Learn PyINLA

Likelihood families

Overview of common family=... choices and their default links.

Continuous

Gaussian

Measurement errors around a mean; classic regression workhorse.
Discrete

Poisson

Event counts and rates (with exposure); queues, arrivals, incidences.
Discrete

Binomial (Bernoulli)

0/1 outcomes or successes out of trials; conversions, response/no‑response.
Continuous

Gamma

Positive, right‑skewed data; durations, costs, waiting times.

Coming soon
Discrete

Negative Binomial

Over‑dispersed counts; many zeros or extra variability vs Poisson.
Continuous

Beta

Proportions in (0,1); shares, rates, probabilities.
Discrete

Beta‑Binomial

Binomial with over‑dispersion; heterogeneous success rates.
Continuous

Exponential

Time‑to‑event with constant hazard; quick baseline survival model.
Continuous

Log‑Normal

Multiplicative effects; incomes, reaction times, sizes.

Coming soon
Continuous

Logistic

Symmetric, heavy‑tailed alternative to Gaussian; robust errors.

Coming soon
Continuous

Log‑Logistic

Survival with heavy tails; long‑lived events.

Coming soon
Continuous

Skew Normal

Allows skew in continuous data; asymmetric errors.

Coming soon
Continuous

Student's t

Heavy‑tailed continuous outcomes; outlier‑robust modeling.

Coming soon
Continuous

Weibull

Flexible survival/time‑to‑event with changing hazard.

Coming soon

Understanding Link Functions

New to link functions? Learn how they connect your linear predictor to the response variable and why each likelihood uses a specific default link.

Explore Link Functions →

Supported Likelihoods Reference

pyINLA currently supports 21 tested likelihood families. The 14 families above have detailed documentation articles. Below is a complete reference of all supported likelihoods organized by category.

Continuous Response

Keyword Description
gaussianStandard Gaussian / Normal distribution
tStudent's t distribution (heavy-tailed)
logisticLogistic distribution
snSkew-normal distribution
betaBeta distribution for (0,1) data
gammaGamma distribution
lognormalLog-normal distribution
exponentialExponential distribution
loglogisticLog-logistic distribution

Count / Discrete Response

Keyword Description
poissonStandard Poisson for count data
nbinomialNegative binomial (overdispersed counts)
nbinomial2Negative binomial (alternative parameterization)
binomialBinomial distribution
xbinomialExtended binomial model
betabinomialBeta-binomial (overdispersed binomial)

Survival / Time-to-Event

Keyword Description
exponentialsurvCensored exponential survival
weibullWeibull distribution
weibullsurvCensored Weibull survival
lognormalsurvCensored log-normal survival
loglogisticsurvCensored log-logistic survival
gammasurvCensored gamma survival