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1076 | 1076 | "cell_type": "markdown",
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1077 | 1077 | "metadata": {},
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1078 | 1078 | "source": [
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1079 |
| - "PLot posterior joint distribution" |
| 1079 | + "Plot posterior joint distribution" |
1080 | 1080 | ]
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1081 | 1081 | },
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1082 | 1082 | {
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2026 | 2026 | "source": [
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2027 | 2027 | "**Observe**:\n",
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2028 | 2028 | "\n",
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2029 |
| - "##### The posterior preditive fit for:\n", |
| 2029 | + "The posterior preditive fit for:\n", |
2030 | 2030 | "+ the **OLS model** is shown in **Green** and as expected, it doesn't appear to fit the majority of our datapoints very well, skewed by outliers\n",
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2031 | 2031 | "+ the **Student-T model** is shown in **Orange** and does appear to fit the 'main axis' of datapoints quite well, ignoring outliers\n",
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2032 | 2032 | "+ the **Hogg Signal vs Noise model** is shown in two parts:\n",
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2033 | 2033 | " + **Blue** for inliers fits the 'main axis' of datapoints well, ignoring outliers\n",
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2034 | 2034 | " + **Red** for outliers has a very large variance and has assigned 'outlier' points with more log likelihood than the Blue inlier model \n",
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2035 | 2035 | " \n",
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2036 | 2036 | " \n",
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2037 |
| - "##### We see that the **Hogg Signal vs Noise model** also yields specific estimates of _which_ datapoints are outliers:\n", |
| 2037 | + "We see that the **Hogg Signal vs Noise model** also yields specific estimates of _which_ datapoints are outliers:\n", |
2038 | 2038 | "+ 17 'inlier' datapoints, in **Blue** and\n",
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2039 | 2039 | "+ 3 'outlier' datapoints shown in **Red**.\n",
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2040 | 2040 | "+ From a simple visual inspection, the classification seems fair, and agrees with Jake Vanderplas' findings.\n",
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2041 | 2041 | "+ I've annotated these Red and the most outlying inliers to aid visual investigation\n",
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2042 | 2042 | " \n",
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2043 | 2043 | " \n",
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2044 |
| - "##### Overall:\n", |
| 2044 | + "Overall:\n", |
2045 | 2045 | "+ the **Hogg Signal vs Noise model** behaves as promised, yielding a robust regression estimate and explicit labelling of inliers / outliers, but\n",
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2046 | 2046 | "+ the **Hogg Signal vs Noise model** is quite complex, and whilst the regression seems robust, the traceplot shoes many divergences, and the model is potentially unstable\n",
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2047 | 2047 | "+ if you simply want a robust regression without inlier / outlier labelling, the **Student-T model** may be a good compromise, offering a simple model, quick sampling, and a very similar estimate."
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