{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting a model to data with both x and y errors with `Bilby`\n",
    "\n",
    "Usually when we fit a model to data with a Gaussian Likelihood we assume that we know x values exactly. This is almost never the case. Here we show how to fit a model with errors in both x and y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:20:09.234194Z",
     "iopub.status.busy": "2024-05-20T23:20:09.233683Z",
     "iopub.status.idle": "2024-05-20T23:20:10.543558Z",
     "shell.execute_reply": "2024-05-20T23:20:10.542893Z"
    }
   },
   "outputs": [],
   "source": [
    "import bilby\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate data\n",
    "\n",
    "First we create the data and plot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:20:10.548146Z",
     "iopub.status.busy": "2024-05-20T23:20:10.547627Z",
     "iopub.status.idle": "2024-05-20T23:20:10.702107Z",
     "shell.execute_reply": "2024-05-20T23:20:10.700689Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define our model, a line\n",
    "def model(x, m, c, **kwargs):\n",
    "    y = m * x + c\n",
    "    return y\n",
    "\n",
    "\n",
    "# make a function to create and plot our data\n",
    "def make_data(points, m, c, xerr, yerr, seed):\n",
    "    np.random.seed(int(seed))\n",
    "    xtrue = np.linspace(0, 100, points)\n",
    "    ytrue = model(x=xtrue, m=m, c=c)\n",
    "\n",
    "    xerr_vals = xerr * np.random.randn(points)\n",
    "    yerr_vals = yerr * np.random.randn(points)\n",
    "    xobs = xtrue + xerr_vals\n",
    "    yobs = ytrue + yerr_vals\n",
    "\n",
    "    plt.errorbar(xobs, yobs, xerr=xerr, yerr=yerr, fmt=\"x\")\n",
    "    plt.errorbar(xtrue, ytrue, yerr=yerr, color=\"black\", alpha=0.5)\n",
    "    plt.xlim(0, 100)\n",
    "    plt.show()\n",
    "    plt.close()\n",
    "\n",
    "    data = {\n",
    "        \"xtrue\": xtrue,\n",
    "        \"ytrue\": ytrue,\n",
    "        \"xobs\": xobs,\n",
    "        \"yobs\": yobs,\n",
    "        \"xerr\": xerr,\n",
    "        \"yerr\": yerr,\n",
    "    }\n",
    "\n",
    "    return data\n",
    "\n",
    "\n",
    "data = make_data(points=30, m=5, c=10, xerr=5, yerr=5, seed=123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define our prior and sampler settings\n",
    "\n",
    "Now lets set up the prior and bilby output directory/sampler settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:20:10.708332Z",
     "iopub.status.busy": "2024-05-20T23:20:10.707853Z",
     "iopub.status.idle": "2024-05-20T23:20:10.713683Z",
     "shell.execute_reply": "2024-05-20T23:20:10.712845Z"
    }
   },
   "outputs": [],
   "source": [
    "# setting up bilby priors\n",
    "priors = dict(\n",
    "    m=bilby.core.prior.Uniform(0, 30, \"m\"), c=bilby.core.prior.Uniform(0, 30, \"c\")\n",
    ")\n",
    "\n",
    "sampler_kwargs = dict(priors=priors, sampler=\"bilby_mcmc\", nsamples=1000, printdt=5, outdir=\"outdir\", verbose=False, clean=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit with exactly known x-values\n",
    "\n",
    "Our first step is to recover the straight line using a simple Gaussian Likelihood that only takes into account the y errors. Under the assumption we know x exactly. In this case, we pass in xtrue for x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:20:10.716661Z",
     "iopub.status.busy": "2024-05-20T23:20:10.716282Z",
     "iopub.status.idle": "2024-05-20T23:20:37.832716Z",
     "shell.execute_reply": "2024-05-20T23:20:37.832081Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Running for label 'known_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Analysis likelihood class: <class 'bilby.core.likelihood.GaussianLikelihood'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Single likelihood evaluation took nan s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Using sampler Bilby_MCMC with kwargs {'nsamples': 1000, 'nensemble': 1, 'pt_ensemble': False, 'ntemps': 1, 'Tmax': None, 'Tmax_from_SNR': 20, 'initial_betas': None, 'adapt': True, 'adapt_t0': 100, 'adapt_nu': 10, 'pt_rejection_sample': False, 'burn_in_nact': 10, 'thin_by_nact': 1, 'fixed_discard': 0, 'autocorr_c': 5, 'L1steps': 100, 'L2steps': 3, 'printdt': 5, 'check_point_delta_t': 1800, 'min_tau': 1, 'proposal_cycle': 'default', 'stop_after_convergence': False, 'fixed_tau': None, 'tau_window': None, 'evidence_method': 'stepping_stone', 'initial_sample_method': 'prior', 'initial_sample_dict': None}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Initializing BilbyPTMCMCSampler with:\n",
