https://github.com/jluttine/truncnorm
Moments for truncated multivariate normal distributions
https://github.com/jluttine/truncnorm
Last synced: 3 months ago
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Moments for truncated multivariate normal distributions
- Host: GitHub
- URL: https://github.com/jluttine/truncnorm
- Owner: jluttine
- License: mit
- Created: 2024-02-28T11:11:30.000Z (over 1 year ago)
- Default Branch: master
- Last Pushed: 2024-02-28T15:24:23.000Z (over 1 year ago)
- Last Synced: 2025-02-18T00:04:30.914Z (4 months ago)
- Language: Python
- Size: 12.7 KB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# TruncNorm
Arbitrary order moments for truncated multivariate normal distributions.
## Introduction
Given
```
X ~ N(m, C), a <= X <= b
```
with mean vector `m`, covariance matrix `C`, lower limit vector `a` and upper
limit vector `b`,
``` python
import truncnorm
truncnorm.moments(m, C, a, b, 4)
```
returns all the following moments of total order less or equal to 4 as a list:
```
[
P(a<=X<=b), (scalar)
E[X_i], (N vector)
E[X_i*X_j], (NxN matrix)
E[X_i*X_j*X_k], (NxNxN array)
E[X_i*X_j*X_k*X_l], (NxNxNxN array)
]
```
for all `i`, `j`, `k` and `l`. Note that the first element in the list is a bit
of a special case. That's because `E[1]` is trivially `1` so giving the
normalisation constant instead is much more useful.
## TODO
- Double truncation
- Numerical stability could probably be increased by using logarithic scale in
critical places of the algorithm
- Sampling (see Gessner et al below)
- Folded distribution
- Optimize recurrent integrals by using vector and index-mapping representation
instead of arrays. Using arrays makes computations efficient and simple, but
same elements are computed multiple times because of symmetry in the moments.
## References
- "On Moments of Folded and Truncated Multivariate Normal Distributions" by
Raymond Kan & Cesare Robotti, 2016
- "Integrals over Gaussians under Linear Domain Constraints" by Alexandra Gessner
& Oindrila Kanjilal & Philipp Hennig, 2020