{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", "\n", "**This is a fixed-text formatted version of a Jupyter notebook**\n", "\n", "- Try online [![Binder](https://static.mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.18?urlpath=lab/tree/mcmc_sampling.ipynb)\n", "- You can contribute with your own notebooks in this\n", "[GitHub repository](https://github.com/gammapy/gammapy/tree/master/docs/tutorials).\n", "- **Source files:**\n", "[mcmc_sampling.ipynb](../_static/notebooks/mcmc_sampling.ipynb) |\n", "[mcmc_sampling.py](../_static/notebooks/mcmc_sampling.py)\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Fitting and error estimation with MCMC\n", "\n", "## Introduction\n", "\n", "The goal of Markov Chain Monte Carlo (MCMC) algorithms is to approximate the posterior distribution of your model parameters by random sampling in a probabilistic space. For most readers this sentence was probably not very helpful so here we'll start straight with and example but you should read the more detailed mathematical approaches of the method [here](https://www.pas.rochester.edu/~sybenzvi/courses/phy403/2015s/p403_17_mcmc.pdf) and [here](https://github.com/jakevdp/BayesianAstronomy/blob/master/03-Bayesian-Modeling-With-MCMC.ipynb).\n", "\n", "### How does it work ?\n", "\n", "The idea is that we use a number of walkers that will sample the posterior distribution (i.e. sample the Likelihood profile).\n", "\n", "The goal is to produce a \"chain\", i.e. a list of $\\theta$ values, where each $\\theta$ is a vector of parameters for your model.
\n", "If you start far away from the truth value, the chain will take some time to converge until it reaches a stationary state. Once it has reached this stage, each successive elements of the chain are samples of the target posterior distribution.
\n", "This means that, once we have obtained the chain of samples, we have everything we need. We can compute the distribution of each parameter by simply approximating it with the histogram of the samples projected into the parameter space. This will provide the errors and correlations between parameters.\n", "\n", "\n", "Now let's try to put a picture on the ideas described above. With this notebook, we have simulated and carried out a MCMC analysis for a source with the following parameters:
\n", "$Index=2.0$, $Norm=5\\times10^{-12}$ cm$^{-2}$ s$^{-1}$ TeV$^{-1}$, $Lambda =(1/Ecut) = 0.02$ TeV$^{-1}$ (50 TeV) for 20 hours.\n", "\n", "The results that you can get from a MCMC analysis will look like this :\n", "\n", "\n", "\n", "On the first two top panels, we show the pseudo-random walk of one walker from an offset starting value to see it evolve to a better solution.\n", "In the bottom right panel, we show the trace of each 16 walkers for 500 runs (the chain described previsouly). For the first 100 runs, the parameter evolve towards a solution (can be viewed as a fitting step). Then they explore the local minimum for 400 runs which will be used to estimate the parameters correlations and errors.\n", "The choice of the Nburn value (when walkers have reached a stationary stage) can be done by eye but you can also look at the autocorrelation time.\n", "\n", "### Why should I use it ?\n", "\n", "When it comes to evaluate errors and investigate parameter correlation, one typically estimate the Likelihood in a gridded search (2D Likelihood profiles). Each point of the grid implies a new model fitting. If we use 10 steps for each parameters, we will need to carry out 100 fitting procedures. \n", "\n", "Now let's say that I have a model with $N$ parameters, we need to carry out that gridded analysis $N*(N-1)$ times. \n", "So for 5 free parameters you need 20 gridded search, resulting in 2000 individual fit. \n", "Clearly this strategy doesn't scale well to high-dimensional models.