elisa.infer.results#

Subsequent analysis of maximum likelihood or Bayesian fit.

class FitResult(helper: Helper)[source]#

Bases: ABC

Fit result.

Attributes

`dof`	Degree of freedom.
`gof`	Goodness of fit p-value.
`ndata`	Data points number.
`plot`	Result plotter.

Methods

`load`(path[, decompress])	Load a previously saved fit result.
`save`(path[, compress])	Save the fit result to a file.
`summary`([file])	Print the summary of fit result.

eiso
flux
lumin

abstract property plot: Plotter#: Result plotter.

summary(file=None) → None[source]#

Print the summary of fit result.

Parameters:

file: file-like: An object with a write(string) method. This is passed to print().

abstractmethod flux(*args, **kwargs) → dict[str, Array] | dict[str, dict[str, Array]][source]#

abstractmethod lumin(*args, **kwargs) → dict[str, Array] | dict[str, dict[str, Array]][source]#

abstractmethod eiso(*args, **kwargs) → dict[str, Array] | dict[str, dict[str, Array]][source]#

property ndata: dict[str, int]#: Data points number.

property dof: int#: Degree of freedom.

abstract property gof: dict[str, float]#: Goodness of fit p-value.

save(path: str, compress: Literal['gzip', 'bz2', 'lzma'] = 'gzip', **kwargs: dict) → None[source]#

Save the fit result to a file.

Parameters:

pathstr: The file path to save fit result.
compress{‘gzip’, ‘bz2’, ