Getting confidence intervals for MLE after fitting the model

[ozanyesil]

The estimated parameters can be seen after fitting the model but is there a way to see parameter estimations with upper and lower bounds as in the get_return_value method?

[georgebv]

You can get all distribution parameters from the models and then calculate confidence bounds for each.

For MLE it is fit_parameter_cache attribute, you must call the get_return_value method with alpha argument and with n_samples set to the desired sample size

pyextremes/src/pyextremes/models/model_mle.py

Line 50 in ca4f368

self.fit_parameter_cache: typing.List[typing.Tuple[float, ...]] = []

For Emcee it is _trace attribute which stores chains for each parameter

pyextremes/src/pyextremes/models/model_emcee.py

Line 84 in ca4f368

self._trace: np.ndarray = sampler.get_chain().transpose((1, 0, 2))

For Emcee you can visualize them using the plot_trace method

pyextremes/src/pyextremes/eva.py

Lines 1089 to 1126 in ca4f368

	def plot_trace(
	self,
	burn_in: int = 0,
	labels: typing.Optional[typing.List[str]] = None,
	figsize: typing.Optional[typing.Tuple[float, float]] = None,
	) -> typing.Tuple[plt.Figure, list]: # pragma: no cover
	"""
	Plot trace plot for MCMC sampler trace.
	Parameters
	----------
	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).
	labels : array-like, optional
	Sequence of strings with parameter names, used to label axes.
	If None (default), then axes are labeled sequentially.
	figsize : tuple, optional
	Figure size in inches.
	If None (default), then figure size is calculated automatically
	as 8 by 2 times number of parameters.
	Returns
	-------
	figure : matplotlib.figure.Figure
	Figure object.
	axes : list
	List with n_parameters Axes objects.
	"""
	trace, trace_map, labels = self._get_mcmc_plot_inputs(labels=labels)
	return plot_trace(
	trace=trace,
	trace_map=trace_map,
	burn_in=burn_in,
	labels=labels,
	figsize=figsize,
	)

This is an example from README: https://raw.githubusercontent.com/georgebv/pyextremes-notebooks/master/notebooks/documentation/readme%20figures/trace.png

[ozanyesil]

Thank you for your detailed answer, but there are still things that I could not understand. If we think the following code as an example, where can I find parameter estimations or which code I should write?

model = EVA(data = data)
model.get_extremes(method = 'BM', extremes_type = 'high')
model.fit_model()
model.get_return_value(
return_period=[1, 2, 5, 10, 25, 50, 100],
alpha=0.95,
n_samples=1000,
)

Thank you.

[georgebv]

The models I referenced above can be accessed via model.model. FYI, by default you fit with MLE.

[ozanyesil]

Thanks again for the answer. I have one more question. When I run model.model it returns fit parameter cache size which I don't know what it means. So, still can not see the bounds of parameter estimations. How should i interpret the results of model.model.
Thank you.

[georgebv]

This is an n by m array with n being number of parameters and m being number of samples. You should be able to calculate confidence bounds for each of the parameters using this array. You can assume that they follow normal distribution.

[ozanyesil]

Alright, thank you for your time and help. I got my answers and closing the discussion.