{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Consistent scores\n", "## Introduction \n", "\n", "A \"consistent scoring function\" is a scoring function where a forecaster's expected score will be optimised by following a forecast directive. An example of a forecast directive is to \"predict the mean (i.e., expected) rainfall amount\". Using a consistent scoring function ensures that a forecaster or forecast system developer isn't faced with the dilemma of whether to \n", "\n", "1. produce forecasts (or develop a forecast system) that optimises the expected verification score, or\n", "2. produce an honest\\* forecast (or develop an honest forecast system) that is optimal for the forecast directive. \n", "\n", "\\* note that by \"honest\" we mean issuing a forecast that corresponds to a forecaster's true belief and has not been \"hedged\" ([Murphy 1978](https://doi.org/10.1175/1520-0477(1978)059<0371:HATMOE>2.0.CO;2)) to try and improve the verification score by producing a forecast that does not correspond to their true belief.\n", "\n", "Using a consistent scoring function to evaluate forecast performance ensures that objectives both 1 and 2 can be met without any tensions. For example, the Mean Squared Error (MSE) is a consistent score for forecasting the mean (i.e., expected) rainfall amount, since forecasting the \"mean rainfall amount\" will minimise the expected MSE. However the Mean Absolute Error (MAE) is not consistent with forecasting the mean value and is instead consistent with forecasting the median value. Consistent scoring functions are formally defined in ([Gneiting et al., 2011a](https://doi.org/10.1198/jasa.2011.r10138)).\n", "\n", "\n", "You may already know that the MSE is a consistent score for forecasting the mean and the MAE is a consistent score for forecasting the median. But did you know that there are a whole family of scores that are consistent for predicting the mean, median, or quantiles? \n", "\n", "The consistent scoring module in `scores` provides access to these families of consistent scores that can be used to tailor emphasis of predictive performance based on decision thresholds of interest.\n", "\n", "
\n", "Note: Threshold weighted scoring functions will be added to scores. These threshold weighted scoring functions will use these consistent scoring functions and will allow users a more simplified approach to evaluating forecasts using scores that emphasise performance across different decision thresholds. The planned tutorial notebook for threshold weighted scoring functions is expected to complement this tutorial.\n", "
\n", "\n", "## Example 1. A score consistent with the mean\n", "Let's jump into an example that illustrates a scoring function that is consistent with predicting the mean value using `scores`. Suppose we want to evaluate the performance of expected daily precipitation forecasts, but we want to place increasing importance on correctly forecasting extreme values. MSE is consistent with predicting the mean value, but weights all decision thresholds equally (as discussed further on).\n", "\n", "The mean (or expectation) functional is equivalent to the 0.5-[expectile](https://en.wikipedia.org/wiki/Expectile), so we want to use the `consistent_expectile_score` in `scores` to evaluate the expected daily precipitation forecasts. Note that the mean is identical to the 0.5-expectile in the same way that the median is identical to the 0.5-quantile (or 50th percentile).\n", "\n", "A scoring function $S$ that is consistent for the alpha-expectile takes the following form ([Savage 1971](https://doi.org/10.2307/2284229)):\n", "\n", " $$ S(x, y) =\n", " \\begin{cases}\n", " (1 - \\alpha)(\\phi(y) - \\phi(x) - \\phi'(x)(y-x)), & y < x \\\\\n", " \\alpha(\\phi(y) - \\phi(x) - \\phi'(x)(y-x)), & x \\leq y\n", " \\end{cases}\n", "$$\n", "\n", "where\n", "\n", "- $x$ is the forecast\n", "- $y$ is the observation\n", "- $\\alpha$ is the expectile level\n", "- $\\phi$ is a [convex function](https://en.wikipedia.org/wiki/Convex_function) of a single variable\n", "- $\\phi'$ is the [subderivative](https://en.wikipedia.org/wiki/Subderivative) of $\\phi$. The subderivative is a generalisation of the derivative for convex functions and coincides with the derivative when the convex function is differentiable\n", "- $S(x,y)$ is the score.\n", "\n", "In this case, we choose $\\alpha=0.5$, since the 0.5-expectile is identical to the mean.\n", "\n", "If one wants to control the relative importance of predictive performance across different decision thresholds, they must first create a weighting function $\\phi''$ which is the second derivative of $\\phi$.\n", "\n", "Let's assume that the importance of accurate prediction increases exponentially with increasing decision threshold $z$. We then need to determine our $\\phi(z)$ and $\\phi'(z)$ functions. \n", "\n", "First we create the weighting function\n", "\n", "$$\\phi''(z) = e^\\frac{z}{10}$$ \n", "\n", "This will place increasing importance on more extreme rainfall thresholds. We will plot this weighting function further below.\n", "\n", "Next we need to integrate $\\phi''(z)$ twice so that we can obtain the functions for our consistent scoring function\n", "\n", "$$\\phi'(z) = 10e^\\frac{z}{10}$$ \n", "and \n", "$$\\phi(z) = 100e^\\frac{z}{10}$$ \n", "\n", "These equations with $\\alpha=0.5$ can be substituted into $S(x, y)$ to create our consistent scoring function\n", "\n", "$$\n", "S(x,y) = \\frac{1}{2}(100e^\\frac{y}{10} - 110e^\\frac{x}{10})(y-x)\n", "$$\n", "\n", "Note that to use the `consistent_expectile_score` in scores, you only need to define $\\phi(z)$ and $\\phi'(z)$, but not $S(x, y)$.\n", "\n", "Also note that the squared loss (used in MSE) can be created with $\\phi(z)=2z^2$ with $\\alpha=0.5$. We leave this as an exercise for the reader to show that $S(x,y)=(x-y)^2$ when $\\phi(z)=2z^2$ and $\\alpha=0.5$.\n", "\n", "Let's illustrate how this can be done in scores using some synthetic rainfall data." ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [], "source": [ "from scores.continuous import consistent_expectile_score, consistent_quantile_score, mse, murphy_score, murphy_thetas\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import skewnorm\n", "import numpy as np\n", "import xarray as xr\n", "\n", "np.random.seed(100)" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# First, let's visualise our weighting function phi''\n", "# Higher weights mean that there is a higher importance place on forecasting values around\n", "# those decision thresholds in the scoring function\n", "x = np.linspace(0, 50, 1000)\n", "y = np.exp(x / 10)\n", "\n", "plt.figure(figsize=(4, 4))\n", "plt.plot(x, y)\n", "plt.xlabel(\"rainfall threshold (mm)\")\n", "plt.ylabel(\"weight\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "# define phi and phi prime\n", "def phi_prime(z):\n", " \"\"\"Phi prime\"\"\"\n", " return 10 * np.exp(z / 10)\n", "\n", "\n", "def phi(z):\n", " \"\"\"Phi\"\"\"\n", " return 100 * np.exp(z / 10)" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [], "source": [ "# Generate some synthetic rainfall observations between 0 and 50mm\n", "N = 1000\n", "obs = xr.DataArray(data=50 * np.random.random(N), dims=[\"time\"], coords={\"time\": np.arange(0, N)})\n", "obs = obs.clip(min=0) # don't allow negative rainfall\n", "\n", "# Generate synthetic forecasts by adding noise to each observation\n", "fcst1 = 0.9 * obs + skewnorm.rvs(4, size=N) # fcst1 has a low bias\n", "fcst1 = fcst1.clip(min=0) # don't allow negative rainfall\n", "fcst2 = 1.1 * obs - skewnorm.rvs(4, size=N) # fcst2 has a high bias\n", "fcst2 = fcst2.clip(min=0) # don't allow negative rainfall" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fcst1 MSE = 5.397562928167134\n", "fcst2 MSE = 5.3763094346565685\n" ] } ], "source": [ "# First if we calculate the MSE of fcst1 and fcst2 we will see that that have similar predictive performance.\n", "print(f\"fcst1 MSE = {mse(fcst1, obs).item()}\")\n", "print(f\"fcst2 MSE = {mse(fcst2, obs).item()}\")" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fcst1 consistent score = 67.77792339205789\n", "fcst2 consistent score = 114.52858223319328\n" ] } ], "source": [ "# However, when we calculate the performance of these forecasts with increasing focus on\n", "# extreme decision thresholds, we see that the performance is quite different.\n", "fcst1_cons_score = consistent_expectile_score(fcst1, obs, alpha=0.5, phi=phi, phi_prime=phi_prime).item()\n", "fcst2_cons_score = consistent_expectile_score(fcst2, obs, alpha=0.5, phi=phi, phi_prime=phi_prime).item()\n", "\n", "print(f\"fcst1 consistent score = {fcst1_cons_score}\")\n", "print(f\"fcst2 consistent score = {fcst2_cons_score}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Why is this? To visualise the difference in performance, we use plot Murphy Diagrams. See the [Murphy Diagrams tutorial](./Murphy_Diagrams.ipynb)." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0.98, 'Murphy Score (for mean)')" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate a list of thresholds of interest\n", "thetas = murphy_thetas([fcst1, fcst2], obs, \"expectile\")\n", "\n", "# Calculate the average elementary score for the mean (0.5 expectile) for each threshold theta\n", "ms1 = murphy_score(fcst1, obs, thetas, functional=\"expectile\", alpha=0.5)\n", "ms2 = murphy_score(fcst2, obs, thetas, functional=\"expectile\", alpha=0.5)\n", "\n", "# Rename date variable for plotting\n", "ms1 = ms1.rename({\"total\": \"Mean elementary score\", \"theta\": \"rainfall decision threshold (mm)\"})\n", "ms2 = ms2.rename({\"total\": \"Mean elementary score\", \"theta\": \"rainfall decision threshold (mm)\"})\n", "\n", "# Plot the results\n", "ms1[\"Mean elementary score\"].plot()\n", "ms2[\"Mean elementary score\"].plot()\n", "plt.title(\"Rainfall fcst1 (blue), Rainfall fcst2 (orange)\")\n", "plt.suptitle(\"Murphy Score (for mean)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lower values are better on the Murphy Diagram. Fcst2 (orange) performs far worse at higher rainfall thresholds, so is penalised more heavily due to out weighting function $\\phi''(z) = \\exp ^\\frac{z}{10}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2. A score consistent with a quantile\n", "\n", "Suppose we have a 90th percentile wind speed forecast that we want to evaluate. Additionally, we wish to emphasise predictive performance for higher decision thresholds. We can use the `consistent_quantile_score` in `scores`.\n", "\n", "Every consistent score for an alpha-quantile has the form $S$ ([Gneiting 2011b](https://doi.org/10.1016/j.ijforecast.2009.12.015)), where\n", "\n", "$$ S(x, y) = \\begin{cases}(1 - \\alpha)(g(x) - g(y)), & y < x \\\\\\alpha(g(y) - g(x)), & x \\leq y\\end{cases}$$\n", "\n", "where\n", "\n", "- $x$ is the forecast\n", "- $y$ is the observation\n", "- $\\alpha$ is the quantile level\n", "- $g$ is a nondecreasing function of a single variable\n", "- $S(x,y)$ is the score.\n", "\n", "\n", "Similar to how $\\phi''$ was our weighting function in the first example, in this case $g'$ is our weighting function.\n", "\n", "Now suppose we want to emphasise the performance for higher thresholds, but we don't want our weights to increase exponentially like in rainfall example above. We first define our weighting function as \n", "\n", "$$g'(z)= \\frac{-1}{(z+10)}+0.5$$\n", "\n", "Let's visualise our weighting function" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 50, 1000)\n", "y = -1 / (x + 4) + 0.5\n", "\n", "plt.figure(figsize=(4, 4))\n", "plt.plot(x, y)\n", "plt.xlabel(\"wind threshold (kt)\")\n", "plt.ylabel(\"weight\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need to obtain $g$ for our `consistent_quantile_score` by integrating $g'$\n", "\n", "$$g(z) = 0.5z - ln(z+4)$$\n", "\n", "To evaluate the 90th percentile forecast, we need to set $\\alpha=0.9$. Now we can use the `consistent_quantile_score`.