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+ + + + + + + + + + + + + + + + + + +pyextremes.eva.EVA
+
+
+¶Extreme Value Analysis (EVA) class.
+This class brings together most of the tools available in the pyextremes package +bundled together in a pipeline to perform univariate extreme value analysis.
+A typical workflow using the EVA class would consist of the following: + - extract extreme values (.get_extremes) + - fit a model (.fit_model) + - generate outputs (.get_summary) + - visualize the model (.plot_diagnostic, .plot_return_values)
+Multiple additional graphical and numerical methods are available +within this class to analyze extracted extreme values, visualize them, +assess goodness-of-fit of selected model, and to visualize its outputs.
+ +src/pyextremes/eva.py
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|
__init__(data)
+
+¶Initialize EVA model.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
data |
+
+ Series
+ |
+
+
+
+ Time series to be analyzed. +Index must be date-time and values must be numeric. + |
+ + required + | +
src/pyextremes/eva.py
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|
fit_model(model='MLE', distribution=None, distribution_kwargs=None, **kwargs)
+
+¶Fit a model to the extracted extreme values.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
model |
+
+ str
+ |
+
+
+
+ Name of model. By default it is 'MLE'. +Name of model. +Supported models: + MLE - Maximum Likelihood Estimate (MLE) model. + Based on 'scipy' package (scipy.stats.rv_continuous.fit). + Emcee - Markov Chain Monte Carlo (MCMC) model. + Based on 'emcee' package by Daniel Foreman-Mackey. + |
+
+ 'MLE'
+ |
+
distribution |
+
+ str or rv_continuous
+ |
+
+
+
+ Distribution name compatible with scipy.stats +or a subclass of scipy.stats.rv_continuous. +See https://docs.scipy.org/doc/scipy/reference/stats.html +By default the distribution is selected automatically +as best between 'genextreme' and 'gumbel_r' for 'BM' extremes +and 'genpareto' and 'expon' for 'POT' extremes. +Best distribution is selected using the AIC metric. + |
+
+ None
+ |
+
distribution_kwargs |
+
+ dict
+ |
+
+
+
+ Special keyword arguments, passed to the |
+
+ None
+ |
+
kwargs |
+ + | +
+
+
+ Keyword arguments passed to a model .fit method.
+MLE model:
+ MLE model takes no additional arguments.
+Emcee model:
+ n_walkers : int, optional
+ The number of walkers in the ensemble (default=100).
+ n_samples : int, optional
+ The number of steps to run (default=500).
+ progress : bool or str, optional
+ If True, a progress bar will be shown as the sampler progresses.
+ If a string, will select a specific tqdm progress bar.
+ Most notable is 'notebook', which shows a progress bar
+ suitable for Jupyter notebooks.
+ If False (default), no progress bar will be shown.
+ This progress bar is a part of the |
+
+ {}
+ |
+
src/pyextremes/eva.py
887 + 888 + 889 + 890 + 891 + 892 + 893 + 894 + 895 + 896 + 897 + 898 + 899 + 900 + 901 + 902 + 903 + 904 + 905 + 906 + 907 + 908 + 909 + 910 + 911 + 912 + 913 + 914 + 915 + 916 + 917 + 918 + 919 + 920 + 921 + 922 + 923 + 924 + 925 + 926 + 927 + 928 + 929 + 930 + 931 + 932 + 933 + 934 + 935 + 936 + 937 + 938 + 939 + 940 + 941 + 942 + 943 + 944 + 945 + 946 + 947 + 948 + 949 + 950 + 951 + 952 + 953 + 954 + 955 + 956 + 957 + 958 + 959 + 960 + 961 + 962 + 963 + 964 + 965 + 966 + 967 + 968 + 969 + 970 + 971 + 972 + 973 + 974 + 975 + 976 + 977 + 978 + 979 + 980 + 981 + 982 + 983 + 984 + 985 + 986 + 987 + 988 + 989 + 990 + 991 + 992 + 993 + 994 + 995 + 996 + 997 + 998 + 999 +1000 +1001 +1002 +1003 +1004 +1005 +1006 +1007 +1008 +1009 +1010 +1011 +1012 +1013 +1014 +1015 +1016 +1017 +1018 +1019 +1020 +1021 +1022 +1023 +1024 +1025 +1026 +1027 +1028 +1029 +1030 +1031 +1032 +1033 +1034 +1035 +1036 +1037 +1038 +1039 +1040 +1041 +1042 +1043 +1044 +1045 +1046 +1047 +1048 +1049 +1050 +1051 +1052 +1053 +1054 +1055 +1056 +1057 +1058 |
|
from_extremes(extremes, method='BM', extremes_type='high', **kwargs)
+
+
+ classmethod
+
+
+¶Create an EVA model using pre-defined extremes
.
