Bernoulli: Any random variable taking values in \(\{0, 1\}\).
param RealVar probability: Probability \(p \in [0, 1]\) that the realization is one.
BetaBinomial: A sum of \(n\) iid Bernoulli variables, with a marginalized Beta prior on the success probability. Values in \(\{0, 1, 2, \dots, n\}\).
param IntVar numberOfTrials: The number \(n\) of Bernoulli variables being summed. \(n > 0\)
param RealVar alpha: Higher values brings mean closer to one. \(\alpha > 0 \)
param RealVar beta: Higher values brings mean closer to zero. \(\beta > 0 \)
BetaNegativeBinomial: Negative Binomial Distribution with a marginalized Beta prior. Values in \(\{0, 1, 2, \dots\}\).
param RealVar r: Number of failures until experiment is stopped (generalized to the reals). \(r > 0\)
param RealVar alpha: Higher values brings mean accept probability closer to one. \(\alpha > 0 \)
param RealVar beta: Higher values brings mean accept probabilitycloser to zero. \(\beta > 0 \)
Binomial: A sum of \(n\) iid Bernoulli variables. Values in \(\{0, 1, 2, \dots, n\}\).
param IntVar numberOfTrials: The number \(n\) of Bernoulli variables being summed. \(n > 0\)
param RealVar probabilityOfSuccess: The parameter \(p \in [0, 1]\) shared by all the Bernoulli variables (probability that they be equal to 1).
Categorical: Any random variable over a finite set \(\{0, 1, 2, \dots, n-1\}\).
param Simplex probabilities: Vector of probabilities \((p_0, p_1, \dots, p_{n-1})\) for each of the \(n\) integers.
DiscreteUniform: Uniform random variable over the contiguous set of integers \(\{m, m+1, \dots, M-1\}\).
param IntVar minInclusive: The left point of the set (inclusive). \(m \in (-\infty, M)\)
param IntVar maxExclusive: The right point of the set (exclusive). \(M \in (m, \infty)\)
Geometric: The number of unsuccessful Bernoulli trials until a success. Values in \(\{0, 1, 2, \dots\}\)
param RealVar p: The probability of success for each Bernoulli trial.
HyperGeometric: A population of size \(N\), \(K\) of which are marked, and drawing without replacement \(n\) samples from the population; the HyperGeometric models the number in the sample that are marked.
param IntVar numberOfDraws: Number sampled. \(n\)
param IntVar population: Population size. \(N\)
param IntVar populationConditioned: Number marked in the population. \(K\)
NegativeBinomial: Number of successes in a sequence of iid Bernoulli until \(r\) failures occur. Values in \(\{0, 1, 2, \dots\}\).
param RealVar r: Number of failures until experiment is stopped (generalized to the reals). \(r > 0\)
param RealVar p: Probability of success of each experiment. \(p \in (0, 1)\)
Poisson: Poisson random variable. Values in \(0, 1, 2, \dots\)
param RealVar mean: Mean parameter \(\lambda\). \(\lambda > 0\)
YuleSimon: An exponential-geometric mixture.
param RealVar rho: The rate of the mixing exponential distribution.
Beta: Beta random variable on the open interval \((0, 1)\).
param RealVar alpha: Higher values brings mean closer to one. \(\alpha > 0 \)
param RealVar beta: Higher values brings mean closer to zero. \(\beta > 0 \)
ChiSquared: Chi Squared random variable. Values in \((0, \infty)\).
param IntVar nu: The degrees of freedom \(\nu\). \( \nu > 0 \)
ContinuousUniform: Uniform random variable over a close interval \([m, M]\).
param RealVar min: The left end point \(m\) of the interval. \(m \in (-\infty, M)\)
param RealVar max: The right end point \(M\) of the interval. \(M \in (m, \infty)\)
Exponential: Exponential random variable. Values in \((0, \infty)\)
param RealVar rate: The rate \(\lambda\), inversely proportional to the mean. \( \lambda > 0 \)
F: The F-distribution. Also known as Fisher-Snedecor distribution. Values in \((0, +\infty) \)
param RealVar d1, d2: The degrees of freedom \( d_1 \) and \( d_2 \) . \( d_1, d_2 > 0 \)
Gamma: Gamma random variable. Values in \((0, \infty)\).
param RealVar shape: The shape \(\alpha\) is proportional to the mean and variance. \( \alpha > 0 \)
param RealVar rate: The rate \(\beta\) is inverse proportional to the mean and quadratically inverse proportional to the variance. \( \beta > 0 \)
Gompertz: The Gompertz distribution. Values in \([0, \infty) \).
