{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Different Information Scenarios in maxent_disaggregation\n", "\n", "This notebook demonstrates how the sampling behavior of `maxent_disagg()` changes based on the information you provide.\n", "\n", "The `maxent_disagg()` function internally handles two key aspects:\n", "\n", "- Sampling **share distributions** (how the total is divided)\n", "- Sampling **aggregate distributions** (the total value)\n", "\n", "The package uses decision trees to automatically select appropriate probability distributions based on available information:\n", "\n", "1. For the aggregate value: The distribution choice depends on whether you provide mean, standard deviation, minimum, and maximum bounds.\n", "\n", "\n", "\n", "\n", "```{mermaid}\n", "flowchart-elk LR\n", " MeanDecision{{\"Best guess/\n", " mean available?\"}} -- no --> BoundsDecision1{{\"Bounds available?\"}}\n", " MeanDecision -- yes --> SDDecision{{\"Standard deviation available?\"}}\n", " SDDecision -- yes --> BoundsDecision2{{\"Bounds available?\"}}\n", " BoundsDecision2 -- yes --> GeneralBounds{{\"General Bounds a,b\"}}\n", " GeneralBounds -- \"no, $$a=0, b=\\infty$$\" --> LogNorm(\"LogNormal distribution\n", " or\n", " Truncated Normal\")\n", " GeneralBounds -- yes --> TruncNorm(\"Truncated Normal \n", " (Maximum Entropy distribution)\")\n", " BoundsDecision2 -- no --> Normal(\"Normal distribution\")\n", " SDDecision -- no --> LowerBound0{{\"Lower bound = 0?\"}}\n", " LowerBound0 -- yes --> Exponential(\"Exponential distribution\")\n", " LowerBound0 -- no --> NotImplemented[\"No MaxEnt solution\n", " (currently not implemented)\"]\n", " BoundsDecision1 -- yes --> Uniform(\"Uniform distribution on [a,b]\")\n", " BoundsDecision1 -- no --> GoBackToStart[\"☠️ !Game Over!\n", " We suggest to rethink your problem... 🤓\"]\n", " MeanDecision:::decision\n", " BoundsDecision1:::decision\n", " SDDecision:::decision\n", " BoundsDecision2:::decision\n", " GeneralBounds:::decision\n", " LogNorm:::distribution\n", " TruncNorm:::distribution\n", " Normal:::distribution\n", " LowerBound0:::decision\n", " Exponential:::distribution\n", " NotImplemented:::notimplementednode\n", " Uniform:::distribution\n", " GoBackToStart:::notimplementednode\n", " classDef decision fill:#e28743,color:black,stroke:none\n", " classDef distribution fill:#abdbe3,color:black,stroke:none\n", " classDef notimplementednode fill:#eeeee4,color:black,stroke:none\n", "```\n", "\n", "\n", "2. For the shares: The distribution choice depends on whether you provide best estimates and standard deviations.\n", "\n", "\n", "```{mermaid}\n", "flowchart-elk LR\n", " %% Define node classes\n", " classDef decision fill:#e28743,color:black,stroke:none;\n", " classDef distribution fill:#abdbe3,color:black,stroke:none;\n", " classDef explanationnode fill:#eeeee4,color:black,stroke:none;\n", "\n", " MeanDecision{{\"Best guess/mean available?\"}}:::decision\n", " SDDecision{{\"Standard deviation available?\"}}:::decision\n", " MaxEntDir(\"Maximum Entropy Dirichlet\"):::distribution\n", " GenDir(\"Generalised Dirichlet\"):::distribution\n", " hybridDir(\"Hybrid Dirichlet\"):::distribution\n", " UniformDir(\"Uniform Dirichlet\"):::distribution\n", " \n", " %% Define connections\n", " MeanDecision -- \"no\" --> UniformDir\n", " MeanDecision -- \"yes\" --> SDDecision\n", " MeanDecision -- \"paritially\" --> hybridDir\n", " SDDecision -- \"no\" --> MaxEntDir\n", " SDDecision -- \"yes\" --> GenDir\n", " SDDecision -- \"partially\" --> hybridDir\n", "```\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Import necessary libraries\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from maxent_disaggregation import maxent_disagg, plot_samples_hist, sample_aggregate, sample_shares\n", "\n", "# Set sample size for demonstrations\n", "N = 10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sampling Shares\n", "\n", "The `maxent_disagg()` function samples the relative proportions that must sum to 1. The sampling method depends on what information you provide." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Uniform Dirichlet Distribution\n", "\n", "When no information about shares is available (using `np.nan`), the function uses a uniform Dirichlet distribution where all components are equally likely." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define shares with no information\n", "shares_disaggregates = [np.nan, np.nan, np.nan]\n", "\n", "# Sample using maxent_disagg\n", "samples, _ = sample_shares(n=N, \n", " shares=shares_disaggregates)\n", "\n", "# Plot the results\n", "plot_samples_hist(samples, shares=shares_disaggregates,\n", " plot_agg=False, \n", " title=\"Uniform Dirichlet Distribution - Equal Probability for All Shares\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Maximum Entropy Dirichlet Distribution\n", "\n", "When you provide best estimates for the shares but no uncertainty information, `maxent_disagg()` uses a Maximum Entropy Dirichlet distribution." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define shares with best estimates\n", "shares_disaggregates = [0.6, 0.3, 0.1]\n", "\n", "# Sample using maxent_disagg\n", "samples, _ = sample_shares(n=N, \n", " shares=shares_disaggregates)\n", "\n", "# Plot the results\n", "plot_samples_hist(samples, shares=shares_disaggregates,\n", " plot_agg=False,\n", " title=\"Maximum Entropy Dirichlet - Based on Best Estimates Only\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generalized Dirichlet Distribution\n", "\n", "When you provide both best estimates and standard deviations for the shares, `maxent_disagg()` uses a generalized Dirichlet distribution." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sds above threshold: [1.18506436], sds: [0.01], sample_sd: [0.02185064], indices: [0]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/ajakobs/Documents/code_projects/maxent_disaggregation/maxent_disaggregation/shares.py:475: UserWarning: The generated samples for the shares have a standard deviation that is more than 20.0% different from the specified sd's. Please note that the specified sd's might be incompetibale with the other constraints. Please check your inputs. To surpress this warning you can set a higher threshold_sd.\n", " warnings.warn(\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define shares with best estimates and standard deviations\n", "shares_disaggregates = [0.6, 0.3, 0.1]\n", "sds_shares = [0.01, 0.02, 0.03]\n", "\n", "# Sample using maxent_disagg\n", "samples, _ = sample_shares(n=N, \n", " shares=shares_disaggregates, \n", " sds=sds_shares)\n", "\n", "# Plot the results\n", "plot_samples_hist(samples, shares=shares_disaggregates,\n", " sds=sds_shares,\n", " plot_agg=False,\n", " title=\"Generalized Dirichlet - With Specified Uncertainties\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hybrid Dirichlet Distribution\n", "\n", "When you provide partial information on the best estimates and standard deviations for the shares, `maxent_disagg()` uses a hybrid sampling using Beta- and Maximum Entropy Dirichlet- distributions." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define shares with best estimates and standard deviations\n", "shares_disaggregates = [0.6, 0.3, np.nan]\n", "sds_shares = [0.01, np.nan, np.nan]\n", "\n", "# Sample using maxent_disagg\n", "samples, _ = sample_shares(n=N, \n", " shares=shares_disaggregates, \n", " sds=sds_shares)\n", "\n", "# Plot the results\n", "plot_samples_hist(samples, shares=shares_disaggregates,\n", " sds=sds_shares,\n", " plot_agg=False,\n", " title=\"Hybrid Dirichlet - With partial information\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sampling the Aggregate\n", "\n", "The `maxent_disagg()` function samples the total value to be disaggregated. Different distributions are chosen based on available information." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Uniform Distribution\n", "\n", "When only minimum and maximum bounds are provided:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sample aggregate using uniform distribution\n", "sample = sample_aggregate(n=N,\n", " low_bound=0, \n", " high_bound=100,)\n", "\n", "# Plot the results\n", "plt.hist(sample, bins=30)\n", "plt.axvline(sample.mean(), ls='--', color='k', label=\"sample mean\")\n", "plt.title(\"Uniform Distribution - Only Bounds Provided\")\n", "plt.xlabel(\"Value\")\n", "plt.ylabel(\"Frequency\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exponential Distribution\n", "\n", "When a mean but no standard deviation are provided and the low_bound = 0 and upper_bound=np.inf or None" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sample aggregate using exponential distribution\n", "sample = sample_aggregate(n=N, \n", " mean=10, \n", " low_bound=0,\n", " ) \n", "# Plot the results\n", "plt.hist(sample, bins=30)\n", "plt.axvline(sample.mean(), ls='--', color='k', label=\"sample mean\")\n", "plt.axvline(10, ls=':', color='orange', label='Input mean')\n", "plt.title(\"Exponential Distribution - Mean Provided and low_bound=0\")\n", "plt.xlabel(\"Value\")\n", "plt.ylabel(\"Frequency\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Normal Distribution\n", "\n", "When a mean and standard deviation are provided:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sample aggregate using normal distribution\n", "sample = sample_aggregate(n=N, \n", " mean=10, \n", " sd = 5,\n", " low_bound=-np.inf, # default is 0 so set to -inf or None to use normal distribution\n", " )\n", "\n", "# Plot the results\n", "plt.hist(sample, bins=30)\n", "plt.axvline(sample.mean(), ls='--', color='k', label=\"sample mean\")\n", "plt.axvline(10, ls=':', color='orange', label='Input mean')\n", "plt.title(\"Normal Distribution - Mean and SD Provided\")\n", "plt.xlabel(\"Value\")\n", "plt.ylabel(\"Frequency\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Truncated Normal Distribution\n", "\n", "For non-negative variables, you can set a lower bound of zero. For general bounds $[a,b]$ you can set the `low_bound` and `high_bound` to $a$ and $b$ resepctively. The truncated normal distribution is the MaxEnt solution for a known best guess and standard deviation on a bound interval. To use the truncated normal please set `log=False`.\n", "\n", "For bounds $[0,\\infty)$, an alternative often used in Industrial Ecology is to use the lognormal. (The lognormal is the MaxEnt solution when the mean and standard deviation of rhe natural logarithm of the random variable are known.) To use the lognormal distribution set `log=True` (this is the default for ```maxent_disaggregation```). Please Note that the boundaries of the lognormal are always $[a,b) \\equiv [0,\\infty)$. If other bounds are given these are set to $[0,\\infty)$ and a warning is raised. \n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sample mean: 9.956556841161218\n", "Input mean: 10\n", "Sample median: 9.710258424684524\n", "Input bounds: [0, None]\n", "Input Standard Deviation: 5\n", "sample standard deviation: 5.055988114029651\n" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sample aggregate using truncated normal distribution\n", "mean = 10\n", "sd = 5\n", "low_bound = 0\n", "high_bound = None # same as np.inf\n", "sample = sample_aggregate(n=N, \n", " mean=mean, \n", " sd = sd,\n", " low_bound=low_bound,\n", " high_bound=high_bound,\n", " log=False, # Set to False to sample from the truncated normal distribution\n", " ) \n", "\n", "print(f\"Sample mean: {sample.mean()}\")\n", "print(f\"Input mean: {mean}\")\n", "print(f\"Sample median: {np.median(sample)}\")\n", "print(f\"Input bounds: [{low_bound}, {high_bound}]\")\n", "print(f\"Input Standard Deviation: {sd}\")\n", "print(f\"sample standard deviation: {sample.std()}\")\n", "\n", "\n", "# Plot the results\n", "plt.hist(sample, bins=30)\n", "plt.axvline(sample.mean(), ls='--', color='k', label=\"sample mean\")\n", "plt.axvline(mean, ls=':', color='orange', label='Input mean')\n", "plt.legend()\n", "plt.title(\"Truncated Normal Distribution - With Lower Bound\")\n", "plt.xlabel(\"Value\")\n", "plt.ylabel(\"Frequency\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lognormal Distribution\n", "\n", "An alternative approach for non-negative variables is using a lognormal distribution:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sample mean: 10.050525441884421\n", "Input mean: 10\n", "Sample median: 8.96354983128007\n", "Input bounds: [0, None]\n", "Input Standard Deviation: 5\n", "sample standard deviation: 5.064476353528188\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/ajakobs/Documents/code_projects/maxent_disaggregation/maxent_disaggregation/aggregate.py:69: UserWarning: You provided a finite high bound, currently this not supported for the lognormal distribution. High bound is ignored. Alternatively set log=False.\n", " warnings.warn(\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sample aggregate using lognormal distribution\n", "mean = 10\n", "sd = 5\n", "low_bound = 0\n", "high_bound = None # same as np.inf\n", "sample = sample_aggregate(n=N, \n", " mean=mean, \n", " sd = sd,\n", " low_bound=low_bound,\n", " high_bound=high_bound,\n", " log=True, # Set to True to sample from the lognormal distribution\n", " ) \n", "\n", "print(f\"Sample mean: {sample.mean()}\")\n", "print(f\"Input mean: {mean}\")\n", "print(f\"Sample median: {np.median(sample)}\")\n", "print(f\"Input bounds: [{low_bound}, {high_bound}]\")\n", "print(f\"Input Standard Deviation: {sd}\")\n", "print(f\"sample standard deviation: {sample.std()}\")\n", "\n", "# Plot the results\n", "plt.hist(sample, bins=30)\n", "plt.axvline(sample.mean(), ls='--', color='k', label=\"sample mean\")\n", "plt.axvline(10, ls=':', color='orange', label='Input mean')\n", "plt.legend()\n", "plt.title(\"Lognormal Distribution - With Lower Bound\")\n", "plt.xlabel(\"Value\")\n", "plt.ylabel(\"Frequency\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "The `maxent_disaggregation` package automatically selects appropriate distributions based on the information you provide:\n", "\n", "1. For shares:\n", " - No information → Uniform Dirichlet\n", " - Best estimates only → Maximum Entropy Dirichlet\n", " - Best estimates with SDs → Generalized Dirichlet\n", "\n", "2. For aggregates:\n", " - Min/max only → Uniform\n", " - Mean/SD only → Normal\n", " - Mean with min=0 → Exponential\n", " - Mean/SD with min/max → Truncated Normal\n", " - Mean/SD with log=True (Default) → Lognormal\n", "\n", "This flexibility allows you to incorporate the precise level of information you have available while ensuring statistically valid disaggregation." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "a = np.random.rand(10)\n", "b = np.random.rand(10)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "c = np.abs(a-b)\n", "d = np.abs(np.log(a/b))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.38573169, 0.25775963, 0.71622173, 0.41450263, 1.41002268,\n", " 0.21554481, 0.00746703, 0.07712375, 1.17521701, -0.97454063])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(14.142135623730951)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sqrt((high_bound-mean)*(mean-low_bound))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "maxent_disag_dev", "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": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 4 }