A typical reason to use this method is when full timeseries is not available +and only the extracted extremes (i.e. annual maxima) are known.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
extremes |
+
+ Series
+ |
+
+
+
+ Time series of extreme values. + |
+ + required + | +
method |
+
+ str
+ |
+
+
+
+ Extreme value extraction method. +Supported values: + BM (default) - Block Maxima + POT - Peaks Over Threshold + |
+
+ 'BM'
+ |
+
extremes_type |
+
+ str
+ |
+
+
+
+ high (default) - extreme high values +low - extreme low values + |
+
+ 'high'
+ |
+
kwargs |
+ + | +
+
+
+ if method is BM: + block_size : str or pandas.Timedelta, optional + Block size. + If None (default), then is calculated as median distance + between extreme events. + errors : str, optional + raise - raise an exception + when encountering a block with no data + ignore (default) - ignore blocks with no data + coerce - get extreme values for blocks with no data + as mean of all other extreme events in the series + with index being the middle point of corresponding interval + min_last_block : float, optional + Minimum data availability ratio (0 to 1) in the last block + for it to be used to extract extreme value from. + This is used to discard last block when it is too short. + If None (default), last block is always used. +if method is POT: + threshold : float, optional + Threshold used to find exceedances. + By default is taken as smallest value. + r : pandas.Timedelta or value convertible to timedelta, optional + Duration of window used to decluster the exceedances. + By default r='24H' (24 hours). + See pandas.to_timedelta for more information. + |
+
+ {}
+ |
+
Returns:
+Type | +Description | +
---|---|
+ EVA
+ |
+
+
+
+ EVA model initialized with |
+
src/pyextremes/eva.py
753 +754 +755 +756 +757 +758 +759 +760 +761 +762 +763 +764 +765 +766 +767 +768 +769 +770 +771 +772 +773 +774 +775 +776 +777 +778 +779 +780 +781 +782 +783 +784 +785 +786 +787 +788 +789 +790 +791 +792 +793 +794 +795 +796 +797 +798 +799 +800 +801 +802 +803 +804 +805 +806 +807 +808 +809 +810 +811 +812 +813 +814 +815 +816 +817 +818 +819 |
|
get_extremes(method, extremes_type='high', **kwargs)
+
+¶Get extreme events from time series.
+Extracts extreme values from the 'self.data' attribute. +Stores extreme values in the 'self.extremes' attribute.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
method |
+
+ str
+ |
+
+
+
+ Extreme value extraction method. +Supported values: + BM - Block Maxima + POT - Peaks Over Threshold + |
+ + required + | +
extremes_type |
+
+ str
+ |
+
+
+
+ high (default) - get extreme high values +low - get extreme low values + |
+
+ 'high'
+ |
+
kwargs |
+ + | +
+
+
+ if method is BM: + block_size : str or pandas.Timedelta, optional + Block size (default='365.2425D'). + See pandas.to_timedelta for more information. + errors : str, optional + raise (default) - raise an exception + when encountering a block with no data + ignore - ignore blocks with no data + coerce - get extreme values for blocks with no data + as mean of all other extreme events in the series + with index being the middle point of corresponding interval + min_last_block : float, optional + Minimum data availability ratio (0 to 1) in the last block + for it to be used to extract extreme value from. + This is used to discard last block when it is too short. + If None (default), last block is always used. +if method is POT: + threshold : float + Threshold used to find exceedances. + r : pandas.Timedelta or value convertible to timedelta, optional + Duration of window used to decluster the exceedances. + By default r='24H' (24 hours). + See pandas.to_timedelta for more information. + |
+
+ {}
+ |
+
src/pyextremes/eva.py
453 +454 +455 +456 +457 +458 +459 +460 +461 +462 +463 +464 +465 +466 +467 +468 +469 +470 +471 +472 +473 +474 +475 +476 +477 +478 +479 +480 +481 +482 +483 +484 +485 +486 +487 +488 +489 +490 +491 +492 +493 +494 +495 +496 +497 +498 +499 +500 +501 +502 +503 +504 +505 +506 +507 +508 +509 +510 +511 +512 +513 +514 +515 +516 +517 +518 +519 +520 +521 +522 +523 +524 +525 +526 +527 +528 +529 +530 +531 +532 +533 +534 +535 +536 |
|
get_return_value(return_period, return_period_size='365.2425D', alpha=None, **kwargs)
+
+¶Get return value and confidence interval for given return period(s).
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
return_period |
+
+ array - like
+ |
+
+
+
+ Return period or 1D array of return periods.
+Given as a multiple of |
+ + required + | +
return_period_size |
+
+ str or Timedelta
+ |
+
+
+
+ Size of return periods (default='365.2425D'). +If set to '30D', then a return period of 12 +would be roughly equivalent to a 1 year return period (360 days). + |
+
+ '365.2425D'
+ |
+
alpha |
+
+ float
+ |
+
+
+
+ Width of confidence interval (0, 1). +If None (default), return None +for upper and lower confidence interval bounds. + |
+
+ None
+ |
+
kwargs |
+ + | +
+
+
+ Model-specific keyword arguments. +If alpha is None, keyword arguments are ignored +(error still raised for unrecognized arguments). +MLE model: + n_samples : int, optional + Number of bootstrap samples used to estimate + confidence interval bounds (default=100). +Emcee model: + burn_in : int + Burn-in value (number of first steps to discard for each walker). + |
+
+ {}
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
return_value |
+ array - like
+ |
+
+
+
+ Return values. + |
+
ci_lower |
+ array - like
+ |
+
+
+
+ Lower confidence interval bounds. + |
+
ci_upper |
+ array - like
+ |
+
+
+
+ Upper confidence interval bounds. + |
+
src/pyextremes/eva.py
1175 +1176 +1177 +1178 +1179 +1180 +1181 +1182 +1183 +1184 +1185 +1186 +1187 +1188 +1189 +1190 +1191 +1192 +1193 +1194 +1195 +1196 +1197 +1198 +1199 +1200 +1201 +1202 +1203 +1204 +1205 +1206 +1207 +1208 +1209 +1210 +1211 +1212 +1213 +1214 +1215 +1216 +1217 +1218 +1219 +1220 +1221 +1222 +1223 +1224 +1225 +1226 +1227 +1228 +1229 +1230 +1231 +1232 +1233 +1234 +1235 +1236 +1237 +1238 +1239 +1240 +1241 +1242 +1243 +1244 +1245 +1246 +1247 +1248 +1249 +1250 +1251 +1252 +1253 +1254 +1255 +1256 +1257 +1258 +1259 |
|
get_summary(return_period, return_period_size='365.2425D', alpha=None, **kwargs)
+
+¶Generate a pandas DataFrame with return values and confidence interval bounds.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
return_period |
+
+ array - like
+ |
+
+
+
+ Return period or 1D array of return periods.
+Given as a multiple of |
+ + required + | +
return_period_size |
+
+ str or Timedelta
+ |
+
+
+
+ Size of return periods (default='365.2425D'). +If set to '30D', then a return period of 12 +would be roughly equivalent to a 1 year return period (360 days). + |
+
+ '365.2425D'
+ |
+
alpha |
+
+ float
+ |
+
+
+
+ Width of confidence interval (0, 1). +If None (default), return None +for upper and lower confidence interval bounds. + |
+
+ None
+ |
+
kwargs |
+ + | +
+
+
+ Model-specific keyword arguments. +If alpha is None, keyword arguments are ignored +(error still raised for unrecognized arguments). +MLE model: + n_samples : int, optional + Number of bootstrap samples used to estimate + confidence interval bounds (default=100). +Emcee model: + burn_in : int + Burn-in value (number of first steps to discard for each walker). + |
+
+ {}
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
summary |
+ DataFrame
+ |
+
+
+
+ DataFrame with return values and confidence interval bounds. + |
+
src/pyextremes/eva.py
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|
plot_corner(burn_in=0, labels=None, levels=None, figsize=(8, 8))
+
+¶Plot corner plot for MCMC sampler trace.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
burn_in |
+
+ int
+ |
+
+
+
+ Burn-in value (number of first steps to discard for each walker). +By default it is 0 (no values are discarded). + |
+
+ 0
+ |
+
labels |
+
+ array - like
+ |
+
+
+
+ Sequence of strings with parameter names, used to label axes. +If None (default), then axes are labeled sequentially. + |
+
+ None
+ |
+
levels |
+
+ int
+ |
+
+
+
+ Number of Gaussian KDE contours to plot. +If None (default), then not shown. + |
+
+ None
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches. By default it is (8, 8). + |
+
+ (8, 8)
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ list
+ |
+
+
+
+ 2D list with Axes objects of size N by N, where N is |
+
src/pyextremes/eva.py
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|
plot_diagnostic(return_period=None, return_period_size='365.2425D', alpha=None, plotting_position='weibull', figsize=(8, 8), **kwargs)
+
+¶Plot a diagnostic plot.
+This plot shows four key plots characterizing the EVA model: + - top left : return values plot + - top right : probability density (PDF) plot + - bottom left : quantile (Q-Q) plot + - bottom right : probability (P-P) plot
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
return_period |
+
+ array - like
+ |
+
+
+
+ Return period or 1D array of return periods.
+Given as a multiple of |
+
+ None
+ |
+
return_period_size |
+
+ str or Timedelta
+ |
+
+
+
+ Size of return periods (default='365.2425D'). +If set to '30D', then a return period of 12 +would be roughly equivalent to a 1 year return period (360 days). + |
+
+ '365.2425D'
+ |
+
alpha |
+
+ float
+ |
+
+
+
+ Width of confidence interval (0, 1). +If None (default), confidence interval bounds are not plotted. + |
+
+ None
+ |
+
plotting_position |
+
+ str
+ |
+
+
+
+ Plotting position name (default='weibull'), not case-sensitive. +Supported plotting positions: + ecdf, hazen, weibull, tukey, blom, median, cunnane, gringorten, beard + |
+
+ 'weibull'
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches in format (width, height). +By default it is (8, 8). + |
+
+ (8, 8)
+ |
+
kwargs |
+ + | +
+
+
+ Model-specific keyword arguments. +If alpha is None, keyword arguments are ignored +(error still raised for unrecognized arguments). +MLE model: + n_samples : int, optional + Number of bootstrap samples used to estimate + confidence interval bounds (default=100). +Emcee model: + burn_in : int + Burn-in value (number of first steps to discard for each walker). + |
+
+ {}
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ tuple
+ |
+
+
+
+ Tuple with four Axes objects: return values, pdf, qq, pp + |
+
src/pyextremes/eva.py
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|
plot_extremes(figsize=(8, 5), ax=None, show_clusters=False)
+
+¶Plot extreme events.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches in format (width, height). +By default it is (8, 5). + |
+
+ (8, 5)
+ |
+
ax |
+
+ Axes
+ |
+
+
+
+ Axes onto which extremes plot is drawn. +If None (default), a new figure and axes objects are created. + |
+
+ None
+ |
+
show_clusters |
+
+ bool
+ |
+
+
+
+ If True, show cluster boundaries for POT extremes.
+Has no effect if extremes were extracted using BM method.
+May produce wrong cluster boundaries if extremes were set using the
+ |
+
+ False
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ Axes
+ |
+
+
+
+ Axes object. + |
+
src/pyextremes/eva.py
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|
plot_probability(plot_type, return_period_size='365.2425D', plotting_position='weibull', ax=None, figsize=(8, 8))
+
+¶Plot a probability plot (QQ or PP).
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
plot_type |
+
+ str
+ |
+
+
+
+ Probability plot type. +Supported values: + PP - probability plot + QQ - quantile plot + |
+ + required + | +
return_period_size |
+
+ str or Timedelta
+ |
+
+
+
+ Size of return periods (default='365.2425D'). +If set to '30D', then a return period of 12 +would be roughly equivalent to a 1 year return period (360 days). + |
+
+ '365.2425D'
+ |
+
plotting_position |
+
+ str
+ |
+
+
+
+ Plotting position name (default='weibull'), not case-sensitive. +Supported plotting positions: + ecdf, hazen, weibull, tukey, blom, median, cunnane, gringorten, beard + |
+
+ 'weibull'
+ |
+
ax |
+
+ Axes
+ |
+
+
+
+ Axes onto which the probability plot is drawn. +If None (default), a new figure and axes objects are created. + |
+
+ None
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches in format (width, height). +By default it is (8, 8). + |
+
+ (8, 8)
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ Axes
+ |
+
+
+
+ Axes object. + |
+
src/pyextremes/eva.py
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|
plot_return_values(return_period=None, return_period_size='365.2425D', alpha=None, plotting_position='weibull', ax=None, figsize=(8, 5), **kwargs)
+
+¶Plot return values and confidence intervals for given return periods.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
return_period |
+
+ array - like
+ |
+
+
+
+ Return period or 1D array of return periods.
+Given as a multiple of |
+
+ None
+ |
+
return_period_size |
+
+ str or Timedelta
+ |
+
+
+
+ Size of return periods (default='365.2425D'). +If set to '30D', then a return period of 12 +would be roughly equivalent to a 1 year return period (360 days). + |
+
+ '365.2425D'
+ |
+
alpha |
+
+ float
+ |
+
+
+
+ Width of confidence interval (0, 1). +If None (default), confidence interval bounds are not plotted. + |
+
+ None
+ |
+
plotting_position |
+
+ str
+ |
+
+
+
+ Plotting position name (default='weibull'), not case-sensitive. +Supported plotting positions: + ecdf, hazen, weibull, tukey, blom, median, cunnane, gringorten, beard + |
+
+ 'weibull'
+ |
+
ax |
+
+ Axes
+ |
+
+
+
+ Axes onto which the return value plot is drawn. +If None (default), a new figure and axes objects are created. + |
+
+ None
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches in format (width, height). +By default it is (8, 5). + |
+
+ (8, 5)
+ |
+
kwargs |
+ + | +
+
+
+ Model-specific keyword arguments. +If alpha is None, keyword arguments are ignored +(error still raised for unrecognized arguments). +MLE model: + n_samples : int, optional + Number of bootstrap samples used to estimate + confidence interval bounds (default=100). +Emcee model: + burn_in : int + Burn-in value (number of first steps to discard for each walker). + |
+
+ {}
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ Axes
+ |
+
+
+
+ Axes object. + |
+
src/pyextremes/eva.py
1332 +1333 +1334 +1335 +1336 +1337 +1338 +1339 +1340 +1341 +1342 +1343 +1344 +1345 +1346 +1347 +1348 +1349 +1350 +1351 +1352 +1353 +1354 +1355 +1356 +1357 +1358 +1359 +1360 +1361 +1362 +1363 +1364 +1365 +1366 +1367 +1368 +1369 +1370 +1371 +1372 +1373 +1374 +1375 +1376 +1377 +1378 +1379 +1380 +1381 +1382 +1383 +1384 +1385 +1386 +1387 +1388 +1389 +1390 +1391 +1392 +1393 +1394 +1395 +1396 +1397 +1398 +1399 +1400 +1401 +1402 +1403 +1404 +1405 +1406 +1407 +1408 +1409 +1410 +1411 +1412 +1413 +1414 +1415 +1416 +1417 +1418 +1419 +1420 +1421 +1422 +1423 +1424 +1425 +1426 +1427 +1428 +1429 +1430 +1431 +1432 +1433 +1434 +1435 +1436 +1437 +1438 +1439 +1440 +1441 +1442 +1443 +1444 +1445 +1446 +1447 |
|
plot_trace(burn_in=0, labels=None, figsize=None)
+
+¶Plot trace plot for MCMC sampler trace.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
burn_in |
+
+ int
+ |
+
+
+
+ Burn-in value (number of first steps to discard for each walker). +By default it is 0 (no values are discarded). + |
+
+ 0
+ |
+
labels |
+
+ array - like
+ |
+
+
+
+ Sequence of strings with parameter names, used to label axes. +If None (default), then axes are labeled sequentially. + |
+
+ None
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches. +If None (default), then figure size is calculated automatically +as 8 by 2 times number of parameters. + |
+
+ None
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ list
+ |
+
+
+
+ List with n_parameters Axes objects. + |
+
src/pyextremes/eva.py
1092 +1093 +1094 +1095 +1096 +1097 +1098 +1099 +1100 +1101 +1102 +1103 +1104 +1105 +1106 +1107 +1108 +1109 +1110 +1111 +1112 +1113 +1114 +1115 +1116 +1117 +1118 +1119 +1120 +1121 +1122 +1123 +1124 +1125 +1126 +1127 +1128 +1129 |
|
set_extremes(extremes, method='BM', extremes_type='high', **kwargs)
+
+¶Set extreme values.
+This method is used to set extreme values onto the model instead +of deriving them from data directly using the 'get_extremes' method. +This way user can set extremes calculated using a custom methodology.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
extremes |
+
+ Series
+ |
+
+
+
+ Time series of extreme values to be set onto the model. +Must be numeric, have date-time index, and have the same name +as self.data. + |
+ + required + | +
method |
+
+ str
+ |
+
+
+
+ Extreme value extraction method. +Supported values: + BM (default) - Block Maxima + POT - Peaks Over Threshold + |
+
+ 'BM'
+ |
+
extremes_type |
+
+ str
+ |
+
+
+
+ high (default) - extreme high values +low - extreme low values + |
+
+ 'high'
+ |
+
kwargs |
+ + | +
+
+
+ if method is BM: + block_size : str or pandas.Timedelta, optional + Block size. + If None (default), then is calculated as median distance + between extreme events. + errors : str, optional + raise - raise an exception + when encountering a block with no data + ignore (default) - ignore blocks with no data + coerce - get extreme values for blocks with no data + as mean of all other extreme events in the series + with index being the middle point of corresponding interval + min_last_block : float, optional + Minimum data availability ratio (0 to 1) in the last block + for it to be used to extract extreme value from. + This is used to discard last block when it is too short. + If None (default), last block is always used. +if method is POT: + threshold : float, optional + Threshold used to find exceedances. + By default is taken as smallest value. + r : pandas.Timedelta or value convertible to timedelta, optional + Duration of window used to decluster the exceedances. + By default r='24H' (24 hours). + See pandas.to_timedelta for more information. + |
+
+ {}
+ |
+
src/pyextremes/eva.py
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|
pyextremes.extremes.get_extremes(ts, method, extremes_type='high', **kwargs)
+
+¶Get extreme events from time series.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
ts |
+
+ Series
+ |
+
+
+
+ Time series of the signal. + |
+ + required + | +
method |
+
+ str
+ |
+
+
+
+ Extreme value extraction method. +Supported values: + BM - Block Maxima + POT - Peaks Over Threshold + |
+ + required + | +
extremes_type |
+
+ str
+ |
+
+
+
+ high (default) - get extreme high values +low - get extreme low values + |
+
+ 'high'
+ |
+
kwargs |
+ + | +
+
+
+ if method is BM: + block_size : str or pandas.Timedelta, optional + Block size (default='365.2425D'). + errors : str, optional + raise (default) - raise an exception + when encountering a block with no data + ignore - ignore blocks with no data + coerce - get extreme values for blocks with no data + as mean of all other extreme events in the series + with index being the middle point of corresponding interval + min_last_block : float, optional + Minimum data availability ratio (0 to 1) in the last block + for it to be used to extract extreme value from. + This is used to discard last block when it is too short. + If None (default), last block is always used. +if method is POT: + threshold : float + Threshold used to find exceedances. + r : pandas.Timedelta or value convertible to timedelta, optional + Duration of window used to decluster the exceedances. + By default r='24H' (24 hours). + See pandas.to_timedelta for more information. + |
+
+ {}
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
extremes |
+ Series
+ |
+
+
+
+ Time series of extreme events. + |
+
src/pyextremes/extremes/extremes.py
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|
pyextremes.extremes.get_return_periods(ts, extremes, extremes_method, extremes_type, block_size=None, return_period_size='365.2425D', plotting_position='weibull')
+
+¶Calculate return periods for given extreme values using given plotting position.
+Return periods are multiples of return_period_size
.
+Plotting positions were taken from
+https://matplotlib.org/mpl-probscale/tutorial/closer_look_at_plot_pos.html
Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
ts |
+
+ Series
+ |
+
+
+
+ Time series of the signal. + |
+ + required + | +
extremes |
+
+ Series
+ |
+
+
+
+ Time series of extreme events. + |
+ + required + | +
extremes_method |
+
+ str
+ |
+
+
+
+ Extreme value extraction method. +Supported values: + BM - Block Maxima + POT - Peaks Over Threshold + |
+ + required + | +
extremes_type |
+
+ str
+ |
+
+
+
+ high - provided extreme values are extreme high values +low - provided extreme values are extreme low values + |
+ + required + | +
block_size |
+
+ str or Timedelta
+ |
+
+
+
+ Block size in the 'BM' |
+
+ None
+ |
+
return_period_size |
+
+ str or Timedelta
+ |
+
+
+
+ Size of return periods (default='365.2425D'). +If set to '30D', then a return period of 12 +would be roughly equivalent to a 1 year return period (360 days). + |
+
+ '365.2425D'
+ |
+
plotting_position |
+
+ str
+ |
+
+
+
+ Plotting position name (default='weibull'), not case-sensitive. +Supported plotting positions: + ecdf, hazen, weibull, tukey, blom, median, cunnane, gringorten, beard + |
+
+ 'weibull'
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
extreme_events |
+ DataFrame
+ |
+
+
+
+ A DataFrame with extreme values, exceedance probabilities,
+and return periods as multiples of |
+
src/pyextremes/extremes/return_periods.py
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|
pyextremes.models.models.get_model(model, extremes, distribution, distribution_kwargs=None, **kwargs)
+
+¶Get distribution fitting model and fit it to given extreme values.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
model |
+
+ str
+ |
+
+
+
+ Name of model. +Supported models: + MLE - Maximum Likelihood Estimate (MLE) model. + Based on 'scipy' package (scipy.stats.rv_continuous.fit). + Emcee - Markov Chain Monte Carlo (MCMC) model. + Based on 'emcee' package by Daniel Foreman-Mackey. + |
+ + required + | +
extremes |
+
+ Series
+ |
+
+
+
+ Time series of extreme events. + |
+ + required + | +
distribution |
+
+ str or rv_continuous
+ |
+
+
+
+ Distribution name compatible with scipy.stats +or a subclass of scipy.stats.rv_continuous. +See https://docs.scipy.org/doc/scipy/reference/stats.html + |
+ + required + | +
distribution_kwargs |
+
+ dict
+ |
+
+
+
+ Special keyword arguments, passed to the |
+
+ None
+ |
+
kwargs |
+ + | +
+
+
+ Keyword arguments passed to a model .fit method.