      "  Convergence settings: ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n",
      "  Parallel-tempering settings: ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n",
      "  proposal_cycle: default\n",
      "  pt_rejection_sample: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Setting parallel tempering inputs=ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Initializing BilbyPTMCMCSampler with:ntemps=1, nensemble=1, pt_ensemble=False, initial_betas=[1], initial_sample_method=prior, initial_sample_dict=None\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Using initial sample {'m': 15.810698997802085, 'c': 11.844516583873343}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Using ProposalCycle:\n",
      "  AdaptiveGaussianProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  DifferentialEvolutionProposal(acceptance_ratio:nan,n:0,)\n",
      "  UniformProposal(acceptance_ratio:nan,n:0,)\n",
      "  KDEProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "  FisherMatrixProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  GMMProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Setting convergence_inputs=ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby WARNING : Non-negligible print progress time (ppt_frac=0.04)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Written checkpoint file outdir/known_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:2.7e+04,scale:0.0052,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.46,n:2.7e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : UniformProposal(acceptance_ratio:1,n:1.6e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : KDEProposal(acceptance_ratio:3.4e-05,n:2.9e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.56,n:2.4e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : GMMProposal(acceptance_ratio:0.00011,n:2.7e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Current taus={'m': 1, 'c': 1.0}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Sampling time: 0:00:15.031416\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Summary of results:\n",
      "nsamples: 1264\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence:    nan +/-    nan\n",
      "ln_bayes_factor:    nan +/-    nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "known_x = bilby.core.likelihood.GaussianLikelihood(\n",
    "    x=data[\"xtrue\"], y=data[\"yobs\"], func=model, sigma=data[\"yerr\"]\n",
    ")\n",
    "result_known_x = bilby.run_sampler(\n",
    "    likelihood=known_x,\n",
    "    label=\"known_x\",\n",
    "    **sampler_kwargs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:20:37.836944Z",
     "iopub.status.busy": "2024-05-20T23:20:37.836432Z",
     "iopub.status.idle": "2024-05-20T23:20:39.159491Z",
     "shell.execute_reply": "2024-05-20T23:20:39.158694Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_known_x.plot_corner(truth=dict(m=5, c=10), titles=True, save=False)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit with unmodeled uncertainty in the x-values\n",
    "\n",
    "As expected this is easy to recover and the sampler does a good job. However this was made too easy - by passing in the 'true' values of x. Lets see what happens when we pass in the observed values of x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:20:39.162975Z",
     "iopub.status.busy": "2024-05-20T23:20:39.162364Z",
     "iopub.status.idle": "2024-05-20T23:21:09.771025Z",
     "shell.execute_reply": "2024-05-20T23:21:09.769642Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Running for label 'incorrect_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Analysis likelihood class: <class 'bilby.core.likelihood.GaussianLikelihood'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Single likelihood evaluation took nan s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Using sampler Bilby_MCMC with kwargs {'nsamples': 1000, 'nensemble': 1, 'pt_ensemble': False, 'ntemps': 1, 'Tmax': None, 'Tmax_from_SNR': 20, 'initial_betas': None, 'adapt': True, 'adapt_t0': 100, 'adapt_nu': 10, 'pt_rejection_sample': False, 'burn_in_nact': 10, 'thin_by_nact': 1, 'fixed_discard': 0, 'autocorr_c': 5, 'L1steps': 100, 'L2steps': 3, 'printdt': 5, 'check_point_delta_t': 1800, 'min_tau': 1, 'proposal_cycle': 'default', 'stop_after_convergence': False, 'fixed_tau': None, 'tau_window': None, 'evidence_method': 'stepping_stone', 'initial_sample_method': 'prior', 'initial_sample_dict': None}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Initializing BilbyPTMCMCSampler with:\n",
      "  Convergence settings: ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n",
