{ "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/v0.17?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/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", ")\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": [], "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": [ { "name": "stdout", "output_type": "stream", "text": [ "SkyModel\n", "\n", " Name : source\n", " Datasets names : None\n", " Spectral model type : ExpCutoffPowerLawSpectralModel\n", " Spatial model type : GaussianSpatialModel\n", " Temporal model type : None\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", "\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", "print(sky_model_simu)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Define map geometry\n", "axis = MapAxis.from_edges(\n", " np.logspace(-1, 2, 30), unit=\"TeV\", name=\"energy\", interp=\"log\"\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)\n", "dataset.models.append(sky_model_simu)\n", "dataset.fake()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dataset.counts.sum_over_axes().plot(add_cbar=True);" ] }, { "cell_type": "code", "execution_count": 8, "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": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MapDataset\n", "----------\n", "\n", " Name : dataset-mcmc \n", "\n", " Total counts : 247854 \n", " Total predicted counts : 247622.53\n", " Total background counts : 238665.45\n", "\n", " Exposure min : 9.42e+09 m2 s\n", " Exposure max : 3.67e+11 m2 s\n", "\n", " Number of total bins : 46400 \n", " Number of fit bins : 46400 \n", "\n", " Fit statistic type : cash\n", " Fit statistic value (-2 log(L)) : -938346.01\n", "\n", " Number of models : 2 \n", " Number of parameters : 13\n", " Number of free parameters : 7\n", "\n", " Component 0: BackgroundModel\n", " \n", " Name : dataset-mcmc-bkg\n", " Datasets names : ['dataset-mcmc']\n", " Parameters:\n", " norm : 1.000 \n", " tilt (frozen) : 0.000 \n", " reference (frozen) : 1.000 TeV \n", " \n", " Component 1: SkyModel\n", " \n", " Name : source\n", " Datasets names : None\n", " Spectral model type : ExpCutoffPowerLawSpectralModel\n", " Spatial model type : GaussianSpatialModel\n", " Temporal model type : None\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", " \n" ] } ], "source": [ "print(dataset)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Models\n", "\n", "Component 0: BackgroundModel\n", "\n", " Name : dataset-mcmc-bkg\n", " Datasets names : ['dataset-mcmc']\n", " Parameters:\n", " norm (frozen) : 1.000 \n", " tilt (frozen) : 0.000 \n", " reference (frozen) : 1.000 TeV \n", "\n", "Component 1: SkyModel\n", "\n", " Name : source\n", " Datasets names : None\n", " Spectral model type : ExpCutoffPowerLawSpectralModel\n", " Spatial model type : GaussianSpatialModel\n", " Temporal model type : None\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", "\n", "stat = -938334.037000552\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": 11, "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 18.5 s, sys: 191 ms, total: 18.7 s\n", "Wall time: 19 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": 12, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "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": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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": 16, "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 }