"sample path" meaning in English

{
  "forms": [
    {
      "form": "sample paths",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "sample path (plural sample paths)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Statistics",
          "orig": "en:Statistics",
          "parents": [
            "Formal sciences",
            "Mathematics",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "1968, Leo Breiman, Probability, 1992, Society for Industrial and Applied Mathematics, Unabridged corrected republication, page 298,\nThese processes cannot have versions with continuous sample paths, otherwise the argument given in Chapter 12 forces them to be Brownian motion."
        },
        {
          "text": "1981 [Wiley], Robert J. Adler, The Geometry of Random Fields, 2010, Society for Industrial and Applied Mathematics, Unabridged republication, page 39,\nIn order to study the 'finite' situation it is necessary to impose a number of conditions on the sample paths of the fields. Indeed, what we shall later generally assume is that sample paths belong, with probability one, to the special class of functions we now define."
        },
        {
          "ref": "2008, Linda J. S. Allen, “Chapter 3: An Introduction to Stochastic Epidemic Models”, in Fred Brauer, Pauline van den Driessche, Jianhong Wu, editors, Mathematical Epidemiology, Springer, page 90",
          "text": "A sample path or stochastic realization of the stochastic process #x5C;#x7B;#x5C;mathcal#x7B;I#x7D;(t)#x5C;#x7D;#x5C;infty#x5F;#x7B;t#x3D;0#x7D; for t#x5C;in#x5C;#x7B;0,#x5C;Deltat,2#x5C;Deltat,...#x5C;#x7D; is an assignment of a possible value to #x5C;mathcal#x7B;I#x7D;(t) based on the probability vector p(t).[…]Three sample paths of the stochastic model are compared to the deterministic solution in Fig.3.4. One of the sample paths is absorbed before 200 time steps (the population following this path becomes disease-free) but two sample paths are not absorbed during 2,000 time steps.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any set of possible values to which the appropriate random variables determined by a stochastic process might map a given point in the sample space, taken over all values of the index space (often regarded as time)."
      ],
      "id": "en-sample_path-en-noun-DuINPxe0",
      "links": [
        [
          "statistics",
          "statistics"
        ],
        [
          "random variable",
          "random variable"
        ],
        [
          "stochastic process",
          "stochastic process"
        ],
        [
          "sample space",
          "sample space"
        ]
      ],
      "raw_glosses": [
        "(statistics) Any set of possible values to which the appropriate random variables determined by a stochastic process might map a given point in the sample space, taken over all values of the index space (often regarded as time)."
      ],
      "synonyms": [
        {
          "sense": "set of values for a given point of sample space",
          "word": "stochastic realisation"
        },
        {
          "sense": "set of values for a given point of sample space",
          "word": "stochastic realization"
        },
        {
          "sense": "set of values for a given point of sample space",
          "word": "trajectory"
        },
        {
          "tags": [
            "attributive"
          ],
          "word": "sample-path"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "statistics"
      ]
    }
  ],
  "word": "sample path"
}

{
  "forms": [
    {
      "form": "sample paths",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "sample path (plural sample paths)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "en:Statistics"
      ],
      "examples": [
        {
          "text": "1968, Leo Breiman, Probability, 1992, Society for Industrial and Applied Mathematics, Unabridged corrected republication, page 298,\nThese processes cannot have versions with continuous sample paths, otherwise the argument given in Chapter 12 forces them to be Brownian motion."
        },
        {
          "text": "1981 [Wiley], Robert J. Adler, The Geometry of Random Fields, 2010, Society for Industrial and Applied Mathematics, Unabridged republication, page 39,\nIn order to study the 'finite' situation it is necessary to impose a number of conditions on the sample paths of the fields. Indeed, what we shall later generally assume is that sample paths belong, with probability one, to the special class of functions we now define."
        },
        {
          "ref": "2008, Linda J. S. Allen, “Chapter 3: An Introduction to Stochastic Epidemic Models”, in Fred Brauer, Pauline van den Driessche, Jianhong Wu, editors, Mathematical Epidemiology, Springer, page 90",
          "text": "A sample path or stochastic realization of the stochastic process #x5C;#x7B;#x5C;mathcal#x7B;I#x7D;(t)#x5C;#x7D;#x5C;infty#x5F;#x7B;t#x3D;0#x7D; for t#x5C;in#x5C;#x7B;0,#x5C;Deltat,2#x5C;Deltat,...#x5C;#x7D; is an assignment of a possible value to #x5C;mathcal#x7B;I#x7D;(t) based on the probability vector p(t).[…]Three sample paths of the stochastic model are compared to the deterministic solution in Fig.3.4. One of the sample paths is absorbed before 200 time steps (the population following this path becomes disease-free) but two sample paths are not absorbed during 2,000 time steps.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any set of possible values to which the appropriate random variables determined by a stochastic process might map a given point in the sample space, taken over all values of the index space (often regarded as time)."
      ],
      "links": [
        [
          "statistics",
          "statistics"
        ],
        [
          "random variable",
          "random variable"
        ],
        [
          "stochastic process",
          "stochastic process"
        ],
        [
          "sample space",
          "sample space"
        ]
      ],
      "raw_glosses": [
        "(statistics) Any set of possible values to which the appropriate random variables determined by a stochastic process might map a given point in the sample space, taken over all values of the index space (often regarded as time)."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "statistics"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "set of values for a given point of sample space",
      "word": "stochastic realisation"
    },
    {
      "sense": "set of values for a given point of sample space",
      "word": "stochastic realization"
    },
    {
      "sense": "set of values for a given point of sample space",
      "word": "trajectory"
    },
    {
      "tags": [
        "attributive"
      ],
      "word": "sample-path"
    }
  ],
  "word": "sample path"
}