Bernstein–von Mises theorem
theorem that the posterior converges in the infinite-data limit 𝑁≫1 to a multivariate normal distribution centred at the maximum likelihood estimator with covariance 𝑁⁻¹𝐼(𝜃₀)⁻¹ with 𝜃₀ the true population parameter and 𝐼(𝜃₀) the Fisher information
| rdfs:label |
"Bernstein–von Mises theorem"@en
|
| schema:description |
"theorem that the posterior converges in the infinite-data limit 𝑁≫1 to a multivariate normal distribution centred at the maximum likelihood estimator with covariance 𝑁⁻¹𝐼(𝜃₀)⁻¹ with 𝜃₀ the true population parameter and 𝐼(𝜃₀) the Fisher information"@en
|
|
schema:date |
"2026-06-05T19:15:41+00:00"^^xsd:dateTime |
| schema:version | 2502322604 |
| wikibase:identifiers | 2 |
| wikibase:sitelinks | 4 |
| wikibase:statements | 17 |
| p:P1269 | wd:statement/Q4894580-2d51309c-4a2d-e825-1465-6484875b5e79 |
| p:P1318 | wd:statement/Q4894580-5be3502e-4581-aa6c-1f21-bbe44be3e0c4 |
| wd:statement/Q4894580-73662534-40d5-9c36-6329-04ddde3f744e | |
| wd:statement/Q4894580-960156c1-4d51-f281-79a9-e243c320e689 | |
| wd:statement/Q4894580-c47d51f5-4b1f-ed3e-1dba-3141d36b485d | |
| wd:statement/Q4894580-c539f096-4923-b5ba-4f73-4e6c5913704e | |
| p:P138 | wd:statement/Q4894580-24031afd-4698-66d7-1ef2-0eccd3279ef6 |
| wd:statement/Q4894580-fc43d46f-4fa5-1696-41b5-1b76001d9d22 | |
| p:P2534 | wd:statement/Q4894580-4d42fed2-4a72-af32-71d0-a235b3111357 |
| p:P31 | wd:statement/Q4894580-52298E78-ECB3-41E4-A017-EDB2BEC293CB |
| p:P6104 | wd:statement/Q4894580-F2609698-EB60-4C6E-B098-088CF473C0CF |
| p:P6366 | wd:statement/Q4894580-5B5650EF-25D8-4628-97C8-7DCF5B748726 |
| p:P646 | wd:statement/Q4894580-064DA5C6-14AC-45D9-A6E9-1FB7E616178B |
| p:P7235 | wd:statement/Q4894580-1415e7b2-4563-d28f-9657-1c0b66796caa |
| wd:statement/Q4894580-3b7207f4-4d23-4da2-594b-733ebf163ba7 | |
| wd:statement/Q4894580-baebe299-4b69-63d4-b714-3cc87180e80c | |
| wd:statement/Q4894580-f3084a74-4420-cdb1-7a9f-ff7ea20b9be6 | |
|
p:direct- |
<https:/ |
| wdt:P1269 | Bayesian statistics |
| wdt:P1318 | Lorraine Schwartz |
| Joseph Leo Doob | |
| Persi Diaconis | |
| Lucien Le Cam | |
| David A. Freedman | |
| wdt:P138 | Sergei Bernstein |
| Richard von Mises | |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>P</mi><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">|</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒩</mi></mrow><mo stretchy="false">(</mo><msub><mi>θ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>,</mo><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup><mi>I</mi><mo stretchy="false">(</mo><msub><mi>θ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mtext> for </mtext></mrow><mi>n</mi><mo stretchy="false" accent="false">→</mo><mi mathvariant="normal">∞</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P31 | theorem |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "168408371" |
| wdt:P646 | "/m/0gyts5j" |
| wdt:P7235 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>I</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>P</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>n</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒩</mi></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
Download as: