beta_logpdf

std.stats.beta_logpdf · Level L5

The log-density of the beta distribution on (0, 1): (a − 1)·log x + (b − 1)·log(1 − x) − log B(a, b), with log(1 − x) as log1p(−x) and log B from log-gamma.

(a−1)·log x + (b−1)·log1p(−x) − log B(a, b)

Signature

beta_logpdf(x: f64[n], a: f64[], b: f64[]) → f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

xf64[n]1.0af64[]bf64[]LoglogxSubtractam1NegatenxSubtractbm1AddabLogGammalgaLogGammalgbMultiplyt1Log1plog1mxLogGammalgabAddlb1Multiplyt2SubtractlbetaAddsSubtractlogplogpf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference log(xᵃ⁻¹·(1 − x)ᵇ⁻¹·Γ(a+b)/(Γ(a)·Γ(b))) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 154 float64 results inside the running error bound; the closest uses 8% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
3%
bit-equal to the NumPy formula in float64
6%
largest error, in units in the last place
1.7e+3

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls
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Called by
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sha256:67d4c4655a145d12d7943d9fda577419b04229dd1cd4c96a106edcbf87b66e0d

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.