Pulse Documentation

name: op-synth-bernoulli
description: Bernoulli samples emitting 0 or 1 with probability p; pairs with packed_bool or unsigned int fields.
kind: operator
category: SYNTH
operator: bernoulli
type: reference
applies_to: inspect, predict, manifest
examples_tags: [synth, proportion-analysis]

Synth distributions emit per-row values; no Response.Components.

Use when

Draws a yes/no value per row: 1 with a chosen chance p and 0 otherwise, such as whether a customer churned.

Questions it answers:

• How do I mark 12% of synthetic customers as churned?
• How do I generate a random true/false flag?

Use something else:

• weighted_categorical when there are more than two outcomes.
• set_bernoulli when each row can tick several options.
• constant when every row should get the same value.

Params

p — float, default 0.5, probability of emitting 1; must lie in [0, 1].

Inputs

Field type: — packed_bool (1 bit per row), unsigned int (u4/u8/u16/u32/u64), or f32/f64.

Output

Per-row 1.0 with probability p, else 0.0; cast to the declared field type at write time. packed_bool packs into the bit-shared neighbour byte.

Gotchas

• The only honest marginal for a packed_bool. profile create reconstructs every packed_bool as bernoulli with p = observed mean, ahead of --fit-shape. A continuous marginal cannot round-trip through one bit — the writer must threshold, and a thresholded clamped normal reproduces the wrong prevalence (measured on a 90-boolean cohort: mean error 0.47, 89 of 90 fields off by >0.05; an 11% attribute generated at 64%).
• A modelled bernoulli target is a PROBIT. quantileFor’s step Q makes value = Q(Φ(μ + σz)) into P(1 | row) = Φ((μ − Φ⁻¹(1−p)) / σ). Coefficients order rows and hold the marginal exactly; they are NOT probability changes. The fidelity models section scores these on the interval-midpoint probit score, not a latent inversion.
• p outside [0, 1] → SERVICE_VALIDATION at spec parse. p of exactly 0 or 1 is legal and exact but has zero variance, so a model on that target is dropped with a warning.
• For > 2 experiment arms use weighted_categorical.
• Observed p_hat converges at O(1/sqrt(n)) — small cohorts diverge from declared p.
• Same (spec, opts.Seed) ⇒ identical bit pattern.

See

• pulse_examples_search tags=[synth]
• Skills: synth-marginals, op-synth-weighted-categorical, op-synth-constant