GHK algorithm
importance sampling method
The GHK algorithm (Geweke, Hajivassiliou and Keane) is an importance sampling method for simulating choice probabilities in the multivariate probit model. These simulated probabilities can be used to recover parameter estimates from the maximized likelihood equation using any one of the usual well known maximization methods (Newton's method, BFGS, etc.). Train has well documented steps for implementing this algorithm for a multinomial probit model. What follows here will apply to the binary multivariate probit model.
Consider the case where one is attempting to evaluate the choice probability of
Pr
(
y
i
|
X
i
β
,
Σ
)
{\displaystyle \Pr(\mathbf {y_{i}} |\mathbf {X_{i}\beta } ,\Sigma )}
where
y
i
=
(
y
1
,
.
.
.
,
y
J
)
,
(
i
=
1
,
.
.
.
Begin with the source’s own compact description: “GHK algorithm” is importance sampling method. The dossier treats that line as a proposition to test through algorithm, importance and sampling, not as a finished interpretation.
Why this record matters
The phrase “importance sampling method” supplies a clear boundary for inquiry. It also exposes the unanswered questions: who defined that boundary, when it became stable and which sources sit outside it.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Feb 5, 2026. The linked authority identifier is Q30673424. None of the 0 selected statements returned an explicit reference.
A concise general-reference account can conceal disagreements about scope, terminology or the weight assigned to individual sources. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “GHK algorithm”, its source revision and the description used here.
- Expand the search: follow GHK algorithm primary sources, GHK algorithm archive and algorithm research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “GHK algorithm”?
- What terminology or title could unlock a more precise catalogue search?
- Which cited source is closest to the event, object or claim?
Search terms from this dossier
This entry incorporates text from “GHK algorithm” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.