"Bayes' theorem" meaning in All languages combined

{
  "etymology_text": "Named after English mathematician Thomas Bayes (1701–1761), who developed an early formulation. The modern expression of the theorem is due to Pierre-Simon Laplace, who extended Bayes's work but was apparently unaware of it.",
  "forms": [
    {
      "form": "Bayes theorem",
      "tags": [
        "alternative"
      ]
    },
    {
      "form": "Bayes's theorem",
      "tags": [
        "alternative"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "Bayes' theorem"
      },
      "expansion": "Bayes' theorem",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Probability theory",
          "orig": "en:Probability theory",
          "parents": [
            "Mathematical analysis",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2010, Jonathan Harrington, Phonetic Analysis of Speech Corpora, page 327:",
          "text": "The starting point for many techniques in probabilistic classification is Bayes' theorem, which provides a way of relating evidence to a hypothesis.",
          "type": "quote"
        },
        {
          "ref": "2011, Allen Downey, Think Stats, O'Reilly, page 56:",
          "text": "Bayes's theorem is a relationship between the conditional probabilities of two events.",
          "type": "quote"
        },
        {
          "ref": "2013, Norman Fenton, Martin Neil, Risk Assessment and Decision Analysis with Bayesian Networks, Taylor & Francis (CRC Press), page 131:",
          "text": "We have now seen how Bayes' theorem enables us to correctly update a prior probability for some unknown event when we see evidence about the event.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event."
      ],
      "id": "en-Bayes'_theorem-en-name-lFOR~ZFM",
      "links": [
        [
          "probability theory",
          "probability theory"
        ],
        [
          "equation",
          "equation"
        ],
        [
          "conditional probability",
          "conditional probability"
        ]
      ],
      "raw_glosses": [
        "(probability theory) A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event."
      ],
      "related": [
        {
          "word": "Bayesian"
        },
        {
          "word": "conditional probability"
        },
        {
          "word": "posterior probability"
        },
        {
          "word": "prior probability"
        }
      ],
      "synonyms": [
        {
          "sense": "theorem or equation describing conditional probability",
          "word": "Bayes' law"
        },
        {
          "sense": "theorem or equation describing conditional probability",
          "word": "Bayes' rule"
        }
      ],
      "topics": [
        "mathematics",
        "probability-theory",
        "sciences"
      ],
      "wikipedia": [
        "Bayes' theorem",
        "Pierre-Simon Laplace",
        "Thomas Bayes"
      ]
    }
  ],
  "word": "Bayes' theorem"
}

{
  "etymology_text": "Named after English mathematician Thomas Bayes (1701–1761), who developed an early formulation. The modern expression of the theorem is due to Pierre-Simon Laplace, who extended Bayes's work but was apparently unaware of it.",
  "forms": [
    {
      "form": "Bayes theorem",
      "tags": [
        "alternative"
      ]
    },
    {
      "form": "Bayes's theorem",
      "tags": [
        "alternative"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "Bayes' theorem"
      },
      "expansion": "Bayes' theorem",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "related": [
    {
      "word": "Bayesian"
    },
    {
      "word": "conditional probability"
    },
    {
      "word": "posterior probability"
    },
    {
      "word": "prior probability"
    }
  ],
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics",
        "en:Probability theory"
      ],
      "examples": [
        {
          "ref": "2010, Jonathan Harrington, Phonetic Analysis of Speech Corpora, page 327:",
          "text": "The starting point for many techniques in probabilistic classification is Bayes' theorem, which provides a way of relating evidence to a hypothesis.",
          "type": "quote"
        },
        {
          "ref": "2011, Allen Downey, Think Stats, O'Reilly, page 56:",
          "text": "Bayes's theorem is a relationship between the conditional probabilities of two events.",
          "type": "quote"
        },
        {
          "ref": "2013, Norman Fenton, Martin Neil, Risk Assessment and Decision Analysis with Bayesian Networks, Taylor & Francis (CRC Press), page 131:",
          "text": "We have now seen how Bayes' theorem enables us to correctly update a prior probability for some unknown event when we see evidence about the event.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event."
      ],
      "links": [
        [
          "probability theory",
          "probability theory"
        ],
        [
          "equation",
          "equation"
        ],
        [
          "conditional probability",
          "conditional probability"
        ]
      ],
      "raw_glosses": [
        "(probability theory) A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event."
      ],
      "topics": [
        "mathematics",
        "probability-theory",
        "sciences"
      ],
      "wikipedia": [
        "Bayes' theorem",
        "Pierre-Simon Laplace",
        "Thomas Bayes"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "theorem or equation describing conditional probability",
      "word": "Bayes' law"
    },
    {
      "sense": "theorem or equation describing conditional probability",
      "word": "Bayes' rule"
    }
  ],
  "word": "Bayes' theorem"
}