{ "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://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.13?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.spectrum.models import ExponentialCutoffPowerLaw\n", "from gammapy.image.models import SkyGaussian\n", "from gammapy.cube.models import SkyModel\n", "from gammapy.cube.simulate import simulate_dataset\n", "from gammapy.utils.fitting import Fit\n", "from gammapy.utils.fitting.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", ")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SkyModel\n", "\n", "Parameters: \n", "\n", "\t name value error unit min max frozen\n", "\t--------- --------- ----- -------------- ---------- --------- ------\n", "\t lon_0 0.000e+00 nan deg -1.800e+02 1.800e+02 False\n", "\t lat_0 0.000e+00 nan deg -9.000e+01 9.000e+01 False\n", "\t sigma 2.000e-01 nan deg 0.000e+00 nan False\n", "\t index 2.000e+00 nan nan nan False\n", "\tamplitude 3.000e-12 nan cm-2 s-1 TeV-1 nan nan False\n", "\treference 1.000e+00 nan TeV nan nan True\n", "\t lambda_ 5.000e-02 nan TeV-1 nan nan False\n" ] } ], "source": [ "# Define sky model to simulate the data\n", "spatial_model = SkyGaussian(lon_0=\"0 deg\", lat_0=\"0 deg\", sigma=\"0.2 deg\")\n", "\n", "spectral_model = ExponentialCutoffPowerLaw(\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\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), coordsys=\"GAL\", axes=[axis]\n", ")\n", "\n", "# Define some observation parameters\n", "pointing = SkyCoord(0 * u.deg, 0 * u.deg, frame=\"galactic\")\n", "\n", "\n", "dataset = simulate_dataset(\n", " sky_model_simu, geom, pointing, irfs, livetime=20 * u.h, random_state=42\n", ")" ] }, { "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": [ "SkyModels\n", "\n", "Component 0: SkyModel\n", "\n", "Parameters: \n", "\n", "\t name value error unit min max frozen\n", "\t--------- --------- ----- -------------- ---------- --------- ------\n", "\t lon_0 0.000e+00 nan deg -1.800e+02 1.800e+02 True\n", "\t lat_0 0.000e+00 nan deg -9.000e+01 9.000e+01 True\n", "\t sigma 2.000e-01 nan deg 5.000e-02 1.000e+00 True\n", "\t index 2.000e+00 nan 1.000e+00 5.000e+00 False\n", "\tamplitude 3.200e-12 nan cm-2 s-1 TeV-1 3.000e-14 3.000e-10 False\n", "\treference 1.000e+00 nan TeV nan nan True\n", "\t lambda_ 5.000e-02 nan TeV-1 1.000e-03 1.000e+00 False\n", "\n", "\t\n", "\n", "\n", "log(L) = -937934.5779251754\n" ] } ], "source": [ "# Define the free parameters and min, max values\n", "\n", "dataset.parameters[\"sigma\"].frozen = True\n", "dataset.parameters[\"lon_0\"].frozen = True\n", "dataset.parameters[\"lat_0\"].frozen = True\n", "dataset.parameters[\"amplitude\"].frozen = False\n", "dataset.parameters[\"index\"].frozen = False\n", "dataset.parameters[\"lambda_\"].frozen = False\n", "\n", "\n", "dataset.background_model.parameters[\"norm\"].frozen = True\n", "dataset.background_model.parameters[\"tilt\"].frozen = True\n", "\n", "dataset.background_model.parameters[\"norm\"].min = 0.5\n", "dataset.background_model.parameters[\"norm\"].max = 2\n", "\n", "dataset.parameters[\"index\"].min = 1\n", "dataset.parameters[\"index\"].max = 5\n", "dataset.parameters[\"lambda_\"].min = 1e-3\n", "dataset.parameters[\"lambda_\"].max = 1\n", "\n", "dataset.parameters[\"amplitude\"].min = (\n", " 0.01 * dataset.parameters[\"amplitude\"].value\n", ")\n", "dataset.parameters[\"amplitude\"].max = (\n", " 100 * dataset.parameters[\"amplitude\"].value\n", ")\n", "\n", "dataset.parameters[\"sigma\"].min = 0.05\n", "dataset.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", "dataset.parameters[\"index\"].value = 2.0\n", "dataset.parameters[\"amplitude\"].value = 3.2e-12\n", "dataset.parameters[\"lambda_\"].value = 0.05\n", "\n", "print(dataset.model)\n", "print(\"log(L) =\", dataset.likelihood())" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO:gammapy.utils.fitting.sampling:Free parameters: ['index', 'amplitude', 'lambda_']\n", "INFO:gammapy.utils.fitting.sampling:Starting MCMC sampling: nwalkers=6, nrun=150\n", "INFO:gammapy.utils.fitting.sampling: 0%\n", "INFO:gammapy.utils.fitting.sampling: 50%\n", "INFO:gammapy.utils.fitting.sampling:100% => sampling completed\n" ] } ], "source": [ "# 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": 11, "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": 13, "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.model.skymodels[0].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": 14, "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": 15, "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 }, "pycharm": { "stem_cell": { "cell_type": "raw", "metadata": { "collapsed": false }, "source": [] } } }, "nbformat": 4, "nbformat_minor": 2 }