+MLE model:
+ MLE model takes no additional arguments.
+Emcee model:
+ n_walkers : int, optional
+ The number of walkers in the ensemble (default=100).
+ n_samples : int, optional
+ The number of steps to run (default=500).
+ progress : bool or str, optional
+ If True, a progress bar will be shown as the sampler progresses.
+ If a string, will select a specific tqdm progress bar.
+ Most notable is 'notebook', which shows a progress bar
+ suitable for Jupyter notebooks.
+ If False (default), no progress bar will be shown.
+ This progress bar is a part of the |
+
+ {}
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
model |
+ MLE or Emcee
+ |
+
+
+
+ Distribution fitting model fitted to the |
+
src/pyextremes/models/models.py
34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 |
|
pyextremes.models.model_base.AbstractModelBaseClass
+
+
+¶
+ Bases: ABC
src/pyextremes/models/model_base.py
14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 +150 +151 +152 +153 +154 +155 +156 +157 +158 +159 +160 +161 +162 +163 +164 +165 +166 +167 +168 +169 +170 +171 +172 +173 +174 +175 +176 +177 +178 +179 +180 +181 +182 +183 +184 +185 +186 +187 +188 +189 +190 +191 +192 |
|
AIC: float
+
+
+ property
+
+
+¶Return corrected Akaike Information Criterion (AIC) of the model.
+Smaller AIC value corresponds to better model. +This formula scales well for small sample sizes. +See https://en.wikipedia.org/wiki/Akaike_information_criterion
+name: str
+
+
+ abstractmethod
+ property
+
+
+¶Return model name.
+__init__(extremes, distribution, distribution_kwargs=None, **kwargs)
+
+¶Initialize the model.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
extremes |
+
+ Series
+ |
+
+
+
+ Time series of extreme events. + |
+ + required + | +
distribution |
+
+ str or rv_continuous
+ |
+
+
+
+ Distribution name compatible with scipy.stats +or a subclass of scipy.stats.rv_continuous. +See https://docs.scipy.org/doc/scipy/reference/stats.html + |
+ + required + | +
distribution_kwargs |
+
+ dict
+ |
+
+
+
+ Special keyword arguments, passed to the |
+
+ None
+ |
+
kwargs |
+ + | +
+
+
+ Keyword arguments passed to a model .fit method.
+MLE model:
+ MLE model takes no additional arguments.
+Emcee model:
+ n_walkers : int, optional
+ The number of walkers in the ensemble (default=100).
+ n_samples : int, optional
+ The number of steps to run (default=500).
+ progress : bool or str, optional
+ If True, a progress bar will be shown as the sampler progresses.
+ If a string, will select a specific tqdm progress bar.
+ Most notable is 'notebook', which shows a progress bar
+ suitable for Jupyter notebooks.
+ If False (default), no progress bar will be shown.
+ This progress bar is a part of the |
+
+ {}
+ |
+
src/pyextremes/models/model_base.py
15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +39 +40 +41 +42 +43 +44 +45 +46 +47 +48 +49 +50 +51 +52 +53 +54 +55 +56 +57 +58 +59 +60 +61 +62 +63 +64 +65 +66 +67 +68 +69 +70 +71 +72 +73 +74 +75 |
|
fit(**kwargs)
+
+
+ abstractmethod
+
+
+¶Set values for self.fit_parameters and self.trace.
+self.trace is set only for MCMC-like models. +self.fit_parameters is a dictionary with {parameter_name: value}, +e.g. {'c': 0.1, 'loc': -7, 'scale': 0.3} +self.trace is a numpy.ndarray with shape of +(n_walkers, n_samples, n_free_parameters)
+ +src/pyextremes/models/model_base.py
83 +84 +85 +86 +87 +88 +89 +90 +91 +92 +93 +94 +95 |
|
get_return_value(exceedance_probability, alpha=None, **kwargs)
+
+
+ abstractmethod
+
+
+¶Calculate return value and confidence interval bounds.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
exceedance_probability |
+
+ array - like
+ |
+
+
+
+ Exceedance probability or 1D array of exceedance probabilities. +Each exceedance probability must be in the [0, 1) range. + |
+ + required + | +
alpha |
+
+ float
+ |
+
+
+
+ Width of confidence interval (0, 1). +If None (default), return None +for upper and lower confidence interval bounds. + |
+
+ None
+ |
+
kwargs |
+ + | +
+
+
+ Model-specific keyword arguments. +If alpha is None, keyword arguments are ignored +(error still raised for unrecognized arguments). +MLE model: + n_samples : int, optional + Number of bootstrap samples used to estimate + confidence interval bounds (default=100). +Emcee model: + burn_in : int + Burn-in value (number of first steps to discard for each walker). + |
+
+ {}
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
return_value |
+ array - like
+ |
+
+
+
+ Return values. + |
+
ci_lower |
+ array - like
+ |
+
+
+
+ Lower confidence interval bounds. + |
+
ci_upper |
+ array - like
+ |
+
+
+
+ Upper confidence interval bounds. + |
+
src/pyextremes/models/model_base.py
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|
pyextremes.models.model_emcee.Emcee
+
+
+¶
+ Bases: AbstractModelBaseClass
src/pyextremes/models/model_emcee.py
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|
__init__(extremes, distribution, distribution_kwargs=None, n_walkers=100, n_samples=500, progress=False)
+
+¶Markov Chain Monte Carlo (MCMC) model.