\n", "\n", "Just for fun: if each fit procedure takes 10s, we're talking about 5h of computing time to estimate the correlation plots. \n", "\n", "There are many MCMC packages in the python ecosystem but here we will focus on [emcee](https://emcee.readthedocs.io), a lightweight Python package. A description is provided here : [Foreman-Mackey, Hogg, Lang & Goodman (2012)](https://arxiv.org/abs/1202.3665)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import astropy.units as u\n", "from astropy.coordinates import SkyCoord\n", "from gammapy.irf import load_cta_irfs\n", "from gammapy.maps import WcsGeom, MapAxis\n", "from gammapy.modeling.models import (\n", " ExpCutoffPowerLawSpectralModel,\n", " GaussianSpatialModel,\n", " SkyModel,\n", " Models,\n", " FoVBackgroundModel,\n", ")\n", "from gammapy.datasets import MapDataset\n", "from gammapy.makers import MapDatasetMaker\n", "from gammapy.data import Observation\n", "from gammapy.modeling.sampling import (\n", " run_mcmc,\n", " par_to_model,\n", " plot_corner,\n", " plot_trace,\n", ")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import logging\n", "\n", "logging.basicConfig(level=logging.INFO)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate an observation\n", "\n", "Here we will start by simulating an observation using the `simulate_dataset` method." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING:gammapy.irf.background:Invalid unit found in background table! Assuming (s-1 MeV-1 sr-1)\n" ] } ], "source": [ "irfs = load_cta_irfs(\n", " \"$GAMMAPY_DATA/cta-1dc/caldb/data/cta/1dc/bcf/South_z20_50h/irf_file.fits\"\n", ")\n", "\n", "observation = Observation.create(\n", " pointing=SkyCoord(0 * u.deg, 0 * u.deg, frame=\"galactic\"),\n", " livetime=20 * u.h,\n", " irfs=irfs,\n", ")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Define map geometry\n", "axis = MapAxis.from_edges(\n", " np.logspace(-1, 2, 15), unit=\"TeV\", name=\"energy\", interp=\"log\"\n", ")\n", "\n", "geom = WcsGeom.create(\n", " skydir=(0, 0), binsz=0.05, width=(2, 2), frame=\"galactic\", axes=[axis]\n", ")\n", "\n", "empty_dataset = MapDataset.create(geom=geom, name=\"dataset-mcmc\")\n", "maker = MapDatasetMaker(selection=[\"background\", \"edisp\", \"psf\", \"exposure\"])\n", "dataset = maker.run(empty_dataset, observation)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Models\n", "\n", "Component 0: SkyModel\n", "\n", " Name : source\n", " Datasets names : None\n", " Spectral model type : ExpCutoffPowerLawSpectralModel\n", " Spatial model type : GaussianSpatialModel\n", " Temporal model type : \n", " Parameters:\n", " index : 2.000 \n", " amplitude : 3.00e-12 1 / (cm2 s TeV)\n", " reference (frozen) : 1.000 TeV \n", " lambda_ : 0.050 1 / TeV \n", " alpha (frozen) : 1.000 \n", " lon_0 : 0.000 deg \n", " lat_0 : 0.000 deg \n", " sigma : 0.200 deg \n", " e (frozen) : 0.000 \n", " phi (frozen) : 0.000 deg \n", "\n", "Component 1: FoVBackgroundModel\n", "\n", " Name : dataset-mcmc-bkg\n", " Datasets names : ['dataset-mcmc']\n", " Spectral model type : PowerLawNormSpectralModel\n", " Parameters:\n", " norm : 1.000 \n", " tilt (frozen) : 0.000 \n", " reference (frozen) : 1.000 TeV \n", "\n", "\n" ] } ], "source": [ "# Define sky model to simulate the data\n", "spatial_model = GaussianSpatialModel(\n", " lon_0=\"0 deg\", lat_0=\"0 deg\", sigma=\"0.2 deg\", frame=\"galactic\"\n", ")\n", "\n", "spectral_model = ExpCutoffPowerLawSpectralModel(\n", " index=2,\n", " amplitude=\"3e-12 cm-2 s-1 TeV-1\",\n", " reference=\"1 TeV\",\n", " lambda_=\"0.05 TeV-1\",\n", ")\n", "\n", "sky_model_simu = SkyModel(\n", " spatial_model=spatial_model, spectral_model=spectral_model, name=\"source\"\n", ")\n", "\n", "bkg_model = FoVBackgroundModel(dataset_name=\"dataset-mcmc\")\n", "models = Models([sky_model_simu, bkg_model])\n", "print(models)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "dataset.models = models\n", "dataset.fake()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dataset.counts.sum_over_axes().plot(add_cbar=True);" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# If you want to fit the data for comparison with MCMC later\n", "\n", "# fit = Fit(dataset)\n", "# result = fit.run(optimize_opts={\"print_level\": 1})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate parameter correlations with MCMC\n", "\n", "Now let's analyse the simulated data.\n", "Here we just fit it again with the same model we had before as a starting point.\n", "The data that would be needed are the following: \n", "- counts cube, psf cube, exposure cube and background model\n", "\n", "Luckily all those maps are already in the Dataset object.\n", "\n", "We will need to define a Likelihood function and define priors on parameters.
\n", "Here we will assume a uniform prior reading the min, max parameters from the sky model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define priors\n", "\n", "This steps is a bit manual for the moment until we find a better API to define priors.
\n", "Note the you **need** to define priors for each parameter otherwise your walkers can explore uncharted territories (e.g. negative norms)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MapDataset\n", "----------\n", "\n", " Name : dataset-mcmc \n", "\n", " Total counts : 248028 \n", " Total background counts : 238923.09\n", " Total excess counts : 9104.91\n", "\n", " Predicted counts : 248096.18\n", " Predicted background counts : 238923.09\n", " Predicted excess counts : 9173.09\n", "\n", " Exposure min : 1.14e+10 m2 s\n", " Exposure max : 3.45e+11 m2 s\n", "\n", " Number of total bins : 22400 \n", " Number of fit bins : 22400 \n", "\n", " Fit statistic type : cash\n", " Fit statistic value (-2 log(L)) : -1295112.21\n", "\n", " Number of models : 2 \n", " Number of parameters : 13\n", " Number of free parameters : 7\n", "\n", " Component 0: SkyModel\n", " \n", " Name : source\n", " Datasets names : None\n", " Spectral model type : ExpCutoffPowerLawSpectralModel\n", " Spatial model type : GaussianSpatialModel\n", " Temporal model type : \n", " Parameters:\n", " index : 2.000 \n", " amplitude : 3.00e-12 1 / (cm2 s TeV)\n", " reference (frozen) : 1.000 TeV \n", " lambda_ : 0.050 1 / TeV \n", " alpha (frozen) : 1.000 \n", " lon_0 : 0.000 deg \n", " lat_0 : 0.000 deg \n", " sigma : 0.200 deg \n", " e (frozen) : 0.000 \n", " phi (frozen) : 0.000 deg \n", " \n", " Component 1: FoVBackgroundModel\n", " \n", " Name : dataset-mcmc-bkg\n", " Datasets names : ['dataset-mcmc']\n", " Spectral model type : PowerLawNormSpectralModel\n", " Parameters:\n", " norm : 1.000 \n", " tilt (frozen) : 0.000 \n", " reference (frozen) : 1.000 TeV \n", " \n", " \n" ] } ], "source": [ "print(dataset)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DatasetModels\n", "\n", "Component 0: SkyModel\n", "\n", " Name : source\n", " Datasets names : None\n", " Spectral model type : ExpCutoffPowerLawSpectralModel\n", " Spatial model type : GaussianSpatialModel\n", " Temporal model type : \n", " Parameters:\n", " index : 2.000 \n", " amplitude : 3.20e-12 1 / (cm2 s TeV)\n", " reference (frozen) : 1.000 TeV \n", " lambda_ : 0.050 1 / TeV \n", " alpha (frozen) : 1.000 \n", " lon_0 (frozen) : 0.000 deg \n", " lat_0 (frozen) : 0.000 deg \n", " sigma (frozen) : 0.200 deg \n", " e (frozen) : 0.000 \n", " phi (frozen) : 0.000 deg \n", "\n", "Component 1: FoVBackgroundModel\n", "\n", " Name : dataset-mcmc-bkg\n", " Datasets names : ['dataset-mcmc']\n", " Spectral model type : PowerLawNormSpectralModel\n", " Parameters:\n", " norm (frozen) : 1.000 \n", " tilt (frozen) : 0.000 \n", " reference (frozen) : 1.000 TeV \n", "\n", "\n", "stat = -1295094.550622083\n" ] } ], "source": [ "# Define the free parameters and min, max values\n", "parameters = dataset.models.parameters\n", "\n", "parameters[\"sigma\"].frozen = True\n", "parameters[\"lon_0\"].frozen = True\n", "parameters[\"lat_0\"].frozen = True\n", "parameters[\"amplitude\"].frozen = False\n", "parameters[\"index\"].frozen = False\n", "parameters[\"lambda_\"].frozen = False\n", "\n", "\n", "parameters[\"norm\"].frozen = True\n", "parameters[\"tilt\"].frozen = True\n", "\n", "parameters[\"norm\"].min = 0.5\n", "parameters[\"norm\"].max = 2\n", "\n", "parameters[\"index\"].min = 1\n", "parameters[\"index\"].max = 5\n", "parameters[\"lambda_\"].min = 1e-3\n", "parameters[\"lambda_\"].max = 1\n", "\n", "parameters[\"amplitude\"].min = 0.01 * parameters[\"amplitude\"].value\n", "parameters[\"amplitude\"].max = 100 * parameters[\"amplitude\"].value\n", "\n", "parameters[\"sigma\"].min = 0.05\n", "parameters[\"sigma\"].max = 1\n", "\n", "# Setting amplitude init values a bit offset to see evolution\n", "# Here starting close to the real