Statistics
How physics handles data: 106 methods and practices — fitting, hypothesis testing, Bayesian sampling, machine learning. Papers rarely name them, they just use them, so this section is built as a reference rather than mined from texts.
All concepts →Estimation and fitting · 12
linear regression 49Fits a linear dynamical model to the Drake equation population dynamics.
least squares 22A standard statistical method for fitting a model to data by minimizing the sum of squared residuals.
least squares fitting 22Fitting by minimising the sum of squared residuals — the special case of maximum likelihood when errors are Gaussian and equal.
regularisation 22Adding a penalty term to a fit to suppress wild solutions when the data underdetermine the model.
maximum likelihood estimation 18Choosing the parameter values that make the observed data most probable under the model; the workhorse fit of experimental physics.
weighted mean 18Combining measurements of different precision by weighting each by the inverse square of its uncertainty.
profile likelihood 16Handling nuisance parameters by maximising the likelihood over them at each value of the parameter of interest.
spectral fitting 10The model fits the observed spectrum from X-rays to highest energies.
chi squared minimisation 7Fitting by minimising chi-squared, the sum of squared residuals weighted by their uncertainties; its value at the minimum also measures goodness of fit.
unfoldingCorrecting a measured distribution for detector smearing to recover the true one — an ill-posed inversion that needs regularisation.
Uncertainties · 11
error propagation 54The process by which errors in one part of a quantum circuit spread and affect other parts.
sigma clipping 14Discarding points beyond a chosen number of standard deviations, iteratively — the common defence against outliers.
standard error 14The uncertainty of an estimated quantity, such as the mean, rather than the spread of the data.
binning 12Redshift binning is used as a method for reconstructing the equation of state.
standard deviation 10A measure of the amount of variation or dispersion of a set of values from its mean.
covariance matrix 9A covariance matrix is a matrix that describes the variance and covariance of multiple variables.
pull distribution 8The distribution of residuals divided by their uncertainties; a check that the errors themselves are right.
systematic uncertainty 7A type of measurement error that arises from imperfect calibration or modeling, affecting accuracy rather than precision.
outlier rejection 1They searched for objects flickering near the shadow's edge, filtering out known cataloged objects.
Hypothesis testing · 19
five sigma 33The Hubble tension is quantified as a 5 sigma discrepancy between expansion rate measurements.
model comparison 29Bayesian evidence used to compare black hole versus boson star models.
null hypothesis testing 22Asking how improbable the data would be if there were no effect — the frame in which discoveries are declared.
cls method 12The modified frequentist limit-setting used at colliders, which refuses to exclude models the experiment has no power to test.
wilks theorem 12Result that twice the log likelihood ratio approaches a chi-squared distribution, which turns fits into significance.
p value 10Probability of data at least as extreme as observed if the null hypothesis holds; not the probability that the hypothesis is true.
confidence interval 8The frequentist interval that would contain the true value in a stated fraction of repeated experiments.
kolmogorov smirnov test 8Comparing two distributions by the largest gap between their cumulative curves, without binning.
likelihood ratio test 8Comparing two nested models by the ratio of their maximum likelihoods; its distribution follows Wilks' theorem.
look elsewhere effect 7The inflation of significance that comes from searching many places at once; the reason local and global significance differ.
trials factor 7The number of independent chances a search had to produce a fluctuation, by which local significance must be corrected.
anderson darling test 5A distribution comparison weighted towards the tails, where the Kolmogorov-Smirnov test is weakest.
goodness of fit 5The quality of the description of the fluxes by the model components indicates a goodness-of-fit assessment.
chi squared test 3Used to assess the goodness of fit between the model and observed cosmic-ray spectra.
type i error 3Rejecting a true null hypothesis — a false discovery.
type ii error 3Failing to reject a false null hypothesis — a missed effect.
statistical significance 2A measure of how likely a result is not due to chance, here quantified by a low error probability.
student t test 1Comparing means of small samples when the variance itself is estimated from the data.
Distributions · 9
Gaussian distribution 23A probability distribution characterized by a bell-shaped curve, often used to model random fluctuations.
central limit theorem 23Why the Gaussian is everywhere: sums of many independent contributions tend to it whatever their own shape.
Poisson distribution 17Photon counting statistics at the interferometer ports follow a Poisson distribution.
power law distribution 15A statistical distribution where a few large events dominate and many small ones occur, common in complex systems.
log-normal distribution 12The distribution of a quantity whose logarithm is Gaussian; arises from multiplicative processes.
exponential distribution 10The distribution of waiting times between events that happen at a constant rate; the law of radioactive decay.
chi squared distribution 8The distribution of a sum of squared Gaussian variables; the reference curve for goodness of fit.
landau distribution 7The strongly asymmetric distribution of energy loss by a charged particle in a thin absorber.