\n", "\n", "Note that taking $\\alpha=0.5$ and $g(z)=2z$ recovers the absolute loss. Since $g'(z)$ is a constant, MAE can be interpreted as having equal weights for all decision thresholds." ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [], "source": [ "def g(z):\n", " \"\"\"g(z) for our conistent score\"\"\"\n", " return 0.5 * z - np.log(z + 4)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fcst1 consistent quantile score = 0.7710748324858289\n", "fcst2 consistent quantile score = 0.12031432648877705\n" ] } ], "source": [ "# Let's assume that the synthetic rainfall data that we created before is now synthetic\n", "# wind speed data\n", "fcst3 = fcst1.copy()\n", "fcst4 = fcst2.copy()\n", "\n", "fcst3_cons_quant_score = consistent_quantile_score(fcst3, obs, alpha=0.9, g=g).item()\n", "fcst4_cons_quant_score = consistent_quantile_score(fcst4, obs, alpha=0.9, g=g).item()\n", "\n", "print(f\"fcst1 consistent quantile score = {fcst3_cons_quant_score}\")\n", "print(f\"fcst2 consistent quantile score = {fcst4_cons_quant_score}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, fcst2 performs better. This is because it has an overforecast bias for a mean forecast, but it performs better than fcst1 as a 90th percentile forecast. Let's visualise this on a Murphy Diagram that shows the performance for 90th percentile forecasts across each decision threshold." ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0.98, 'Murphy Score (for 90th percentile)')" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate a list of thresholds of interest\n", "thetas = murphy_thetas([fcst3, fcst4], obs, \"quantile\")\n", "\n", "ms3 = murphy_score(fcst3, obs, thetas, functional=\"quantile\", alpha=0.9)\n", "ms4 = murphy_score(fcst4, obs, thetas, functional=\"quantile\", alpha=0.9)\n", "\n", "# Rename date variable for plotting\n", "ms3 = ms3.rename({\"total\": \"Mean elementary score\", \"theta\": \"wind speed decision threshold (kts)\"})\n", "ms4 = ms4.rename({\"total\": \"Mean elementary score\", \"theta\": \"wind speed decision threshold (kts)\"})\n", "\n", "# Plot the results\n", "ms3[\"Mean elementary score\"].plot(color=\"red\")\n", "ms4[\"Mean elementary score\"].plot(color=\"blue\")\n", "plt.ylim(0, 0.1)\n", "plt.title(\"Wind speed fcst3 (red), Wind speed fcst4 (dark blue)\")\n", "plt.suptitle(\"Murphy Score (for 90th percentile)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What we can see is that fcst4 (dark blue) performs best for most decision thresholds. Despite weighting higher wind speed thresholds more heavily and fcst4 performing worse for thresholds above 50kt, fcst4 still scored better because it performed substantially better for many decision thresholds and the weights did not exponentially increase." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Things to try next\n", "\n", "- Test out different weighting functions. \n", "- Try out `consistent_huber_score`. This uses $\\phi$ and $\\phi'$ like `consistent_expectile_score`, but also takes a huber parameter.\n", "\n", "## Further reading\n", "- [Gneiting, T. (2011a). Making and evaluating point forecasts. Journal of the American Statistical Association, 106(494), 746-762.](https://doi.org/10.1198/jasa.2011.r10138)\n", "- [Gneiting, T. (2011b). Quantiles as optimal point forecasts. International Journal of forecasting, 27(2), 197-207.](https://doi.org/10.1016/j.ijforecast.2009.12.015)\n", "- [Savage, L. J. (1971). Elicitation of personal probabilities and expectations. Journal of the American Statistical Association, 66(336), 783-801.](https://doi.org/10.2307/2284229)\n", "- [Taggart, R. (2022). Evaluation of point forecasts for extreme events using consistent scoring functions. Quarterly Journal of the Royal Meteorological Society, 148(742), 306-320.](https://doi.org/10.1002/qj.4206)\n", "- [Taggart, R. J. (2022). Point forecasting and forecast evaluation with generalized Huber loss. Electronic Journal of Statistics, 16(1), 201-231.](https://doi.org/10.1214/21-EJS1957)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 4 }