative ModelsMathematics & Statistics
Law of Large Numbers
The law of large numbers gives conditions under which an average converges to an expected value as observations accumulate
Quantitative ModelsMathematics & Statistics
Multiplying by Zero
A finite product is zero when any factor is zero
Quantitative ModelsMathematics & Statistics
Nonlinearity
Nonlinearity means that a relationship fails the relevant linearity conditions
Quantitative ModelsMathematics & Statistics
Normal Distribution
The normal distribution is specified by a mean and positive standard deviation
Quantitative ModelsMathematics & Statistics
Order of Magnitude
Order-of-magnitude reasoning compares quantities through powers of ten and approximate scale
Quantitative ModelsMathematics & Statistics
Overfitting
Overfitting is fitting or selecting a model around development-data features that do not generalize to the intended population
Quantitative ModelsMathematics & Statistics
P-Hacking
P-hacking refers to analysis or data-collection flexibility used to obtain and selectively report favorable statistical significance without properly accounting for the search
Quantitative ModelsMathematics & Statistics
Pareto Efficiency
Pareto efficiency means no feasible change can make someone better off without making anyone worse off, under the specified preferences and constraints
Quantitative ModelsMathematics & Statistics
Pareto Principle
The Pareto principle suggests checking for concentrated contributions, often summarized heuristically as eighty-twenty
Quantitative ModelsMathematics & Statistics
Permutations and Combinations
Permutations count ordered arrangements and combinations count unordered selections under specified repetition and distinguishability rules
Quantitative ModelsMathematics & Statistics
Power Laws
Power laws express scale relationships through an exponent
Quantitative ModelsMathematics & Statistics
Price's Law (Square Root of Contributors Do Half the Work)
Price's square-root law is a rough bibliometric hypothesis that half the publication output in a defined field may come from approximately the square root of its contributing authors
Quantitative ModelsMathematics & Statistics
Principle of Least Effort (Zipf's Law)
The principle of least effort proposes that effort tradeoffs influence behavior, including communication
Quantitative ModelsMathematics & Statistics
Probabilistic Thinking
Probabilistic thinking expresses uncertainty through degrees of confidence about defined outcomes and updates those beliefs using evidence
Quantitative ModelsMathematics & Statistics
Randomness
Randomness concerns variation represented by a probability model or unpredictability under specified information
Quantitative ModelsMathematics & Statistics
Regression Toward the Mean in Social Systems
In social measurements, selection on an extreme observed score can be followed by a less extreme score because temporary influences and measurement noise need not repeat
Quantitative ModelsMathematics & Statistics
Regression to the Mean
Regression to the mean occurs when observations selected for extreme values on one measure have less extreme expected values on a related, imperfectly correlated measure under appropriate conditions
Quantitative ModelsMathematics & Statistics
Replication Crisis
The replication crisis refers to concerns that many influential research claims have not held up consistently in new studies
Quantitative ModelsMathematics & Statistics
Sampling
Sampling selects a subset of observations to learn about a defined population or process
Quantitative ModelsMathematics & Statistics
Scale
Scale concerns how properties and behavior change as a system's size changes
Quantitative ModelsMathematics & Statistics
Scaling Laws (3/4 Power Law)
Biological scaling laws relate traits such as metabolic rate to body mass through power relationships
Quantitative ModelsMathematics & Statistics
Sensitivity Analysis
Sensitivity analysis examines how model outputs or decisions change when inputs or assumptions vary
Quantitative ModelsMathematics & Statistics
Simpson’s Paradox
Simpson's paradox is a reversal or disappearance of an association when groups are combined, often because the compared alternatives have different mixtures of subgroups with different outcome rates
Quantitative ModelsMathematics & Statistics
Simulation
Simulation executes a model under specified rules and inputs to explore behavior or hypothetical outcomes
Quantitative ModelsMathematics & Statistics
Stochastic Processes (Poisson, Markov, Random Walk)
Stochastic processes model collections of random variables across time or another index
Quantitative ModelsMathematics & Statistics
Sublinear vs Superlinear Scaling
Sublinear scaling means an outcome increases less than proportionally with size; superlinear scaling means it increases more than proportionally
Quantitative ModelsMathematics & Statistics
Surface Area
Surface area measures an object's boundary
Quantitative ModelsMathematics & Statistics
Underfitting
Underfitting describes failure to capture relevant structure adequately for a prediction task, often associated with insufficient flexibility or excessive regularization
Quantitative ModelsMedicine & Health
Absolute vs Relative Risk
Absolute risk is the probability of an outcome over a specified period
Medical ModelsMedicine & Health
Allostatic Load (Cumulative Stress Burden)
Allostatic load describes cumulative physiological burden associated with repeated or dysregulated adaptation to demands
Medical ModelsMedicine & Health
Circadian Rhythm Effects
Circadian rhythms are roughly twenty-four-hour biological cycles influenced by internal clocks and environmental cues
Medical ModelsMedicine & Health
Dose-Response Relationship
A dose-response relationship links a defined exposure level with a specified outcome
Medical ModelsMedicine & Health
Herd Immunity
Herd immunity is indirect protection resulting when population immunity reduces transmission
Medical ModelsMedicine & Health
Hormesis (Low-Dose Stimulation, High-Dose Inhibition)
Hormesis is a biphasic dose-response pattern involving differing responses at lower and higher exposure levels for a specified endpoint
Medical ModelsMedicine & Health
Microbiome as Ecosystem
The microbiome can be studied as an ecosystem of microorganisms interacting with a host and environment
Medical ModelsMedicine & Health
Nocebo Effect (Negative Expectations Cause Harm)
Nocebo effects are adverse changes attributable to treatment context, negative expectations, or learned associations under particular conditions
Medical ModelsMedicine & Health
Number Needed to Treat (NNT)
NNT is the reciprocal of an absolute beneficial risk difference for a specified outcome, comparator, population, and period
Medical ModelsMedicine & Health
Placebo Effect as Expectation Model
Placebo effects are changes attributable to treatment context, expectations, learning, or related processes rather than a specific active component
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