🎲 Probabilistic Programming

Module: prob/* | Operators: 16

Distribution sampling (Gaussian, Beta, Poisson), Bayesian inference via rejection sampling, and statistical summaries.

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Operator Reference

prob/seed

Seed PRNG · 1 argument · returns void · ⚠️ has side effects

Sets a seeded Mulberry32 PRNG on the evaluation context. All subsequent prob/* operators use this seed for reproducible results.

Parameter	Type	Description
n	number	Seed value

(prob/seed 42)

prob/flip

Bernoulli Flip · 1 argument · returns boolean

Returns true with probability p and false with probability (1 - p). Uses Box-Muller PRNG if seeded.

Parameter	Type	Description
p	number	Probability (0.0 to 1.0)

(prob/flip 0.7) // => true ~70% of the time

prob/gaussian

Gaussian Sample · 2 arguments · returns number

Samples from a normal (Gaussian) distribution using the Box-Muller transform.

Parameter	Type	Description
mu	number	Mean
sigma	number	Standard deviation

(prob/gaussian 0 1) // => standard normal sample

prob/uniform

Uniform Sample · 2 arguments · returns number

Samples uniformly from the half-open interval [lo, hi).

Parameter	Type	Description
lo	number	Lower bound (inclusive)
hi	number	Upper bound (exclusive)

(prob/uniform 0 1) // => value in [0, 1)

prob/beta

Beta Sample · 2 arguments · returns number

Samples from a Beta distribution using the Marsaglia-Tsang gamma variate method.

Parameter	Type	Description
alpha	number	Shape parameter α > 0
beta	number	Shape parameter β > 0

(prob/beta 2 5) // => value in (0, 1), mean ≈ 0.286

prob/categorical

Categorical Sample · 2 arguments · returns any

Selects an item from a weighted categorical distribution.

Parameter	Type	Description
items	array	Array of items to sample from
weights	number[]	Non-negative weights (need not sum to 1)

(prob/categorical (a "b" "c") [1 2 1]) // => "b" ~50%

prob/poisson

Poisson Sample · 1 argument · returns integer

Samples from a Poisson distribution using Knuth's algorithm.

Parameter	Type	Description
lambda	number	Rate parameter λ > 0

(prob/poisson 4) // => integer, mean ≈ 4

prob/condition

Condition · 1 argument · returns void · ⚠️ has side effects

Used inside inference models. If the predicate is false, marks the current sample as rejected.

Parameter	Type	Description
predicate	boolean	Condition that must hold for the sample to be accepted

(prob/condition (> "@entity.x" 5))

prob/sample

Sample · 2 arguments · returns array

Evaluates an expression n times and returns the results as an array. The expression argument is lazy.

Parameter	Type	Description
n	number	Number of samples
expr	expression	Expression to evaluate (lazy)

(prob/sample 1000 (prob/flip 0.5))

prob/posterior

Posterior · 4 arguments · returns array

Runs rejection sampling: evaluates model, applies evidence condition, collects query values. Returns accepted query values as an array.

Parameter	Type	Description
model	expression	Model expression that sets entity fields (lazy)
evidence	expression	Boolean evidence condition (lazy)
query	expression	Value to collect from accepted samples (lazy)
n	number	Number of simulation runs

(prob/posterior model evidence "@entity.x" 5000)

prob/infer

Infer · 4 arguments · returns { mean, variance, samples, acceptRate }

Like prob/posterior but returns a summary object instead of raw samples.

Parameter	Type	Description
model	expression	Model expression (lazy)
evidence	expression	Boolean evidence condition (lazy)
query	expression	Value to summarize (lazy)
n	number	Number of simulation runs

(prob/infer model evidence "@entity.x" 5000)

prob/expected-value

Expected Value · 1 argument · returns number

Computes the arithmetic mean of a numeric array.

Parameter	Type	Description
samples	number[]	Array of numeric samples

(prob/expected-value [1 2 3 4]) // => 2.5

prob/variance

Variance · 1 argument · returns number

Computes the population variance of a numeric array.

Parameter	Type	Description
samples	number[]	Array of numeric samples

(prob/variance [2 4 4 4 5 5 7 9]) // => 4

prob/histogram

Histogram · 2 arguments · returns { binEdges: number[], counts: number[] }

Bins samples into a histogram.

Parameter	Type	Description
samples	number[]	Numeric samples
bins	number	Number of bins

(prob/histogram samples 10)

prob/percentile

Percentile · 2 arguments · returns number

Returns the value at the given percentile (0-100) of a sorted sample array.

Parameter	Type	Description
samples	number[]	Numeric samples
p	number	Percentile (0 to 100)

(prob/percentile samples 50) // => median

prob/credible-interval

Credible Interval · 2 arguments · returns [number, number]

Returns a (1 - alpha) credible interval [lo, hi] from sorted samples.

Parameter	Type	Description
samples	number[]	Numeric samples
alpha	number	Significance level (e.g. 0.05 for 95% CI)

(prob/credible-interval samples 0.05) // => 95% CI