{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "0", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:47.594883Z", "iopub.status.busy": "2026-06-30T22:40:47.594666Z", "iopub.status.idle": "2026-06-30T22:40:47.602279Z", "shell.execute_reply": "2026-06-30T22:40:47.601450Z" }, "tags": [ "hide-in-docs" ] }, "outputs": [], "source": [ "# Check whether easydiffraction is installed; install it if needed.\n", "# Required for remote environments such as Google Colab.\n", "import importlib.util\n", "\n", "if importlib.util.find_spec('easydiffraction') is None:\n", " %pip install easydiffraction==0.19.1" ] }, { "cell_type": "markdown", "id": "1", "metadata": {}, "source": [ "# Bayesian Analysis (`bumps-dream`): LBCO, HRPT\n", "\n", "This tutorial demonstrates a practical two-stage workflow for powder\n", "diffraction analysis with EasyDiffraction.\n", "\n", "In the first stage, we run a fast local refinement to obtain a sensible\n", "point estimate and parameter uncertainties. In the second stage, we use\n", "these refined values to define fit bounds and then sample the posterior\n", "distribution with DREAM.\n", "\n", "The example uses constant-wavelength neutron powder diffraction data\n", "for La0.5Ba0.5CoO3 measured on HRPT at PSI.\n", "\n", "The goal is not only to obtain a good fit, but also to answer Bayesian\n", "questions such as:\n", "\n", "- Which parameter values are most probable?\n", "- How broad are the credible intervals?\n", "- Which parameters are strongly correlated?\n", "- How much uncertainty propagates into the calculated diffraction\n", " pattern?" ] }, { "cell_type": "markdown", "id": "2", "metadata": {}, "source": [ "## πŸ› οΈ Import Library" ] }, { "cell_type": "code", "execution_count": 2, "id": "3", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:47.604937Z", "iopub.status.busy": "2026-06-30T22:40:47.604565Z", "iopub.status.idle": "2026-06-30T22:40:51.901267Z", "shell.execute_reply": "2026-06-30T22:40:51.900029Z" } }, "outputs": [], "source": [ "import easydiffraction as edi" ] }, { "cell_type": "markdown", "id": "4", "metadata": {}, "source": [ "## πŸ“¦ Define Project\n", "\n", "The project object keeps structures, experiments, fit settings, and\n", "plotting utilities together in a single place. We will build the full\n", "workflow inside this object.\n", "\n", "Save the project to a directory early on so that you can easily reload\n", "it later if needed." ] }, { "cell_type": "code", "execution_count": 3, "id": "5", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:51.902917Z", "iopub.status.busy": "2026-06-30T22:40:51.902638Z", "iopub.status.idle": "2026-06-30T22:40:52.247698Z", "shell.execute_reply": "2026-06-30T22:40:52.246811Z" } }, "outputs": [], "source": [ "project = edi.Project(name='lbco_hrpt_bumps_dream')" ] }, { "cell_type": "code", "execution_count": 4, "id": "6", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:52.249531Z", "iopub.status.busy": "2026-06-30T22:40:52.249365Z", "iopub.status.idle": "2026-06-30T22:40:52.320195Z", "shell.execute_reply": "2026-06-30T22:40:52.319409Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mSaving project πŸ“¦ \u001b[0m\u001b[32m'lbco_hrpt_bumps_dream'\u001b[0m\u001b[1;36m to \u001b[0m\u001b[32m'../../../projects/bayesian-dream-lbco-hrpt'\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“„ project.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“ structures/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“ experiments/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“ analysis/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”‚ └── πŸ“„ analysis.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "└── πŸ“ reports/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " └── πŸ“„ lbco_hrpt_bumps_dream.html\n" ] } ], "source": [ "project.save_as(dir_path='projects/bayesian-dream-lbco-hrpt')" ] }, { "cell_type": "markdown", "id": "7", "metadata": {}, "source": [ "## 🧩 Define Structure\n", "\n", "We define a simple cubic perovskite model for LBCO. La and Ba share the\n", "same crystallographic site with equal occupancy, while Co and O occupy\n", "the remaining ideal perovskite positions." ] }, { "cell_type": "code", "execution_count": 5, "id": "8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:52.321945Z", "iopub.status.busy": "2026-06-30T22:40:52.321707Z", "iopub.status.idle": "2026-06-30T22:40:52.327700Z", "shell.execute_reply": "2026-06-30T22:40:52.327131Z" } }, "outputs": [], "source": [ "project.structures.create(name='lbco')" ] }, { "cell_type": "code", "execution_count": 6, "id": "9", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:52.330053Z", "iopub.status.busy": "2026-06-30T22:40:52.329589Z", "iopub.status.idle": "2026-06-30T22:40:52.334314Z", "shell.execute_reply": "2026-06-30T22:40:52.332928Z" } }, "outputs": [], "source": [ "structure = project.structures['lbco']" ] }, { "cell_type": "code", "execution_count": 7, "id": "10", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:52.336664Z", "iopub.status.busy": "2026-06-30T22:40:52.336448Z", "iopub.status.idle": "2026-06-30T22:40:52.345344Z", "shell.execute_reply": "2026-06-30T22:40:52.341928Z" } }, "outputs": [], "source": [ "structure.space_group.name_h_m = 'P m -3 m'\n", "structure.space_group.coord_system_code = '1'" ] }, { "cell_type": "code", "execution_count": 8, "id": "11", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:52.347546Z", "iopub.status.busy": "2026-06-30T22:40:52.347191Z", "iopub.status.idle": "2026-06-30T22:40:52.351041Z", "shell.execute_reply": "2026-06-30T22:40:52.349913Z" } }, "outputs": [], "source": [ "structure.cell.length_a = 3.88" ] }, { "cell_type": "markdown", "id": "12", "metadata": {}, "source": [ "The atom-site definitions below form the starting structural model. The\n", "parameters are intentionally reasonable rather than fully optimized,\n", "because the refinement step will improve them." ] }, { "cell_type": "code", "execution_count": 9, "id": "13", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:52.352731Z", "iopub.status.busy": "2026-06-30T22:40:52.352534Z", "iopub.status.idle": "2026-06-30T22:40:52.365690Z", "shell.execute_reply": "2026-06-30T22:40:52.365132Z" } }, "outputs": [], "source": [ "structure.atom_sites.create(\n", " id='La',\n", " type_symbol='La',\n", " fract_x=0,\n", " fract_y=0,\n", " fract_z=0,\n", " wyckoff_letter='a',\n", " adp_type='Biso',\n", " adp_iso=0.5151,\n", " occupancy=0.5,\n", ")\n", "structure.atom_sites.create(\n", " id='Ba',\n", " type_symbol='Ba',\n", " fract_x=0,\n", " fract_y=0,\n", " fract_z=0,\n", " wyckoff_letter='a',\n", " adp_type='Biso',\n", " adp_iso=0.5151,\n", " occupancy=0.5,\n", ")\n", "structure.atom_sites.create(\n", " id='Co',\n", " type_symbol='Co',\n", " fract_x=0.5,\n", " fract_y=0.5,\n", " fract_z=0.5,\n", " wyckoff_letter='b',\n", " adp_type='Biso',\n", " adp_iso=0.2190,\n", ")\n", "structure.atom_sites.create(\n", " id='O',\n", " type_symbol='O',\n", " fract_x=0,\n", " fract_y=0.5,\n", " fract_z=0.5,\n", " wyckoff_letter='c',\n", " adp_type='Biso',\n", " adp_iso=1.3916,\n", ")" ] }, { "cell_type": "markdown", "id": "14", "metadata": {}, "source": [ "With the structural model complete, render it to confirm the perovskite\n", "framework before configuring the experiment." ] }, { "cell_type": "code", "execution_count": 10, "id": "15", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:52.367790Z", "iopub.status.busy": "2026-06-30T22:40:52.367584Z", "iopub.status.idle": "2026-06-30T22:40:52.443305Z", "shell.execute_reply": "2026-06-30T22:40:52.442133Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mStructure 🧩 \u001b[0m\u001b[32m'lbco'\u001b[0m\u001b[1;36m \u001b[0m\u001b[1;36m(\u001b[0m\u001b[1;36mAtom view type: \u001b[0m\u001b[32m'covalent'\u001b[0m\u001b[1;36m)\u001b[0m\n" ] }, { "data": { "text/html": [ "
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Loading plot…
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\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.structure(struct_name='lbco')" ] }, { "cell_type": "markdown", "id": "16", "metadata": {}, "source": [ "## πŸ”¬ Define Experiment\n", "\n", "Next we download the measured powder pattern, create a neutron powder\n", "experiment, and configure the instrument, profile, background, and\n", "excluded regions." ] }, { "cell_type": "markdown", "id": "17", "metadata": {}, "source": [ "Download the measured data from the repository. Alternatively, you\n", "could use your own data file by providing the path to it instead of\n", "downloading from the repository." ] }, { "cell_type": "code", "execution_count": 11, "id": "18", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:52.445022Z", "iopub.status.busy": "2026-06-30T22:40:52.444855Z", "iopub.status.idle": "2026-06-30T22:40:52.456532Z", "shell.execute_reply": "2026-06-30T22:40:52.453497Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mGetting data\u001b[0m\u001b[1;36m...\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Data \u001b[32m'meas-lbco-hrpt'\u001b[0m: La0.5Ba0.5CoO3, HRPT \u001b[1m(\u001b[0mPSI\u001b[1m)\u001b[0m, \u001b[1;36m300\u001b[0m K\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "βœ… Data \u001b[32m'meas-lbco-hrpt'\u001b[0m already present at \u001b[32m'../../../data/meas-lbco-hrpt.xye'\u001b[0m. Keeping existing.\n" ] } ], "source": [ "data_path = edi.download_data('meas-lbco-hrpt', destination='data')" ] }, { "cell_type": "markdown", "id": "19", "metadata": {}, "source": [ "Create the experiment object and specify the sample form, beam mode,\n", "and radiation probe." ] }, { "cell_type": "code", "execution_count": 12, "id": "20", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:52.460145Z", "iopub.status.busy": "2026-06-30T22:40:52.459819Z", "iopub.status.idle": "2026-06-30T22:40:53.157286Z", "shell.execute_reply": "2026-06-30T22:40:53.156156Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mData loaded successfully\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Experiment πŸ”¬ \u001b[32m'hrpt'\u001b[0m. Number of data points: \u001b[1;36m3098\u001b[0m.\n" ] } ], "source": [ "project.experiments.add_from_data_path(\n", " name='hrpt',\n", " data_path=data_path,\n", " sample_form='powder',\n", " beam_mode='constant wavelength',\n", " radiation_probe='neutron',\n", ")" ] }, { "cell_type": "code", "execution_count": 13, "id": "21", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.159419Z", "iopub.status.busy": "2026-06-30T22:40:53.159195Z", "iopub.status.idle": "2026-06-30T22:40:53.163409Z", "shell.execute_reply": "2026-06-30T22:40:53.162275Z" } }, "outputs": [], "source": [ "experiment = project.experiments['hrpt']" ] }, { "cell_type": "markdown", "id": "22", "metadata": {}, "source": [ "Link the structural phase to the experiment." ] }, { "cell_type": "code", "execution_count": 14, "id": "23", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.165436Z", "iopub.status.busy": "2026-06-30T22:40:53.165180Z", "iopub.status.idle": "2026-06-30T22:40:53.169981Z", "shell.execute_reply": "2026-06-30T22:40:53.168833Z" } }, "outputs": [], "source": [ "experiment.linked_structures.create(structure_id='lbco', scale=9.1351)" ] }, { "cell_type": "markdown", "id": "24", "metadata": {}, "source": [ "Set instrument and peak profile parameters.\n", "\n", "These values provide the initial instrument description for the local\n", "refinement. Later, a subset of them will be refined." ] }, { "cell_type": "code", "execution_count": 15, "id": "25", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.171848Z", "iopub.status.busy": "2026-06-30T22:40:53.171618Z", "iopub.status.idle": "2026-06-30T22:40:53.176448Z", "shell.execute_reply": "2026-06-30T22:40:53.175834Z" } }, "outputs": [], "source": [ "experiment.instrument.setup_wavelength = 1.494\n", "experiment.instrument.calib_twotheta_offset = 0.0" ] }, { "cell_type": "code", "execution_count": 16, "id": "26", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.178372Z", "iopub.status.busy": "2026-06-30T22:40:53.178230Z", "iopub.status.idle": "2026-06-30T22:40:53.183652Z", "shell.execute_reply": "2026-06-30T22:40:53.181919Z" } }, "outputs": [], "source": [ "experiment.peak.broad_gauss_u = 0.1\n", "experiment.peak.broad_gauss_v = -0.1\n", "experiment.peak.broad_gauss_w = 0.1204\n", "experiment.peak.broad_lorentz_y = 0.0844" ] }, { "cell_type": "markdown", "id": "27", "metadata": {}, "source": [ "Add background points and excluded regions.\n", "\n", "The line-segment background is defined by a few anchor points. We also\n", "exclude regions that are not intended to contribute to the fit." ] }, { "cell_type": "code", "execution_count": 17, "id": "28", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.185632Z", "iopub.status.busy": "2026-06-30T22:40:53.185420Z", "iopub.status.idle": "2026-06-30T22:40:53.199400Z", "shell.execute_reply": "2026-06-30T22:40:53.195383Z" } }, "outputs": [], "source": [ "experiment.background.create(id='1', position=10, intensity=168.5585)\n", "experiment.background.create(id='2', position=30, intensity=164.3357)\n", "experiment.background.create(id='3', position=50, intensity=166.8881)\n", "experiment.background.create(id='4', position=110, intensity=175.4006)" ] }, { "cell_type": "code", "execution_count": 18, "id": "29", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.201488Z", "iopub.status.busy": "2026-06-30T22:40:53.201238Z", "iopub.status.idle": "2026-06-30T22:40:53.212198Z", "shell.execute_reply": "2026-06-30T22:40:53.209844Z" } }, "outputs": [], "source": [ "experiment.excluded_regions.create(id='1', start=0, end=10)\n", "experiment.excluded_regions.create(id='2', start=100, end=180)" ] }, { "cell_type": "markdown", "id": "30", "metadata": {}, "source": [ "## πŸš€ Initial Refinement\n", "\n", "Before Bayesian sampling, it is useful to run a deterministic fit. This\n", "gives us:\n", "\n", "- a good point estimate near the best-fit region,\n", "- uncertainties from the local optimizer,\n", "- a quick check that the model and experiment are configured\n", " sensibly.\n", "\n", "In this tutorial we refine only a small set of parameters that are easy\n", "to interpret in the later Bayesian stage." ] }, { "cell_type": "code", "execution_count": 19, "id": "31", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.213699Z", "iopub.status.busy": "2026-06-30T22:40:53.213532Z", "iopub.status.idle": "2026-06-30T22:40:53.216159Z", "shell.execute_reply": "2026-06-30T22:40:53.215505Z" } }, "outputs": [], "source": [ "structure.cell.length_a.free = True" ] }, { "cell_type": "code", "execution_count": 20, "id": "32", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.217403Z", "iopub.status.busy": "2026-06-30T22:40:53.217260Z", "iopub.status.idle": "2026-06-30T22:40:53.220115Z", "shell.execute_reply": "2026-06-30T22:40:53.219513Z" } }, "outputs": [], "source": [ "experiment.linked_structures['lbco'].scale.free = True\n", "experiment.peak.broad_gauss_u.free = True\n", "experiment.peak.broad_gauss_v.free = True\n", "experiment.instrument.calib_twotheta_offset.free = True" ] }, { "cell_type": "markdown", "id": "33", "metadata": {}, "source": [ "We choose the BUMPS Levenberg-Marquardt minimizer as a fast local\n", "optimizer. Its main purpose here is to provide a stable starting point\n", "and uncertainty estimates for the Bayesian run." ] }, { "cell_type": "code", "execution_count": 21, "id": "34", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.221372Z", "iopub.status.busy": "2026-06-30T22:40:53.221208Z", "iopub.status.idle": "2026-06-30T22:40:53.234586Z", "shell.execute_reply": "2026-06-30T22:40:53.233147Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mMinimizer types\u001b[0m\n" ] }, { "data": { "text/html": [ "
TypeDescription
1bumpsBUMPS library using the default Levenberg-Marquardt method
2bumps (amoeba)BUMPS library with Nelder-Mead simplex method
3bumps (de)BUMPS library with differential evolution method
4bumps (dream)BUMPS library with DREAM Bayesian sampling
5bumps (lm)BUMPS library with Levenberg-Marquardt method
6dfolsDFO-LS library for derivative-free least-squares optimization
7emceeemcee affine-invariant ensemble Bayesian sampling
8lmfitLMFIT library using the default Levenberg-Marquardt method
9lmfit (least_squares)LMFIT library with SciPy's trust region reflective algorithm
10*lmfit (leastsq)LMFIT library with Levenberg-Marquardt least squares method