+Built around the 'emcee' package by Daniel Foreman-Mackey
+ +src/pyextremes/models/model_emcee.py
17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +39 +40 +41 |
|
get_return_value(exceedance_probability, alpha=None, **kwargs)
+
+¶Calculate return value and confidence interval bounds.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
exceedance_probability |
+
+ array - like
+ |
+
+
+
+ Exceedance probability or 1D array of exceedance probabilities. +Each exceedance probability must be in the [0, 1) range. + |
+ + required + | +
alpha |
+
+ float
+ |
+
+
+
+ Width of confidence interval (0, 1). +If None (default), return None +for upper and lower confidence interval bounds. + |
+
+ None
+ |
+
kwargs |
+ + | +
+
+
+ burn_in : int, optional + Burn-in value (number of first steps to discard for each walker). + By default it is 0 (no values are discarded). + |
+
+ {}
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
return_value |
+ array - like
+ |
+
+
+
+ Return values. + |
+
ci_lower |
+ array - like
+ |
+
+
+
+ Lower confidence interval bounds. + |
+
ci_upper |
+ array - like
+ |
+
+
+
+ Upper confidence interval bounds. + |
+
src/pyextremes/models/model_emcee.py
119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 +150 +151 +152 +153 +154 +155 +156 +157 +158 +159 +160 +161 +162 +163 +164 +165 +166 +167 +168 +169 +170 +171 +172 +173 +174 +175 +176 +177 +178 +179 +180 +181 +182 +183 +184 +185 +186 +187 +188 +189 +190 +191 +192 +193 +194 +195 +196 +197 +198 +199 +200 +201 +202 +203 +204 +205 +206 +207 +208 +209 +210 +211 +212 +213 +214 +215 +216 +217 +218 +219 +220 +221 +222 +223 +224 +225 +226 +227 +228 +229 +230 +231 |
|
pyextremes.models.model_mle.MLE
+
+
+¶
+ Bases: AbstractModelBaseClass
src/pyextremes/models/model_mle.py
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|
__init__(extremes, distribution, distribution_kwargs=None)
+
+¶Maximum Likelihood Estimate (MLE) model.
+Built around the scipy.stats.rv_continuous.fit method.
+ +src/pyextremes/models/model_mle.py
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|
get_return_value(exceedance_probability, alpha=None, **kwargs)
+
+¶Calculate return value and confidence interval bounds.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
exceedance_probability |
+
+ array - like
+ |
+
+
+
+ Exceedance probability or 1D array of exceedance probabilities. +Each exceedance probability must be in the [0, 1) range. + |
+ + required + | +
alpha |
+
+ float
+ |
+
+
+
+ Width of confidence interval (0, 1). +If None (default), return None +for upper and lower confidence interval bounds. + |
+
+ None
+ |
+
kwargs |
+ + | +
+
+
+ n_samples : int, optional + Number of bootstrap samples used to estimate + confidence interval bounds (default=100). + |
+
+ {}
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
return_value |
+ array - like
+ |
+
+
+
+ Return values. + |
+
ci_lower |
+ array - like
+ |
+
+
+
+ Lower confidence interval bounds. + |
+
ci_upper |
+ array - like
+ |
+
+
+
+ Upper confidence interval bounds. + |
+
src/pyextremes/models/model_mle.py
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pyextremes.plotting.extremes.plot_extremes(ts, extremes, extremes_method, extremes_type=None, block_size=None, threshold=None, r=None, figsize=(8, 5), ax=None)
+
+¶Plot extreme events.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
ts |
+
+ Series
+ |
+
+
+
+ Time series from which |
+ + required + | +
extremes |
+
+ Series
+ |
+
+
+
+ Time series of extreme events. + |
+ + required + | +
extremes_method |
+
+ str
+ |
+
+
+
+ Extreme value extraction method. +Supported values: + BM - Block Maxima + POT - Peaks Over Threshold + |
+ + required + | +
extremes_type |
+
+ str
+ |
+
+
+
+ Type of |
+
+ None
+ |
+
block_size |
+
+ str or Timedelta
+ |
+
+
+
+ Block size, used only if |
+
+ None
+ |
+
threshold |
+
+ float
+ |
+
+
+
+ Threshold, used only if |
+
+ None
+ |
+
r |
+
+ pandas.Timedelta or value convertible to timedelta
+ |
+
+
+
+ Duration of window used to decluster the exceedances.
+See pandas.to_timedelta for more information.
+Used to show clusters. If None (default) then clusters are not shown.
+Clusters are shown only if both |
+
+ None
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches in format (width, height). +By default it is (8, 5). + |
+
+ (8, 5)
+ |
+
ax |
+
+ Axes
+ |
+
+
+
+ Axes onto which extremes plot is drawn. +If None (default), a new figure and axes objects are created. + |
+
+ None
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ Axes
+ |
+
+
+
+ Axes object. + |
+
src/pyextremes/plotting/extremes.py
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pyextremes.plotting.return_values.plot_return_values(observed_return_values, modeled_return_values, ax=None, figsize=(8, 5))
+
+¶Plot return values and confidence intervals for given return periods.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
observed_return_values |
+
+ DataFrame
+ |
+
+
+
+ DataFrame with observed return values. +First column must have extreme values. +Must have 'return period' column. + |
+ + required + | +
modeled_return_values |
+
+ DataFrame
+ |
+
+
+
+ DataFrame with modeled return values. +Index has return periods. +Must have the following columns: 'return value', 'lower ci', 'upper ci'. + |
+ + required + | +
ax |
+
+ Axes
+ |
+
+
+
+ Axes onto which the return value plot is drawn. +If None (default), a new figure and axes objects are created. + |
+
+ None
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches in format (width, height). +By default it is (8, 5). + |
+
+ (8, 5)
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ Axes
+ |
+
+
+
+ Axes object. + |
+
src/pyextremes/plotting/return_values.py
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pyextremes.plotting.probability_plots.plot_probability(observed, theoretical, ax=None, figsize=(8, 8))
+
+¶Plot a probability plot (QQ or PP).
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
observed |
+
+ ndarray
+ |
+
+
+
+ Observed values. + |
+ + required + | +
theoretical |
+
+ ndarray
+ |
+
+
+
+ Theoretical values. + |
+ + required + | +
ax |
+
+ Axes
+ |
+
+
+
+ Axes onto which the probability plot is drawn. +If None (default), a new figure and axes objects are created. + |
+
+ None
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches in format (width, height). +By default it is (8, 8). + |
+
+ (8, 8)
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ Axes
+ |
+
+
+
+ Axes object. + |
+
src/pyextremes/plotting/probability_plots.py
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pyextremes.plotting.mcmc.plot_trace(trace, trace_map=None, burn_in=0, labels=None, figsize=None)
+
+¶Plot a trace plot for a given MCMC sampler trace.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
trace |
+
+ ndarray
+ |
+
+
+
+ Array with MCMC sampler trace. +Has a shape of (n_walkers, n_samples, n_parameters). + |
+ + required + | +
trace_map |
+
+ tuple
+ |
+
+
+
+ Tuple with maximum aposteriori estimate of distribution parameters. +If provided, MAP values are plotted as orange lines on top of the trace. +If None (default) then MAP estimates are not plotted. + |
+
+ None
+ |
+
burn_in |
+
+ int
+ |
+
+
+
+ Burn-in value (number of first steps to discard for each walker). +By default it is 0 (no values are discarded). + |
+
+ 0
+ |
+
labels |
+
+ list of strings
+ |
+
+
+
+ Sequence of strings with parameter names, used to label axes. +If None (default), then axes are labeled sequentially. + |
+
+ None
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches.
+If None (default), then figure size is calculated automatically
+as 8 by 2 times number of parameters ( |
+
+ None
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ list
+ |
+
+
+
+ List with |
+
src/pyextremes/plotting/mcmc.py
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pyextremes.plotting.mcmc.plot_corner(trace, trace_map=None, burn_in=0, labels=None, levels=None, figsize=(8, 8))
+
+¶Plot a corner plot for a given MCMC sampler trace.
+ + + +Parameters:
+Name | +Type | +Description | +Default | +
---|---|---|---|
trace |
+
+ ndarray
+ |
+
+
+
+ Array with MCMC sampler trace. +Has a shape of (n_walkers, n_samples, n_parameters). + |
+ + required + | +
trace_map |
+
+ tuple
+ |
+
+
+
+ Tuple with maximum aposteriori estimate of distribution parameters. +If provided, MAP values are plotted as orange lines. +If None (default) then MAP estimates are not plotted. + |
+
+ None
+ |
+
burn_in |
+
+ int
+ |
+
+
+
+ Burn-in value (number of first steps to discard for each walker). +By default it is 0 (no values are discarded). + |
+
+ 0
+ |
+
labels |
+
+ array - like
+ |
+
+
+
+ Sequence of strings with parameter names, used to label axes. +If None (default), then axes are labeled sequentially. + |
+
+ None
+ |
+
levels |
+
+ int
+ |
+
+
+
+ Number of Gaussian KDE contours to plot. +If None (default), then not shown. + |
+
+ None
+ |
+
figsize |
+
+ tuple
+ |
+
+
+
+ Figure size in inches. By default it is (8, 8). + |
+
+ (8, 8)
+ |
+
Returns:
+Name | Type | +Description | +
---|---|---|
figure |
+ Figure
+ |
+
+
+
+ Figure object. + |
+
axes |
+ list
+ |
+
+
+
+ 2D list with Axes objects of size N by N, where N is |
+
src/pyextremes/plotting/mcmc.py
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|
{"use strict";/*!
+ * escape-html
+ * Copyright(c) 2012-2013 TJ Holowaychuk
+ * Copyright(c) 2015 Andreas Lubbe
+ * Copyright(c) 2015 Tiancheng "Timothy" Gu
+ * MIT Licensed
+ */var Ha=/["'&<>]/;Un.exports=$a;function $a(e){var t=""+e,r=Ha.exec(t);if(!r)return t;var o,n="",i=0,s=0;for(i=r.index;i