Bayesian analysis · 12
Bayesian inference 38Bayesian inference is a statistical method that updates the probability of a hypothesis as more evidence becomes available.
prior distribution 30What is assumed about a parameter before the data — the input of Bayesian analysis that most often decides its output.
posterior distribution 27The probability distribution of model parameters after updating prior beliefs with observed data, central to Bayesian inference.
nested sampling 26Sampling that computes the Bayesian evidence itself, not only the posterior; standard in gravitational-wave analysis.
bayesian evidence 23The probability of the data under a model with parameters integrated out; penalises complexity automatically.
gibbs sampling 23Sampling a multidimensional posterior one coordinate at a time from its conditional distributions.
hamiltonian monte carlo 19Markov chain sampling that uses gradients of the posterior to take long, well-aimed steps in many dimensions.
bayes factor 13A statistical measure used to compare the evidence for one hypothesis against another.
credible interval 8The Bayesian interval containing a stated fraction of the posterior — the answer to 'where is the parameter', unlike a confidence interval.
Resampling and validation · 5
bootstrap 29A resampling technique that repeatedly draws samples from data to estimate uncertainty.
cross validation 24Assessing a model on data it was not fitted to, by splitting the sample repeatedly.
permutation test 19Building the null distribution by shuffling labels of the data themselves.
blind analysis 8Fixing the analysis before looking at the answer, so that the result cannot be tuned towards the expected one.
Signals and time series · 12
polarization measurement 44Measured X-ray polarization percentage at different energy levels to characterize vacuum birefringence.
matched filter 30Correlating data with the expected shape of the signal — the optimal detector of a known waveform in Gaussian noise.
noise subtraction 23An algorithm subtracts sensor noise from images of entangled photon pairs.
kalman filter 20An algorithm that estimates the state of a system from noisy measurements over time.
lomb scargle periodogram 13Finding periods in unevenly sampled data, where the ordinary Fourier transform cannot be used.
wavelet analysis 12Decomposing a signal in time and frequency at once, for features that come and go.
matched filtering 10Matched circles on the surface of last scattering are searched for.
signal to noise ratio 6A measure comparing the level of a desired signal to the level of background noise, improved by this method.
detrendingRemoving a slow trend before analysing the variability that rides on it.
Multivariate analysis and learning · 11
random forest 52A committee of decorrelated decision trees, robust and hard to overfit.
feature importance 42How much each input variable actually contributes to a trained model's decisions.
boosted decision tree 29A committee of simple trees, each fixing the errors of the last; long the standard classifier in particle physics.
overfitting 19Learning the noise of the training sample; the reason a model that fits perfectly can predict badly.
confusion matrix 17The table of what a classifier got right and wrong, class by class.
roc curve 9The trade-off between signal efficiency and background rejection as the cut is moved.
Simulation and sampling · 7
information criterion 37Model comparison that trades goodness of fit against the number of parameters, as in AIC and BIC.
model selection 27Choosing between competing descriptions of the same data, by evidence, criterion or cross-validation.
importance sampling 19Drawing from a distribution chosen to put samples where they matter, then reweighting.
rejection sampling 10Drawing from a simple distribution and keeping points that fall under the target one.
monte carlo simulation 9Answering a problem by simulating random draws from it — from detector response to lattice field theory.
toy monte carlo 5Repeating the whole analysis on many simulated pseudo-experiments to learn how its answer fluctuates.
monte carlo sampling 4Stochastic method for estimating expectation values and thermal properties in quantum systems.
Other · 8
seasonal cycle 140The regular annual variation in a climate variable, often removed to study other signals.
interannual variability 139The variation of a climate quantity from one year to the next, often used to describe monsoon strength.
natural variability 130Fluctuations in climate variables arising from internal system dynamics, not external forcing.
precipitation anomaly 40The difference between observed precipitation and the climatological mean for a given period and location.
forecast skill 25A measure of the accuracy of a forecast compared to a reference, such as climatology or persistence.
temperature anomaly 22The deviation of a measured temperature from its long-term average for a specific location and time.
composite analysis 12A statistical method that averages data over multiple occurrences of a specific event to isolate its common signal from background variability.
colored noise 10Noise with temporal correlations, in contrast to white noise which has no memory.