param RealVar shape: The shape parameter \(\nu \). \(\nu > 0 \)
param RealVar scale: The scale parameter \(b\). \(b > 0 \)
Gumbel: The Gumbel Distribution. Values in \( \mathbb{R} \)
param RealVar location: The location parameter \(\mu \). \( \mu \in \mathbb{R} \)
param RealVar scale: The scale parameter \(\beta \). \( \beta > 0 \)
HalfStudentT: HalfStudentT random variable. Values in \((0, \infty)\)
param RealVar nu: A degree of freedom parameter \(\nu\). \( \nu > 0 \)
param RealVar sigma: A scale parameter \(\sigma\). \( \sigma > 0 \).
Laplace: The Laplace Distribution over \(\mathbb{R}\)
param RealVar location: The mean parameter.
param RealVar scale: The scale parameter \( b \), equal to the square root of half of the variance. \( b > 0 \)
Logistic: A random variable with a cumulative distribution given by the logistic function. Values in \( \mathbb{R} \)
param RealVar location: The mean. \(\mu \in \mathbb{R}\)
param RealVar scale: The scale parameter. \(s > 0\)
LogLogistic: A log-logistic distribution is the probability distribution of a random variable whose logarithm has a logistic distribution. Values in \([0, +\infty) \)
param RealVar scale: The scale parameter \(\alpha\) and also the median. \(\alpha > 0 \)
param RealVar shape: The shape parameter \(\beta\). \(\beta > 0 \)
LogUniform: The random variable \(X = b^Y\) where \(Y \sim \text{ContinuousUniform}[m, M]\).
param RealVar min: The left end point \(m\) of the interval. \(m \in (-\infty, M)\)
param RealVar max: The right end point \(M\) of the interval. \(M \in (m, \infty)\)
param RealVar base: The base \(b\). \(b > 0\)
LnUniform: The random variable \(X = e^Y\) where \(Y \sim \text{ContinuousUniform}[m, M]\).
param RealVar min: The left end point \(m\) of the interval. \(m \in (-\infty, M)\)
param RealVar max: The right end point \(M\) of the interval. \(M \in (m, \infty)\)
Normal: Normal random variables. Values in \(\mathbb{R}\)
param RealVar mean: Mean \(\mu\). \(\mu \in \mathbb{R}\)
param RealVar variance: Variance \(\sigma^2\). \(\sigma^2 > 0\)
StudentT: Student T random variable. Values in \(\mathbb{R}\)
param RealVar nu: The degrees of freedom \(\nu\). \( \nu > 0 \)
param RealVar mu: Location parameter \(\mu\). \(\mu \in \mathbb{R}\)
param RealVar sigma: Scale parameter \(\sigma\). \(\sigma > 0\)
Weibull: The Weibull Distribution. Values in \((0, \infty)\).
param RealVar scale: The scale parameter \(\lambda\). \( \lambda \in (0, +\infty) \)
param RealVar shape: The shape parameter \(k\). \( k \in (0, +\infty) \)
Dirichlet: The Dirichlet distribution over vectors of probabilities \((p_0, p_1, \dots, p_{n-1})\). \(p_i \in (0, 1), \sum_i p_i = 1.\)
param Matrix concentrations: Vector \((\alpha_0, \alpha_1, \dots, \alpha_{n-1})\) such that increasing the \(i\)th component increases the mean of entry \(p_i\).
MultivariateNormal: Arbitrary linear transformations of \(n\) iid standard normal random variables.
param Matrix mean: An \(n \times 1\) vector \(\mu\). \(\mu \in \mathbb{R}^n\)
param CholeskyDecomposition precision: Inverse covariance matrix \(\Lambda\), a positive definite \(n \times n\) matrix.
NormalField: A mean-zero normal, sparse-precision Markov random field.
param Precision precision: Precision matrix structure.
SimplexUniform: \(n\) dimensional Dirichlet with all concentrations equal to one.
param Integer dim: The dimensionality \(n\). \( n > 0 \)
SymmetricDirichlet: \(n\) dimensional Dirichlet with all concentrations equal to \(\alpha / n\).
param Integer dim: The dimensionality \(n\). \( n > 0 \)
param RealVar concentration: The shared concentration parameter \(\alpha\) before normalization by the dimensionality. \(\alpha > 0\)
LogPotential: Not really a distribution, but rather a way to handle undirected model (AKA random fields). See Ising under the Examples page.
param RealVar logPotential: The log of the current value of this potential.