stan-dev/stan

bivariate normal cdf

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#2,356 opened on Jul 14, 2017

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Description

Summary:

Add a function to compute the bivariate normal cdf.

Description:

For size 2 vectors y and mu and 2 x 2 covariance matrix Sigma, compute

bivar_normal_cdf(y, mu, Sigma)

  = INT_{u < y}  multinormal_pdf(u, mu, Sigma) d.u

where u is also a 2-vector and u < y is defined componentwise as u[1] < y[1] && u[2] < y[2].

There could also be a parameterization where covariance is given in terms of two scale parameters and a correlation parameter.

Additional Info:

This paper is often cited for an algorithm:

  • Boys, R.J., 1989. Algorithm AS R80: A remark on Algorithm AS 76: An integral useful in calculating noncentral t and bivariate normal probabilities. Journal of the Royal Statistical Society. Series C (Applied Statistics), 38(3), pp.580-582. https://www.jstor.org/stable/2347755

Current Version:

v2.16.0

Contributor guide

Research direction
Study the existing univariate normal CDF implementation in the Stan math library and the referenced paper (Boys, 1989) to understand the algorithm. Then implement the bivariate normal CDF following similar patterns.
Tech stack
cpp
Domain
backenddata
Issue type
Feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
3
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1-2 days
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Active
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Clear
Prerequisites
C++GitStatistics
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
40