{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian Processes Inferencing in Stingray\n", "\n", "## Gaussian Processes in Astronomy\n", "\n", "Please Note: this functionality is still under development. Testing and comments are welcome!\n", "\n", "Gaussian Processes (GPs) are a powerful class of Statistical Models, that help us model both the deterministic and stochastic part of a random process. We model the covaraince between pairs of samples (using the kernel function) and the underlying deterministic function (using the mean function) and fit or infer from the data set. \n", "\n", "GP Regression and inferencing (GPR) has become increasingly popular in the astronomical community over the last decade as it can model non-trivial random or unkown signals. Sometimes, we are interested in the stochastic behaviour itself, and we can\n", "infer its characteristics or predict its behaviour using Gaussian Processes.\n", "\n", "\n", "While we can use GP's to produce models for various signals, we often have to identify if the particular time-series has a particular signal and we resort to Bayesian Model Comparison. We compare the two models by the Bayes factor, which is the ratio of the evidences of two comparing models. Since Evidence Calculation is a difficult problem, we will use Nested Sampling, with the Jaxns library to get the Bayes Factor." ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Sample Lightcurve\n", "As an example demonstrating the use of gpmodeling in Stingray, we will make a sample lightcurve based on a QPO (quasi periodic signal), and use the ratio of Evidence of the following two models to identify whether the signal contains a Quasi-Periodic Signal or not. \n", "\n", "The two models being:\n", "\n", "1. A RN (Red-Noise) model, which has a Red noise kernel and Gaussian function for its mean.\n", "2. A QPO_plus_Rn (QPO + RN) model, which uses a QPO kernel and a double skew gaussian function for its mean.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note:** It is important to enable 64 bit precision for the Jaxns sampling to work properly." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Importing the necessary libraries\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import jax\n", "import jax.numpy as jnp\n", "import seaborn as sns\n", "sns.set_style('whitegrid')\n", "\n", "from tinygp import GaussianProcess, kernels\n", "from stingray import Lightcurve\n", "\n", "# suppress warnings\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "# Important to enable 64-bit precision\n", "jax.config.update(\"jax_enable_x64\", True)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "For making the **Toy Lightcurve**, we will use a GP with a QPO_plus_RN kernel, and a Skew-Gaussian Mean function and take a sample from it. We will also add a jitter term to introduce some noise into the sample.\n", "\n", "We will need a kernel and a mean function to make the GP. We can either make our own kernels using Tinygp or we can get some useful kernels using the `gpmodeling.get_kernel` function. \n", "\n", "**`get_kernel`** function takes the kernel type (QPO_plus_RN and RN), and the kernel parameters and returns a TinyGp kernel for it.\n", "\n", "Similarly for the mean function, we can make our own or use `gpmodeling.get_mean` function." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from stingray.modeling.gpmodeling import get_kernel, get_mean\n", "\n", "times = np.linspace(0,1,256)\n", "\n", "# We will take suitable parameters for a high amplitude QPO with a double skew gaussian mean\n", "kernel_params = {\"arn\" : jnp.exp(1.5), \"crn\" : jnp.exp(1.0),\n", " \"aqpo\": jnp.exp(-0.4), \"cqpo\": jnp.exp(1), \"freq\": 20,}\n", "kernel = get_kernel(kernel_type = \"QPO_plus_RN\", kernel_params = kernel_params)\n", "\n", "mean_params = {\"A\" : jnp.array([3.0, 4.0]), \"t0\" : jnp.array([0.2, 0.7]), \n", " \"sig1\" : jnp.array([0.2, 0.1]), \"sig2\" : jnp.array([0.3, 0.4]), }\n", "\n", "mean = get_mean(mean_type = \"skew_gaussian\", mean_params = mean_params)\n", "\n", "jit = 1e-1\n", "gp = GaussianProcess(kernel = kernel, X = times, mean_value = mean(times), diag = jit)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the Sample Lightcurve" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sampling out a lightcurve from the GP\n", "counts = gp.sample(key = jax.random.PRNGKey(6))\n", "yerr = (jit)*np.ones_like(times)\n", "\n", "fig, ax = plt.subplots(1,1, figsize = (14,6))\n", "ax.errorbar(times, counts.T, yerr=yerr, fmt=\".k\", capsize=0, label=\"data\")\n", "ax.plot(times, mean(times), color = \"orange\" ,label = \"Mean\"); ax.legend()\n", "ax.plot(times, counts, label = \"Sample GP\", alpha = 0.5)\n", "ax.set_xlabel(\"Time\"); ax.set_ylabel(\"Counts\")\n", "\n", "lc = Lightcurve(time = times, counts = counts, dt = times[1]- times[0], skip_checks = True)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Parameter Posterior Analysis\n", "\n", "We will now make our two differing model and then compare the evidences (log evidences $log(p(D|M)) $ ) of fitting the data to the model to check which one fits better.\n", "\n", "The main function that we will use will be:\n", "\n", "* `gpmodeling.get_gp_params`: This function gives us a list of the parameters of the model based on the kernel and mean type we select.\n", "\n", "* `gpmodeling.get_prior_dict`: This function will be can be used to get a suitable generater prior function for a jaxns model. We have to give it our parameter list, and a dictionary with suitable tfpd distributions for the priors. \n", "\n", "* `gpmodeling.get_log_likelihood`: This function will give us a log_likelihood function which calculates the log likelihood probabilty of the data for the given parameter $p(D|\\theta, M)$. Here we will have to provide the parameters list, the kernel and mean type of the GP model, as well as the Times and counts of the lightcurve.\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "### Model 1\n", "\n", "The first model which we will make will be a Red-Noise model ,we will use the get_prior and get_likelihood functions to make a suitable prior and log_likelihood function for our Inference. \n", "\n", "The model will have a Red Noise kernel \n", "\n", "$$\n", "k_{rn}(\\tau) = a \\; exp(-c\\tau) $$\n", "\n", "where $\\tau = |x_i - x_j|$ and the mean function as a gaussian distribution." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "parameters list ['log_arn', 'log_crn', 'log_A', 't0', 'log_sig']\n" ] } ], "source": [ "import tensorflow_probability.substrates.jax as tfp\n", "from stingray.modeling.gpmodeling import get_prior, get_log_likelihood, get_gp_params\n", "tfpd = tfp.distributions\n", "tfpb = tfp.bijectors\n", "\n", "params_list = get_gp_params(kernel_type= \"RN\", mean_type = \"gaussian\")\n", "print(\"parameters list\", params_list)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "We make a parameter list as jaxns requires the parameters in the prior function and log likelihood to be of the same order. Thus if one is using the standard kernel and means then parameter list comes handy, otherwise one can make our own prior and likelihood function." ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### Prior and log likelihood\n", "\n", "We use Tensorflow_probility to make the parameter priors and put them into the prior_dictionary. The prior types and bounds can be set according to the user discretion. \n", "\n", "**Note** : The priors can be Tfp priors or bijected priors, but we cannot use tfp.joint_distributions in our priors. To make multi-parameter priors or conditioned parameter priors, one can use the priors in `jaxns.special_priors`. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "total_time = times[-1] - times[0]\n", "f = 1/(times[1]- times[0])\n", "span = jnp.max(counts) - jnp.min(counts)\n", "\n", "# The prior dictionary, with suitable tfpd prior distributions\n", "prior_dict = {\n", " \"log_A\": tfpd.Uniform(low = jnp.log(0.1 * span), high= jnp.log(2 * span)),\n", " \"t0\": tfpd.Uniform(low = times[0] - 0.1*total_time, high = times[-1] + 0.1*total_time),\n", " \"log_sig\": tfpd.Uniform(low = jnp.log(0.5 * 1 / f), high = jnp.log(2 * total_time)),\n", " \"log_arn\": tfpd.Uniform(low = jnp.log(0.1 * span), high = jnp.log(2 * span)),\n", " \"log_crn\": tfpd.Uniform(low = jnp.log(1 / total_time), high = jnp.log(f)),\n", "}\n", "\n", "params_list2 = [\"log_arn\", \"log_crn\", \"log_A\", \"t0\", \"log_sig\"]\n", "\n", "prior_model = get_prior(params_list2, prior_dict)\n", "\n", "log_likelihood_model = get_log_likelihood(params_list2, kernel_type= \"RN\", mean_type = \"gaussian\", times = times, counts = counts)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### Sampling Model 1\n", "\n", "We can initialise the GPResult class using a stingray lightcurve, and then perform a Nested Sampling for the given prior_model and likelihood_model." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO[2023-10-19 22:11:44,231]: Sanity check...\n", "INFO[2023-10-19 22:11:44,432]: Sanity check passed\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Simulation Complete\n" ] } ], "source": [ "from stingray.modeling.gpmodeling import GPResult\n", "\n", "gpresult = GPResult(lc = lc)\n", "gpresult.sample(prior_model = prior_model, likelihood_model = log_likelihood_model)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "We can check the Evidence for the data given the model $Z = p(D|M_1)$, as well see the sampling outcomes for the used parameters." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log Evidence: -252.0393784723225\n" ] } ], "source": [ "print(\"log Evidence: \", gpresult.get_evidence())" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "Using the plotting functionality of the GPResult class, we can visualise the posterior distributions of our parameters, look at sampling run summaries and diagnostics." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot = gpresult.posterior_plot(\"log_A\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--------\n", "Termination Conditions:\n", "Small remaining evidence\n", "--------\n", "# likelihood evals: 309792\n", "# samples: 7500\n", "# slices: 75000.0\n", "# slices / acceptance: 15.0\n", "# likelihood evals / sample: 41.3\n", "# likelihood evals / slice: 3.9\n", "--------\n", "logZ=-252.04 +- 0.12\n", "H=250.0\n", "ESS=1590\n", "--------\n", "log_A: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_A: 0.99 +- 0.15 | 0.82 / 0.99 / 1.16 | 1.13 | 1.13\n", "--------\n", "log_arn: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_arn: 0.39 +- 0.32 | 0.06 / 0.33 / 0.75 | 0.14 | 0.14\n", "--------\n", "log_crn: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_crn: 3.69 +- 0.34 | 3.29 / 3.75 / 4.05 | 3.95 | 3.95\n", "--------\n", "log_sig: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_sig: -0.15 +- 0.54 | -0.81 / -0.11 / 0.51 | -0.84 | -0.84\n", "--------\n", "t0: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "t0: 0.63 +- 0.27 | 0.22 / 0.65 / 0.97 | 0.63 | 0.63\n", "--------\n" ] } ], "source": [ "gpresult.print_summary()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "### Model 2\n", "\n", "For the second model, we will make a QPO_plus_RN kernel \n", "\n", "$$\n", "k_{qpo+rn}(\\tau) = a_{qpo} \\; exp(-c_{qpo} \\tau) \\; cos(2\\pi f\\tau) + a_{rn} \\; exp(-c_{rn} \\tau)\n", "$$\n", "\n", "We will also use a gaussian mean function with two modes as the mean function.\n", "\n", "For this model, we will be making the prior and log_likelihood function on our own instead of using the `get_prior` and `get_likelihood` functions. This will give us more flexibility.\n", "\n", "The prior function must be a jaxns compatible prior function. It is quite similar to making the prior_dictionary, just that here, we will wrap each parameters (tfp) prior into the `jaxns.prior` function and use yield to make it a generator function. Then we will return all the parameters in a specific order." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['log_arn', 'log_crn', 'log_aqpo', 'log_cqpo', 'log_freq', 'log_A', 't0', 'log_sig']\n" ] } ], "source": [ "# Prior Function\n", "from jaxns import Prior\n", "from jaxns.special_priors import ForcedIdentifiability\n", "from jaxns.types import float_type\n", "\n", "params_list2 = get_gp_params(kernel_type= \"QPO_plus_RN\", mean_type = \"gaussian\")\n", "print(params_list2)\n", "\n", "total_time = times[-1] - times[0]\n", "f = 1/(times[1]- times[0])\n", "span = jnp.max(counts) - jnp.min(counts)\n", "\n", "# Here, we have made mutiple mean function with 2 gaussians.\n", "def prior_model2():\n", " log_arn = yield Prior(tfpd.Uniform(low = jnp.log(0.1 * span), high = jnp.log(2 * span)), name='log_arn')\n", " log_crn = yield Prior(tfpd.Uniform(low = jnp.log(1 / total_time), high = jnp.log(f)), name='log_crn')\n", " log_aqpo = yield Prior(tfpd.Uniform(low = jnp.log(0.1 * span), high = jnp.log(2 * span)), name='log_aqpo')\n", " log_cqpo = yield Prior(tfpd.Uniform(low = jnp.log(1/10/total_time), high = jnp.log(f)), name='log_cqpo')\n", " log_freq = yield Prior(tfpd.Uniform(low = jnp.log(2) , high = jnp.log(f/4) ), name='log_freq')\n", "\n", " n = 2\n", " log_A = yield Prior(tfpd.Uniform(low = jnp.log(0.1 * span)*jnp.ones(n), high = jnp.log(2 * span)*jnp.ones(n)), \n", " name='log_A')\n", " \n", " # This is special conditional beta function for the peak times of gaussians which prevents degeneracies\n", " t0 = []\n", " scale_bij = tfp.bijectors.Scale(scale = times[-1] - times[0])\n", " shift_bij = tfp.bijectors.Shift(shift= times[0])\n", " for i in range(n):\n", " underlying_beta = tfpd.Beta(\n", " concentration1=jnp.asarray(1., float_type),\n", " concentration0=jnp.asarray(n - i, float_type)\n", " )\n", " t = yield Prior(shift_bij(scale_bij(underlying_beta)), name=f\"t{i}\")\n", " # Updating the shift and scale here\n", " scale_bij = tfp.bijectors.Scale(scale= times[-1] - t)\n", " shift_bij = tfp.bijectors.Shift(shift=t)\n", " t0.append(t)\n", " t0 = jnp.stack(t0)\n", " \n", " log_sig = yield Prior(tfpd.Uniform(low = jnp.log(0.5 * 1 / f) *jnp.ones(n), high = jnp.log(2 * total_time) *jnp.ones(n)), name='log_sig')\n", "\n", " return log_arn, log_crn, log_aqpo, log_cqpo, log_freq, log_A, t0, log_sig\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "For the log_likelihood function, we have to take the paremeters (same order), and return $log(p(D|M)) $ the log probability of fitting the data to the model. This can be done by making the suitable Gaussian process and returning the ` gp.log_probability(lightcurve_counts)`\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def log_likelihood_model2( log_arn, log_crn, log_aqpo, log_cqpo, log_freq, log_A, t0, log_sig ):\n", " \n", " kernel_params = { \"arn\": jnp.exp(log_arn), \"crn\": jnp.exp(log_crn), \"aqpo\": jnp.exp(log_aqpo), \n", " \"cqpo\": jnp.exp(log_cqpo), \"freq\": jnp.exp(log_freq)}\n", " mean_params = {\"A\": jnp.exp(log_A), \"t0\": t0, \"sig\": jnp.exp(log_sig)}\n", "\n", " kernel = get_kernel(kernel_type=\"QPO_plus_RN\", kernel_params=kernel_params)\n", " mean = get_mean(mean_type=\"gaussian\", mean_params=mean_params)\n", " gp = GaussianProcess(kernel, times, mean_value=mean(times))\n", "\n", " return gp.log_probability(counts)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### Sampling Model 2\n", "\n", "Similar to the previous case, we will make a GPresult object by initialising with the lightcurve. Then we will sample the posterior using the prior and log_likelihood model." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO[2023-10-19 22:13:04,424]: Sanity check...\n", "INFO[2023-10-19 22:13:04,601]: Sanity check passed\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Simulation Complete\n" ] } ], "source": [ "gpresult2 = GPResult(lc = lc)\n", "gpresult2.sample(prior_model = prior_model2, likelihood_model = log_likelihood_model2, max_samples = 2e4)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "This time we get a lower log evidence than the previous model." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log Evidence: -241.34533744186058\n" ] } ], "source": [ "print(\"log Evidence: \", gpresult2.get_evidence())" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Evidence Comparison\n", "\n", "On comapring the evidences of the two model we get the Bayes Factor.\n", "\n", "For $M_1$ being QPO_plus_RN model and $M_2$ being the plain RN model.\n", "\n", "$$\n", "ln(BF) = ln(Z_1) - ln(Z_2) = -245.70 - (-251.77) = 6.06\n", "$$\n", "\n", "As BF is greater than 5.0, this gives us a strong indication that the time series has a Quasi Oscillatory behaviour.\n", "\n", "Also, as we can see in the weighted posterior plot for the frequency, We had used a frequency of 20 Hz for our sample and this has been captured very well by the Nested Sampling Inference." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean of freq: 19.35595259854821\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot = gpresult2.weighted_posterior_plot(\"log_freq\")\n", "print(\"Mean of freq:\", jnp.exp(2.963)) " ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "For more information on the posterior, we can see a comparison plot between two parameters. (Here the peak times of the gaussian means, which we had conditioned as $t_1>t_0$)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Corner Plot between the two peak times\n", "plot = gpresult2.comparison_plot(\"t0\", \"t1\")" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--------\n", "Termination Conditions:\n", "Small remaining evidence\n", "--------\n", "# likelihood evals: 1317371\n", "# samples: 14500\n", "# slices: 396000.0\n", "# slices / acceptance: 33.0\n", "# likelihood evals / sample: 90.9\n", "# likelihood evals / slice: 3.3\n", "--------\n", "logZ=-241.35 +- 0.19\n", "H=240.0\n", "ESS=2411\n", "--------\n", "log_A[#]: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_A[0]: 0.81 +- 0.25 | 0.57 / 0.81 / 1.12 | 0.87 | 0.87\n", "log_A[1]: 0.89 +- 0.25 | 0.62 / 0.89 / 1.19 | 0.99 | 0.99\n", "--------\n", "log_aqpo: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_aqpo: 0.23 +- 0.47 | -0.26 / 0.11 / 0.86 | 0.19 | 0.19\n", "--------\n", "log_arn: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_arn: -0.23 +- 0.11 | -0.33 / -0.27 / -0.1 | -0.33 | -0.33\n", "--------\n", "log_cqpo: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_cqpo: -0.69 +- 0.76 | -1.75 / -0.71 / 0.32 | -0.48 | -0.48\n", "--------\n", "log_crn: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_crn: 4.21 +- 0.17 | 4.0 / 4.23 / 4.41 | 4.34 | 4.34\n", "--------\n", "log_freq: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_freq: 2.967 +- 0.024 | 2.935 / 2.968 / 2.998 | 2.954 | 2.954\n", "--------\n", "log_sig[#]: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "log_sig[0]: -1.1 +- 1.5 | -3.2 / -0.4 / 0.5 | -0.4 | -0.4\n", "log_sig[1]: -1.8 +- 1.6 | -3.3 / -2.7 / 0.4 | -3.3 | -3.3\n", "--------\n", "t0: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "t0: 0.56 +- 0.16 | 0.33 / 0.6 / 0.7 | 0.58 | 0.58\n", "--------\n", "t1: mean +- std.dev. | 10%ile / 50%ile / 90%ile | MAP est. | max(L) est.\n", "t1: 0.751 +- 0.097 | 0.678 / 0.702 / 0.928 | 0.691 | 0.691\n", "--------\n" ] } ], "source": [ "gpresult2.print_summary()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Credits:\n", "\n", "1. [Gaussian Process regression for astronomical time-series](https://arxiv.org/pdf/2209.08940), Suzanne Aigrain, Daniel Foreman-Mackey\n", "\n", "2. [Bayesian Model Comparison](https://ned.ipac.caltech.edu/level5/Sept13/Trotta/Trotta4.html), Roberto Trotta\n", "\n", "3. [Searching for quasi-periodic oscillations in astrophysical transients using Gaussian processes](https://arxiv.org/abs/2205.12716), Moritz Hubner et al." ] } ], "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": "3.11.4" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }