{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Each tuple of mean, variance, and standard deviation estimates represent the (center, (lower, upper)) with center the mean of the conditional pdf of the value given the data and (lower, upper) is a confidence interval centered on the median, containing the estimate to a probability " }, { "__type": "InlineCode", "__tag": 4051, "value": "alpha" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Converts data to 1-D and assumes all data has the same mean and variance. 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Requires 2 or more data points." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "alpha", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Probability that the returned confidence interval contains the true parameter." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "/scipy/stats/_morestats.py", "item_line": 62, "item_type": "function", "aliases": [ "scipy.stats.bayes_mvs" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "First a basic example to demonstrate the outputs:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy import stats\ndata = [6, 9, 12, 7, 8, 8, 13]\nmean, var, std = stats.bayes_mvs(data)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "mean\nvar\nstd\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nNow we generate some normally distributed random data, and get estimates of\nmean and standard deviation with 95% confidence intervals for those\nestimates:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "n_samples = 100000\ndata = stats.norm.rvs(size=n_samples)\nres_mean, res_var, res_std = stats.bayes_mvs(data, alpha=0.95)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "import matplotlib.pyplot as plt\nfig = plt.figure()\nax = fig.add_subplot(111)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax.hist(data, bins=100, density=True, label='Histogram of data')\nax.vlines(res_mean.statistic, 0, 0.5, colors='r', label='Estimated mean')\nax.axvspan(res_mean.minmax[0],res_mean.minmax[1], facecolor='r',\n alpha=0.2, label=r'Estimated mean (95% limits)')\nax.vlines(res_std.statistic, 0, 0.5, colors='g', label='Estimated scale')\nax.axvspan(res_std.minmax[0],res_std.minmax[1], facecolor='g', alpha=0.2,\n label=r'Estimated scale (95% limits)')\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "ax.legend(fontsize=10)\nax.set_xlim([-4, 4])\nax.set_ylim([0, 0.5])\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "plt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-5ddb84debb22d389.png" } } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "mvsdist", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:mvsdist" }, "kind": "module" }, "descriptions": [], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "data", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "alpha", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0.9" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "bayes_mvs" }, "references": [ "T.E. Oliphant, \"A Bayesian perspective on estimating mean, variance, and", "standard-deviation from data\", https://scholarsarchive.byu.edu/facpub/278,", "2006." ], "qa": "scipy.stats._morestats:bayes_mvs", "arbitrary": [], "local_refs": [ "alpha", "data", "mean_cntr", "std_cntr", "var_cntr" ] }