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  "Description": "Implimentations of the univariate CAPA\n<doi:10.1002/sam.11586> and PELT\n<doi:10.1080/01621459.2012.737745> algotithms along with\nvarious cost functions for different distributions and models.\nThe modular design, using R6 classes, favour ease of extension\n(for example user written cost functions) over the performance\nof other implimentations (e.g.\n<doi:10.32614/CRAN.package.changepoint>,\n<doi:10.32614/CRAN.package.anomaly>).",
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      "topics": [
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      "page": "pelt",
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      "filename": "regression_cost_calcs.html",
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        "Baseline: No Anomaly",
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        "Anomaly in Variance",
        "Anomaly in regression parameters and variance",
        "Since[\\sum_{t \\in T_{k}} \\left( \\hat{\\mathbf{y}}{t} - \\mathbf{X}{t} \\theta_{k}\\right)^{\\prime} \\mathbf{S}{t}^{-1} \\left( \\hat{\\mathbf{y}}{t} - \\mathbf{X}{t} \\theta{k}\\right)",
        "Point anomaly"
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      "engine": "knitr::knitr",
      "headings": [
        "Univariate Gaussian",
        "Anomaly in mean and varinace",
        "Anomaly in Mean",
        "Anomaly in Variance",
        "No Anomaly (Baseline)",
        "Point anomaly"
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      "created": "2023-12-20 15:32:32",
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      "headings": [
        "No Anomaly (Baseline)",
        "Collective Anomalies",
        "Anomaly in Mean and Variance",
        "Anomaly in Mean",
        "Anomaly in Variance",
        "Point anomaly",
        "[C_{P_{M}}\\left(y_{t}\\left| m_{t},s_{t},\\hat{\\mu}{k}\\right.\\right) -C{B}\\left(y_{t}\\left| m_{t},s_{t}\\right.\\right)",
        "[C_{P_{V}}\\left(y_{t}\\left| m_{t},s_{t},\\hat{\\sigma}{k}\\right.\\right) -C{B}\\left(y_{t}\\left| m_{t},s_{t}\\right.\\right)",
        "Relating this to the background cost we see that point anomalies may be accepted in the capa search when[f\\left(z_{t},\\gamma,\\beta\\right) =C_{P_{V}}\\left(y_{t}\\left| m_{t},s_{t},\\hat{\\sigma}{k},\\gamma\\right.\\right) -C{B}\\left(y_{t}\\left| m_{t},s_{t}\\right.\\right)"
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        "Using CAPA for anomalies",
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        "CROPS for varaible penalties"
      ],
      "created": "2023-06-06 08:54:58",
      "modified": "2024-12-13 13:43:20",
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