      "  Parallel-tempering settings: ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n",
      "  proposal_cycle: default\n",
      "  pt_rejection_sample: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Setting parallel tempering inputs=ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Initializing BilbyPTMCMCSampler with:ntemps=1, nensemble=1, pt_ensemble=False, initial_betas=[1], initial_sample_method=prior, initial_sample_dict=None\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Using initial sample {'m': 16.814336421520974, 'c': 3.786598865474473}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Using ProposalCycle:\n",
      "  AdaptiveGaussianProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  DifferentialEvolutionProposal(acceptance_ratio:nan,n:0,)\n",
      "  UniformProposal(acceptance_ratio:nan,n:0,)\n",
      "  KDEProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "  FisherMatrixProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  GMMProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Setting convergence_inputs=ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:20 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Written checkpoint file outdir/incorrect_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:3.7e+04,scale:0.0042,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.47,n:3.8e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : UniformProposal(acceptance_ratio:1,n:2.1e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : KDEProposal(acceptance_ratio:0.0001,n:3.8e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.55,n:3.5e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : GMMProposal(acceptance_ratio:0,n:3.8e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Current taus={'m': 1.3, 'c': 1.2}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Sampling time: 0:00:20.018064\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Summary of results:\n",
      "nsamples: 1670\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence:    nan +/-    nan\n",
      "ln_bayes_factor:    nan +/-    nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "incorrect_x = bilby.core.likelihood.GaussianLikelihood(\n",
    "    x=data[\"xobs\"], y=data[\"yobs\"], func=model, sigma=data[\"yerr\"]\n",
    ")\n",
    "result_incorrect_x = bilby.run_sampler(\n",
    "    likelihood=incorrect_x,\n",
    "    label=\"incorrect_x\",\n",
    "    **sampler_kwargs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:21:09.776965Z",
     "iopub.status.busy": "2024-05-20T23:21:09.776534Z",
     "iopub.status.idle": "2024-05-20T23:21:10.005815Z",
     "shell.execute_reply": "2024-05-20T23:21:10.005154Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_incorrect_x.plot_corner(truth=dict(m=5, c=10), titles=True, save=False)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit with modeled uncertainty in x-values\n",
    "\n",
    "This is not good as there is unmodelled uncertainty in our `x` values.\n",
    "Getting around this requires marginalisation of the true x values or sampling over them. \n",
    "See discussion in section 7 of https://arxiv.org/pdf/1008.4686.pdf.\n",
    "\n",
    "For this, we will have to define a new likelihood class.\n",
    "By subclassing the base `bilby.core.likelihood.Likelihood` class we can do this fairly simply."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:21:10.009146Z",
     "iopub.status.busy": "2024-05-20T23:21:10.008797Z",
     "iopub.status.idle": "2024-05-20T23:21:10.014784Z",
     "shell.execute_reply": "2024-05-20T23:21:10.014007Z"
    }
   },
   "outputs": [],
   "source": [
    "class GaussianLikelihoodUncertainX(bilby.core.likelihood.Likelihood):\n",
    "    def __init__(self, xobs, yobs, xerr, yerr, function):\n",
    "        \"\"\"\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        xobs, yobs: array_like\n",
    "            The data to analyse\n",
    "        xerr, yerr: array_like\n",
    "            The standard deviation of the noise\n",
    "        function:\n",
    "            The python function to fit to the data\n",
    "        \"\"\"\n",
    "        super(GaussianLikelihoodUncertainX, self).__init__(dict())\n",
    "        self.xobs = xobs\n",
    "        self.yobs = yobs\n",
    "        self.yerr = yerr\n",
    "        self.xerr = xerr\n",
    "        self.function = function\n",
    "\n",
    "    def log_likelihood(self):\n",
    "        variance = (self.xerr * self.parameters[\"m\"]) ** 2 + self.yerr**2\n",
    "        model_y = self.function(self.xobs, **self.parameters)\n",