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.analysis.minimizer.show_supported()" ] }, { "cell_type": "code", "execution_count": 22, "id": "35", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.236353Z", "iopub.status.busy": "2026-06-30T22:40:53.236139Z", "iopub.status.idle": "2026-06-30T22:40:53.243843Z", "shell.execute_reply": "2026-06-30T22:40:53.242522Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mCurrent minimizer changed to\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "bumps \u001b[1m(\u001b[0mlm\u001b[1m)\u001b[0m\n" ] } ], "source": [ "project.analysis.minimizer.type = 'bumps (lm)'" ] }, { "cell_type": "code", "execution_count": 23, "id": "36", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:53.247867Z", "iopub.status.busy": "2026-06-30T22:40:53.247645Z", "iopub.status.idle": "2026-06-30T22:40:57.056466Z", "shell.execute_reply": "2026-06-30T22:40:57.056058Z" } }, "outputs": [ { "data": { "text/html": [], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", "(function() {\n", " const button = document.getElementById('ed-fit-stop-16b1660e2f374537a638b2578f09f61f-button');\n", " const status = document.getElementById('ed-fit-stop-16b1660e2f374537a638b2578f09f61f-status');\n", " const kernelId = '';\n", " if (!button) {\n", " return;\n", " }\n", "\n", " function setStatus(text) {\n", " if (status) {\n", " status.textContent = text;\n", " }\n", " }\n", "\n", " function pageConfig() {\n", " const element = document.getElementById('jupyter-config-data');\n", " if (!element || !element.textContent) {\n", " return {};\n", " }\n", " try {\n", " return JSON.parse(element.textContent);\n", " } catch (error) {\n", " return {};\n", " }\n", " }\n", "\n", " function baseUrl(config) {\n", " const configured = config.baseUrl || config.base_url ||\n", " (window.Jupyter && Jupyter.notebook && Jupyter.notebook.base_url);\n", " if (configured) {\n", " return configured.endsWith('/') ? 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session.kernel.id : '';\n", " }\n", "\n", " async function interruptKernel(config, resolvedKernelId) {\n", " const url = new URL(\n", " baseUrl(config) + 'api/kernels/' + resolvedKernelId + '/interrupt',\n", " window.location.origin\n", " );\n", " const authToken = token(config);\n", " if (authToken) {\n", " url.searchParams.set('token', authToken);\n", " }\n", " const xsrfToken = cookie('_xsrf');\n", " const headers = {};\n", " if (xsrfToken) {\n", " headers['X-XSRFToken'] = xsrfToken;\n", " }\n", " const response = await fetch(url, {\n", " method: 'POST',\n", " credentials: 'same-origin',\n", " headers: headers\n", " });\n", " return response.ok;\n", " }\n", "\n", " button.addEventListener('click', async function() {\n", " button.disabled = true;\n", " setStatus('Stopping...');\n", " const config = pageConfig();\n", " try {\n", " const resolvedKernelId = kernelId || await kernelFromSessions(config);\n", " if (!resolvedKernelId) {\n", " throw new Error('Could not resolve the current kernel id.');\n", " }\n", " const interrupted = await interruptKernel(config, resolvedKernelId);\n", " if (!interrupted) {\n", " throw new Error('Jupyter Server rejected the interrupt request.');\n", " }\n", " setStatus('Interrupt sent...');\n", " } catch (error) {\n", " button.disabled = false;\n", " setStatus('Use Kernel > Interrupt to stop this fit.');\n", " }\n", " });\n", "})();\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mStandard fitting\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ“‹ Using experiment πŸ”¬ \u001b[32m'hrpt'\u001b[0m for \u001b[32m'single'\u001b[0m fitting\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "πŸš€ Starting fit process with \u001b[32m'bumps \u001b[0m\u001b[32m(\u001b[0m\u001b[32mlm\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m\u001b[33m...\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ“ˆ Goodness-of-fit progress:\n" ] }, { "data": { "text/html": [ "
iterationtime (s)χ²change / status
110.03377.51
270.2356.3185.1% ↓
3130.4539.5429.8% ↓
4200.7837.664.7% ↓
5261.1323.4737.7% ↓
6321.408.7462.7% ↓
7381.571.8578.9% ↓
8441.771.3029.9% ↓
9703.221.29
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ† Best goodness-of-fit \u001b[1m(\u001b[0mreduced χ²\u001b[1m)\u001b[0m is \u001b[1;36m1.29\u001b[0m at iteration \u001b[1;36m70\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "βœ… Fitting complete.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mSaving project πŸ“¦ \u001b[0m\u001b[32m'lbco_hrpt_bumps_dream'\u001b[0m\u001b[1;36m to \u001b[0m\u001b[32m'../../../projects/bayesian-dream-lbco-hrpt'\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“„ project.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“ structures/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”‚ └── πŸ“„ lbco.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“ experiments/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”‚ └── πŸ“„ hrpt.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“ analysis/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”‚ └── πŸ“„ analysis.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "└── πŸ“ reports/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " └── πŸ“„ lbco_hrpt_bumps_dream.html\n" ] } ], "source": [ "project.analysis.fit()" ] }, { "cell_type": "code", "execution_count": 24, "id": "37", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.059032Z", "iopub.status.busy": "2026-06-30T22:40:57.058833Z", "iopub.status.idle": "2026-06-30T22:40:57.430941Z", "shell.execute_reply": "2026-06-30T22:40:57.430433Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "βš™οΈ Settings used:\n" ] }, { "data": { "text/html": [ "
NameValueDescription
1max_iterations1000Maximum solver iterations.
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ“‹ Least-squares fit results:\n" ] }, { "data": { "text/html": [ "
MetricValue
1πŸ§ͺ Minimizerbumps (lm)
2βœ… Overall statussuccess
3⏱️ Fitting time (seconds)3.22
4πŸ“ Goodness-of-fit (reduced χ²)1.29
5πŸ“ R-factor (Rf, %)5.65
6πŸ“ R-factor squared (RfΒ², %)4.92
7πŸ“ Weighted R-factor (wR, %)4.08
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ“ˆ Refined parameters:\n" ] }, { "data": { "text/html": [ "
datablockcategoryentryparameterunitsstartvalues.u.change
1lbcocelllength_aΓ…3.88003.89130.00010.29 % ↑
2hrptlinked_structurelbcoscale9.13519.13290.03330.02 % ↓
3hrptpeakbroad_gauss_udegΒ²0.10000.08170.007818.33 % ↓
4hrptpeakbroad_gauss_vdegΒ²-0.1000-0.11690.005716.91 % ↑
5hrptinstrumenttwotheta_offsetdeg0.00000.63060.0019N/A
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
β€’ start = parameter value before refinement
β€’ value = refined value from least-squares minimization
β€’ s.u. = standard uncertainty (one sigma), from the covariance matrix
β€’ change = relative change from start, in %; ↑ = increase, ↓ = decrease
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.fit.results()" ] }, { "cell_type": "markdown", "id": "38", "metadata": {}, "source": [ "The correlation plot shows how strongly the fitted parameters move\n", "together in the local refinement. The measured-vs-calculated plots show\n", "how well the refined model reproduces the data globally and in a zoomed\n", "region." ] }, { "cell_type": "code", "execution_count": 25, "id": "39", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.438249Z", "iopub.status.busy": "2026-06-30T22:40:57.435594Z", "iopub.status.idle": "2026-06-30T22:40:57.471813Z", "shell.execute_reply": "2026-06-30T22:40:57.471122Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "
\n", "
Loading plot…
\n", "
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.fit.correlations()" ] }, { "cell_type": "code", "execution_count": 26, "id": "40", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.474690Z", "iopub.status.busy": "2026-06-30T22:40:57.473875Z", "iopub.status.idle": "2026-06-30T22:40:57.558504Z", "shell.execute_reply": "2026-06-30T22:40:57.556074Z" } }, "outputs": [ { "data": { "text/html": [ "
Loading plot…
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.pattern(expt_name='hrpt')" ] }, { "cell_type": "markdown", "id": "41", "metadata": {}, "source": [ "## 🎲 Prepare Sampling\n", "\n", "DREAM requires finite bounds for the free parameters. Instead of\n", "setting them manually, we derive them from the uncertainties estimated\n", "in the local refinement.\n", "\n", "The helper method `set_fit_bounds_from_uncertainty` centers the bounds\n", "on the current parameter value and expands them by a chosen multiple of\n", "the reported uncertainty.\n", "\n", "The default `multiplier` is 4. If the local refinement is very tight,\n", "or if you expect a broader posterior, increase it explicitly.\n", "\n", "Show unset fit bounds before setting them from the local refinement uncertainties." ] }, { "cell_type": "code", "execution_count": 27, "id": "42", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.560026Z", "iopub.status.busy": "2026-06-30T22:40:57.559866Z", "iopub.status.idle": "2026-06-30T22:40:57.621677Z", "shell.execute_reply": "2026-06-30T22:40:57.620948Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mFree parameters for both structures \u001b[0m\u001b[1;36m(\u001b[0m\u001b[1;36m🧩 data blocks\u001b[0m\u001b[1;36m)\u001b[0m\u001b[1;36m and experiments \u001b[0m\u001b[1;36m(\u001b[0m\u001b[1;36mπŸ”¬ data blocks\u001b[0m\u001b[1;36m)\u001b[0m\n" ] }, { "data": { "text/html": [ "
datablockcategoryentryparametervalueuncertaintyminmaxunits
1lbcocelllength_a3.891340.00011-infinfΓ…
2hrptlinked_structurelbcoscale9.132880.03329-infinf
3hrptpeakbroad_gauss_u0.081670.00783-infinfdegΒ²
4hrptpeakbroad_gauss_v-0.116910.00566-infinfdegΒ²
5hrptinstrumenttwotheta_offset0.630570.00191-infinfdeg
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.parameters.free()" ] }, { "cell_type": "markdown", "id": "43", "metadata": {}, "source": [ "Set fit bounds for all free parameters using the default multiplier of\n", "4. In this tutorial that means the posterior pair plot will later\n", "refer to a `Β±4 Γ— uncertainty` region in its title. To use a different\n", "region, pass another value, for example `multiplier=6`." ] }, { "cell_type": "code", "execution_count": 28, "id": "44", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.625788Z", "iopub.status.busy": "2026-06-30T22:40:57.625598Z", "iopub.status.idle": "2026-06-30T22:40:57.682446Z", "shell.execute_reply": "2026-06-30T22:40:57.681803Z" } }, "outputs": [], "source": [ "for param in project.free_parameters:\n", " param.set_fit_bounds_from_uncertainty()" ] }, { "cell_type": "markdown", "id": "45", "metadata": {}, "source": [ "Displaying the free parameters again is a convenient way to confirm\n", "that the fit bounds have been assigned as expected before launching the\n", "sampler." ] }, { "cell_type": "code", "execution_count": 29, "id": "46", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.685917Z", "iopub.status.busy": "2026-06-30T22:40:57.685739Z", "iopub.status.idle": "2026-06-30T22:40:57.766230Z", "shell.execute_reply": "2026-06-30T22:40:57.765081Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mFree parameters for both structures \u001b[0m\u001b[1;36m(\u001b[0m\u001b[1;36m🧩 data blocks\u001b[0m\u001b[1;36m)\u001b[0m\u001b[1;36m and experiments \u001b[0m\u001b[1;36m(\u001b[0m\u001b[1;36mπŸ”¬ data blocks\u001b[0m\u001b[1;36m)\u001b[0m\n" ] }, { "data": { "text/html": [ "
datablockcategoryentryparametervalueuncertaintyminmaxunits
1lbcocelllength_a3.891340.000113.890913.89177Γ…
2hrptlinked_structurelbcoscale9.132880.033298.999739.26603
3hrptpeakbroad_gauss_u0.081670.007830.050340.11300degΒ²
4hrptpeakbroad_gauss_v-0.116910.00566-0.13955-0.09427degΒ²
5hrptinstrumenttwotheta_offset0.630570.001910.622920.63823deg
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.parameters.free()" ] }, { "cell_type": "markdown", "id": "47", "metadata": {}, "source": [ "## 🎲 Run Sampling\n", "\n", "We now switch from the local minimizer to the Bayesian DREAM sampler.\n", "\n", "The settings below are intentionally small so the tutorial runs\n", "quickly. For production analysis you would usually increase the number\n", "of steps (`steps`) and often the burn-in (`burn`) as well. When\n", "needed, the DREAM API also lets you tune how chains are initialized\n", "through the `init` setting. Other sampler settings such as `thin` and\n", "`pop` can be adjusted as well. The current EasyDiffraction defaults\n", "use `steps=3000`, `init='lhs'`, and `parallel=0`, which tells\n", "BUMPS-DREAM to use all available CPUs for population evaluations.\n", "\n", "The `burn` setting is auto-resolved when left unset. With the default\n", "`steps=3000` this gives `burn=600`, but if you override `steps` and\n", "keep `burn=None`, the effective burn-in is recomputed automatically.\n", "Here we use a much smaller step count to keep the tutorial fast, but\n", "this is not recommended for production analysis." ] }, { "cell_type": "code", "execution_count": 30, "id": "48", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.767716Z", "iopub.status.busy": "2026-06-30T22:40:57.767554Z", "iopub.status.idle": "2026-06-30T22:40:57.777961Z", "shell.execute_reply": "2026-06-30T22:40:57.777456Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mMinimizer types\u001b[0m\n" ] }, { "data": { "text/html": [ "
TypeDescription
1bumpsBUMPS library using the default Levenberg-Marquardt method
2bumps (amoeba)BUMPS library with Nelder-Mead simplex method
3bumps (de)BUMPS library with differential evolution method
4bumps (dream)BUMPS library with DREAM Bayesian sampling
5*bumps (lm)BUMPS library with Levenberg-Marquardt method
6dfolsDFO-LS library for derivative-free least-squares optimization
7emceeemcee affine-invariant ensemble Bayesian sampling
8lmfitLMFIT library using the default Levenberg-Marquardt method
9lmfit (least_squares)LMFIT library with SciPy's trust region reflective algorithm
10lmfit (leastsq)LMFIT library with Levenberg-Marquardt least squares method
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.analysis.minimizer.show_supported()" ] }, { "cell_type": "code", "execution_count": 31, "id": "49", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.784235Z", "iopub.status.busy": "2026-06-30T22:40:57.782434Z", "iopub.status.idle": "2026-06-30T22:40:57.799529Z", "shell.execute_reply": "2026-06-30T22:40:57.797546Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "⚠️ Switching minimizer type removes these settings: \n", " β€’ max_iterations \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "⚠️ Switching minimizer type adds these settings with defaults: \n", " β€’ burn_in_steps=600 \n", " β€’ initialization_method='latin_hypercube' \n", " β€’ parallel_workers=0 \n", " β€’ population_size=4 \n", " β€’ random_seed=None \n", " β€’ sampling_steps=3000 \n", " β€’ thinning_interval=1 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mCurrent minimizer changed to\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "bumps \u001b[1m(\u001b[0mdream\u001b[1m)\u001b[0m\n" ] } ], "source": [ "project.analysis.minimizer.type = 'bumps (dream)'" ] }, { "cell_type": "code", "execution_count": 32, "id": "50", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.802512Z", "iopub.status.busy": "2026-06-30T22:40:57.802339Z", "iopub.status.idle": "2026-06-30T22:40:57.817133Z", "shell.execute_reply": "2026-06-30T22:40:57.811801Z" } }, "outputs": [], "source": [ "project.analysis.minimizer.sampling_steps = 100 # lower than the default 3000\n", "project.analysis.minimizer.burn_in_steps = 20 # lower than the default 600\n", "project.analysis.minimizer.random_seed = 42 # fixed seed for reproducible output" ] }, { "cell_type": "code", "execution_count": 33, "id": "51", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:40:57.822302Z", "iopub.status.busy": "2026-06-30T22:40:57.822122Z", "iopub.status.idle": "2026-06-30T22:42:11.341232Z", "shell.execute_reply": "2026-06-30T22:42:11.340493Z" } }, "outputs": [ { "data": { "text/html": [], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", "(function() {\n", " const button = document.getElementById('ed-fit-stop-2d542b7782d04027b5637de6ea54a28a-button');\n", " const status = document.getElementById('ed-fit-stop-2d542b7782d04027b5637de6ea54a28a-status');\n", " const kernelId = '';\n", " if (!button) {\n", " return;\n", " }\n", "\n", " function setStatus(text) {\n", " if (status) {\n", " status.textContent = text;\n", " }\n", " }\n", "\n", " function pageConfig() {\n", " const element = document.getElementById('jupyter-config-data');\n", " if (!element || !element.textContent) {\n", " return {};\n", " }\n", " try {\n", " return JSON.parse(element.textContent);\n", " } catch (error) {\n", " return {};\n", " }\n", " }\n", "\n", " function baseUrl(config) {\n", " const configured = config.baseUrl || config.base_url ||\n", " (window.Jupyter && Jupyter.notebook && Jupyter.notebook.base_url);\n", " if (configured) {\n", " return configured.endsWith('/') ? configured : configured + '/';\n", " }\n", " const markers = ['/lab/', '/notebooks/', '/tree/'];\n", " for (const marker of markers) {\n", " const index = window.location.pathname.indexOf(marker);\n", " if (index >= 0) {\n", " return window.location.pathname.slice(0, index + 1);\n", " }\n", " }\n", " return '/';\n", " }\n", "\n", " function token(config) {\n", " return config.token || new URLSearchParams(window.location.search).get('token') || '';\n", " }\n", "\n", " function cookie(name) {\n", " const prefix = name + '=';\n", " for (const part of document.cookie.split(';')) {\n", " const trimmed = part.trim();\n", " if (trimmed.startsWith(prefix)) {\n", " return decodeURIComponent(trimmed.slice(prefix.length));\n", " }\n", " }\n", " return '';\n", " }\n", "\n", " function notebookPath() {\n", " const decoded = decodeURIComponent(window.location.pathname);\n", " const markers = ['/lab/tree/', '/notebooks/', '/tree/'];\n", " for (const marker of markers) {\n", " const index = decoded.indexOf(marker);\n", " if (index >= 0) {\n", " return decoded.slice(index + marker.length);\n", " }\n", " }\n", " return '';\n", " }\n", "\n", " async function kernelFromSessions(config) {\n", " const url = new URL(baseUrl(config) + 'api/sessions', window.location.origin);\n", " const authToken = token(config);\n", " if (authToken) {\n", " url.searchParams.set('token', authToken);\n", " }\n", " const response = await fetch(url, {credentials: 'same-origin'});\n", " if (!response.ok) {\n", " return '';\n", " }\n", " const sessions = await response.json();\n", " const path = notebookPath();\n", " const session = sessions.find((item) => item.path === path) || sessions[0];\n", " return session && session.kernel ? session.kernel.id : '';\n", " }\n", "\n", " async function interruptKernel(config, resolvedKernelId) {\n", " const url = new URL(\n", " baseUrl(config) + 'api/kernels/' + resolvedKernelId + '/interrupt',\n", " window.location.origin\n", " );\n", " const authToken = token(config);\n", " if (authToken) {\n", " url.searchParams.set('token', authToken);\n", " }\n", " const xsrfToken = cookie('_xsrf');\n", " const headers = {};\n", " if (xsrfToken) {\n", " headers['X-XSRFToken'] = xsrfToken;\n", " }\n", " const response = await fetch(url, {\n", " method: 'POST',\n", " credentials: 'same-origin',\n", " headers: headers\n", " });\n", " return response.ok;\n", " }\n", "\n", " button.addEventListener('click', async function() {\n", " button.disabled = true;\n", " setStatus('Stopping...');\n", " const config = pageConfig();\n", " try {\n", " const resolvedKernelId = kernelId || await kernelFromSessions(config);\n", " if (!resolvedKernelId) {\n", " throw new Error('Could not resolve the current kernel id.');\n", " }\n", " const interrupted = await interruptKernel(config, resolvedKernelId);\n", " if (!interrupted) {\n", " throw new Error('Jupyter Server rejected the interrupt request.');\n", " }\n", " setStatus('Interrupt sent...');\n", " } catch (error) {\n", " button.disabled = false;\n", " setStatus('Use Kernel > Interrupt to stop this fit.');\n", " }\n", " });\n", "})();\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mStandard fitting\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ“‹ Using experiment πŸ”¬ \u001b[32m'hrpt'\u001b[0m for \u001b[32m'single'\u001b[0m fitting\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "πŸš€ Starting fit process with \u001b[32m'bumps \u001b[0m\u001b[32m(\u001b[0m\u001b[32mdream\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m\u001b[33m...\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ“ˆ Bayesian sampling progress:\n" ] }, { "data": { "text/html": [ "
stepprogresstime (s)log posteriorphase
10.33-1350.94pre-processing
27/1205.8%3.61-1201.99burn-in
314/12011.7%5.87-1174.18burn-in
420/12016.7%7.78-1168.29burn-in
521/12017.5%8.11-1168.28sampling
626/12021.7%9.77-1165.85sampling
731/12025.8%11.31-1163.59sampling
836/12030.0%12.93-1161.64sampling
941/12034.2%14.53-1161.44sampling
1046/12038.3%16.11-1161.43sampling
1151/12042.5%17.75-1161.40sampling
1256/12046.7%19.28-1160.56sampling
1361/12050.8%20.96-1160.16sampling
1466/12055.0%22.56-1159.82sampling
1571/12059.2%24.04-1159.74sampling
1676/12063.3%25.36-1159.43sampling
1781/12067.5%26.61-1159.83sampling
1886/12071.7%27.93-1160.02sampling
1991/12075.8%29.18-1160.33sampling
2096/12080.0%30.48-1160.18sampling
21101/12084.2%31.76-1160.25sampling
22106/12088.3%33.04-1159.95sampling
23111/12092.5%34.23-1159.69sampling
24116/12096.7%35.54-1159.60sampling
25120/120100.0%36.80-1159.84sampling
2673.11post-processing
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "βœ… Bayesian sampling complete.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "⚠️ Convergence diagnostics indicate the posterior may be poorly mixed. \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;36mSaving project πŸ“¦ \u001b[0m\u001b[32m'lbco_hrpt_bumps_dream'\u001b[0m\u001b[1;36m to \u001b[0m\u001b[32m'../../../projects/bayesian-dream-lbco-hrpt'\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“„ project.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“ structures/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”‚ └── πŸ“„ lbco.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“ experiments/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”‚ └── πŸ“„ hrpt.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”œβ”€β”€ πŸ“ analysis/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”‚ β”œβ”€β”€ πŸ“„ analysis.edi\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "β”‚ └── πŸ“„ mcmc.h5\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "└── πŸ“ reports/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " └── πŸ“„ lbco_hrpt_bumps_dream.html\n" ] } ], "source": [ "project.analysis.fit()" ] }, { "cell_type": "markdown", "id": "52", "metadata": {}, "source": [ "## πŸ“Š Inspect Results\n", "\n", "The fit-results display now includes sampler settings, convergence\n", "diagnostics, committed parameter values, and posterior summary\n", "statistics." ] }, { "cell_type": "code", "execution_count": 34, "id": "53", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:42:11.343001Z", "iopub.status.busy": "2026-06-30T22:42:11.342833Z", "iopub.status.idle": "2026-06-30T22:42:11.382521Z", "shell.execute_reply": "2026-06-30T22:42:11.381850Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "βš™οΈ Settings used:\n" ] }, { "data": { "text/html": [ "
NameValueDescription
1sampling_steps100Total sampler iterations per chain.
2burn_in_steps20Sampler iterations discarded as warm-up.
3thinning_interval1Sampler thinning interval.
4population_size4Number of chains or walkers.
5parallel_workers0Worker count; 0 uses all available CPUs.
6initialization_methodlatin_hypercubeSampler initialization method.
7random_seed42Random seed; None uses a system-derived seed.
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ“‹ Bayesian fit results:\n" ] }, { "data": { "text/html": [ "
MetricValue
1πŸ§ͺ Samplerbumps (dream)
2❌ Overall statusfailed
3πŸ’¬ Engine messageDREAM sampling completed
4⏱️ Fitting time (seconds)73.11
5πŸ“ Goodness-of-fit (reduced χ²)1.29
6πŸ“ R-factor (Rf, %)5.65
7πŸ“ R-factor squared (RfΒ², %)4.92
8πŸ“ Weighted R-factor (wR, %)4.08
9πŸ“‰ Best log-posterior-1157.01
10πŸ“Š Convergence statusfailed
11πŸ“Š Max r-hat1.379
12πŸ“Š Min ess bulk118.182
13πŸ“Š Draws per chain100
14πŸ“Š Chains20
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ“ˆ Committed parameters:\n" ] }, { "data": { "text/html": [ "
datablockcategoryentryparameterunitsstartvalues.u.change
1lbcocelllength_aΓ…3.89133.89130.00010.00 % ↓
2hrptlinked_structurelbcoscale9.13299.13290.03690.00 % ↓
3hrptpeakbroad_gauss_udegΒ²0.08170.08170.00820.00 % ↓
4hrptpeakbroad_gauss_vdegΒ²-0.1169-0.11690.00620.00 % ↓
5hrptinstrumenttwotheta_offsetdeg0.63060.63060.00200.00 % ↓
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β€’ start = parameter value before sampling
β€’ value = estimate written back to the project (best posterior sample)
β€’ s.u. = standard uncertainty (one sigma), posterior standard deviation
β€’ change = relative change from start, in %; ↑ = increase, ↓ = decrease
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "πŸ“Š Posterior distribution:\n" ] }, { "data": { "text/html": [ "
datablockcategoryentryparameterunitsmedian95% CIr-hatess bulk
1lbcocelllength_aΓ…3.8913[3.8911, 3.8915]1.379120.6
2hrptlinked_structurelbcoscale9.1269[9.0638, 9.2080]1.323162.9
3hrptpeakbroad_gauss_udegΒ²0.0827[0.0608, 0.0955]1.368154.5
4hrptpeakbroad_gauss_vdegΒ²-0.1182[-0.1267, -0.1023]1.374161.4
5hrptinstrumenttwotheta_offsetdeg0.6304[0.6261, 0.6334]1.352118.2
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
β€’ median = 50th percentile of the marginal posterior
β€’ 95% CI = 95% credible interval (2.5%-97.5%, asymmetric)
β€’ r-hat = Gelman-Rubin diagnostic (good convergence: r-hat <= 1.01)
β€’ ess bulk = bulk effective sample size (typically >= 400)
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
⚠️ r-hat > 1.01: Consider longer sampling, better initialization, or reparameterization.
⚠️ ess bulk < 400: Consider longer sampling or reparameterization.
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.fit.results()" ] }, { "cell_type": "markdown", "id": "54", "metadata": {}, "source": [ "The correlation and posterior-pair plots are complementary:\n", "\n", "- `plot_param_correlations` summarizes pairwise structure in a compact\n", " matrix.\n", "- `plot_posterior_pairs` shows marginal densities on the diagonal and\n", " posterior contours off-diagonal. In this tutorial its title also\n", " reminds you that the display region follows the `Β±4 Γ— uncertainty`\n", " bounds defined above, while numeric subplot ranges are omitted to\n", " keep the grid readable." ] }, { "cell_type": "code", "execution_count": 35, "id": "55", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:42:11.384254Z", "iopub.status.busy": "2026-06-30T22:42:11.384063Z", "iopub.status.idle": "2026-06-30T22:42:11.405863Z", "shell.execute_reply": "2026-06-30T22:42:11.405140Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.posterior.pairs()" ] }, { "cell_type": "markdown", "id": "57", "metadata": {}, "source": [ "The one-dimensional posterior distributions below make it easier to\n", "inspect individual parameters in isolation, including asymmetry or\n", "multimodality." ] }, { "cell_type": "code", "execution_count": 37, "id": "58", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:42:11.668407Z", "iopub.status.busy": "2026-06-30T22:42:11.668217Z", "iopub.status.idle": "2026-06-30T22:42:11.749320Z", "shell.execute_reply": "2026-06-30T22:42:11.748294Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.posterior.distribution()" ] }, { "cell_type": "markdown", "id": "59", "metadata": {}, "source": [ "Finally, the posterior predictive plot propagates the sampled parameter\n", "uncertainty into the calculated diffraction pattern. Comparing this to\n", "the zoomed measured-vs-calculated view helps assess whether the sampled\n", "model family explains the data in the region of interest." ] }, { "cell_type": "code", "execution_count": 38, "id": "60", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:42:11.751053Z", "iopub.status.busy": "2026-06-30T22:42:11.750811Z", "iopub.status.idle": "2026-06-30T22:42:11.805851Z", "shell.execute_reply": "2026-06-30T22:42:11.805088Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.display.posterior.predictive(expt_name='hrpt')" ] }, { "cell_type": "markdown", "id": "61", "metadata": {}, "source": [ "A final zoomed measured-vs-calculated plot is useful for checking how\n", "the posterior-supported model behaves in a narrow region of the pattern\n", "after the Bayesian run." ] }, { "cell_type": "code", "execution_count": 39, "id": "62", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T22:42:11.809152Z", "iopub.status.busy": "2026-06-30T22:42:11.808965Z", "iopub.status.idle": "2026-06-30T22:42:11.856339Z", "shell.execute_reply": "2026-06-30T22:42:11.855419Z" } }, "outputs": [ { "data": { "text/html": [ "
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