value\n", "parameters[\"index\"].value = 2.0\n", "parameters[\"amplitude\"].value = 3.2e-12\n", "parameters[\"lambda_\"].value = 0.05\n", "\n", "print(dataset.models)\n", "print(\"stat =\", dataset.stat_sum())" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO:gammapy.modeling.sampling:Free parameters: ['index', 'amplitude', 'lambda_']\n", "INFO:gammapy.modeling.sampling:Starting MCMC sampling: nwalkers=6, nrun=150\n", "INFO:gammapy.modeling.sampling: 0%\n", "INFO:gammapy.modeling.sampling: 50%\n", "INFO:gammapy.modeling.sampling:100% => sampling completed\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 7.02 s, sys: 93.1 ms, total: 7.12 s\n", "Wall time: 7.42 s\n" ] } ], "source": [ "%%time\n", "# Now let's define a function to init parameters and run the MCMC with emcee\n", "# Depending on your number of walkers, Nrun and dimensionality, this can take a while (> minutes)\n", "sampler = run_mcmc(dataset, nwalkers=6, nrun=150) # to speedup the notebook\n", "# sampler=run_mcmc(dataset,nwalkers=12,nrun=1000) # more accurate contours" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the results\n", "\n", "The MCMC will return a sampler object containing the trace of all walkers.
\n", "The most important part is the chain attribute which is an array of shape:
\n", "_(nwalkers, nrun, nfreeparam)_\n", "\n", "The chain is then used to plot the trace of the walkers and estimate the burnin period (the time for the walkers to reach a stationary stage)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_trace(sampler, dataset)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_corner(sampler, dataset, nburn=50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the model dispersion\n", "\n", "Using the samples from the chain after the burn period, we can plot the different models compared to the truth model. To do this we need to the spectral models for each parameter state in the sample." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "emin, emax = [0.1, 100] * u.TeV\n", "nburn = 50\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(12, 6))\n", "\n", "for nwalk in range(0, 6):\n", " for n in range(nburn, nburn + 100):\n", " pars = sampler.chain[nwalk, n, :]\n", "\n", " # set model parameters\n", " par_to_model(dataset, pars)\n", " spectral_model = dataset.models[\"source\"].spectral_model\n", "\n", " spectral_model.plot(\n", " energy_range=(emin, emax),\n", " ax=ax,\n", " energy_power=2,\n", " alpha=0.02,\n", " color=\"grey\",\n", " )\n", "\n", "\n", "sky_model_simu.spectral_model.plot(\n", " energy_range=(emin, emax), energy_power=2, ax=ax, color=\"red\"\n", ");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fun Zone\n", "\n", "Now that you have the sampler chain, you have in your hands the entire history of each walkers in the N-Dimensional parameter space.
\n", "You can for example trace the steps of each walker in any parameter space." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Here we plot the trace of one walker in a given parameter space\n", "parx, pary = 0, 1\n", "\n", "plt.plot(sampler.chain[0, :, parx], sampler.chain[0, :, pary], \"ko\", ms=1)\n", "plt.plot(\n", " sampler.chain[0, :, parx],\n", " sampler.chain[0, :, pary],\n", " ls=\":\",\n", " color=\"grey\",\n", " alpha=0.5,\n", ")\n", "\n", "plt.xlabel(\"Index\")\n", "plt.ylabel(\"Amplitude\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PeVatrons in CTA ?\n", "\n", "Now it's your turn to play with this MCMC notebook. For example to test the CTA performance to measure a cutoff at very high energies (100 TeV ?).\n", "\n", "After defining your Skymodel it can be as simple as this :" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "# dataset = simulate_dataset(model, geom, pointing, irfs)\n", "# sampler = run_mcmc(dataset)\n", "# plot_trace(sampler, dataset)\n", "# plot_corner(sampler, dataset, nburn=200)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.0" }, "nbsphinx": { "orphan": true } }, "nbformat": 4, "nbformat_minor": 4 }