{ "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/v0.14?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.cube.simulate import simulate_dataset\n", "from gammapy.modeling import Fit\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", ")" ] }, { "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 nan nan 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 e 0.000e+00 nan 0.000e+00 1.000e+00 True\n", "\t phi 0.000e+00 nan deg nan nan True\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 = 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\n", ")\n", "print(sky_model_simu)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/adonath/github/adonath/gammapy/gammapy/utils/interpolation.py:159: Warning: Interpolated values reached float32 precision limit\n", " \"Interpolated values reached float32 precision limit\", Warning\n" ] } ], "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", "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": 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 nan nan 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 e 0.000e+00 nan 0.000e+00 1.000e+00 True\n", "\t phi 0.000e+00 nan deg nan nan 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) = -937934.5779072815\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": {}, "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" ] } ], "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_trace(sampler, dataset)" ] }, { "cell_type": "code", "execution_count": 12, "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": 13, "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.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", "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": 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 } }, "nbformat": 4, "nbformat_minor": 4 }