    "        residual = self.yobs - model_y\n",
    "\n",
    "        ll = -0.5 * np.sum(residual**2 / variance + np.log(variance))\n",
    "\n",
    "        return -0.5 * np.sum(residual**2 / variance + np.log(variance))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:21:10.017780Z",
     "iopub.status.busy": "2024-05-20T23:21:10.017300Z",
     "iopub.status.idle": "2024-05-20T23:21:36.544851Z",
     "shell.execute_reply": "2024-05-20T23:21:36.544292Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Running for label 'unknown_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Analysis likelihood class: <class '__main__.GaussianLikelihoodUncertainX'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Single likelihood evaluation took nan s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Using sampler Bilby_MCMC with kwargs {'nsamples': 1000, 'nensemble': 1, 'pt_ensemble': False, 'ntemps': 1, 'Tmax': None, 'Tmax_from_SNR': 20, 'initial_betas': None, 'adapt': True, 'adapt_t0': 100, 'adapt_nu': 10, 'pt_rejection_sample': False, 'burn_in_nact': 10, 'thin_by_nact': 1, 'fixed_discard': 0, 'autocorr_c': 5, 'L1steps': 100, 'L2steps': 3, 'printdt': 5, 'check_point_delta_t': 1800, 'min_tau': 1, 'proposal_cycle': 'default', 'stop_after_convergence': False, 'fixed_tau': None, 'tau_window': None, 'evidence_method': 'stepping_stone', 'initial_sample_method': 'prior', 'initial_sample_dict': None}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Initializing BilbyPTMCMCSampler with:\n",
      "  Convergence settings: ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n",
      "  Parallel-tempering settings: ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n",
      "  proposal_cycle: default\n",
      "  pt_rejection_sample: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Setting parallel tempering inputs=ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Initializing BilbyPTMCMCSampler with:ntemps=1, nensemble=1, pt_ensemble=False, initial_betas=[1], initial_sample_method=prior, initial_sample_dict=None\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Using initial sample {'m': 21.8959963110563, 'c': 1.3793055979916036}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Using ProposalCycle:\n",
      "  AdaptiveGaussianProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  DifferentialEvolutionProposal(acceptance_ratio:nan,n:0,)\n",
      "  UniformProposal(acceptance_ratio:nan,n:0,)\n",
      "  KDEProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "  FisherMatrixProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  GMMProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Setting convergence_inputs=ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Written checkpoint file outdir/unknown_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:2.7e+04,scale:0.021,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.47,n:2.8e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : UniformProposal(acceptance_ratio:1,n:2e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : KDEProposal(acceptance_ratio:0.001,n:3.2e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.53,n:2.8e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : GMMProposal(acceptance_ratio:0.001,n:3.1e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Current taus={'m': 1.0, 'c': 1.1}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Sampling time: 0:00:15.013917\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "23:21 bilby INFO    : Summary of results:\n",
      "nsamples: 1374\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence:    nan +/-    nan\n",
      "ln_bayes_factor:    nan +/-    nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "gaussian_unknown_x = GaussianLikelihoodUncertainX(\n",
    "    xobs=data[\"xobs\"],\n",
    "    yobs=data[\"yobs\"],\n",
    "    xerr=data[\"xerr\"],\n",
    "    yerr=data[\"yerr\"],\n",
    "    function=model,\n",
    ")\n",
    "result_unknown_x = bilby.run_sampler(\n",
    "    likelihood=gaussian_unknown_x,\n",
    "    label=\"unknown_x\",\n",
    "    **sampler_kwargs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-20T23:21:36.548341Z",
     "iopub.status.busy": "2024-05-20T23:21:36.547970Z",
     "iopub.status.idle": "2024-05-20T23:21:36.788634Z",
     "shell.execute_reply": "2024-05-20T23:21:36.787740Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_unknown_x.plot_corner(truth=dict(m=5, c=10), titles=True, save=False)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Success! The inferred posterior is consistent with the true values."
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}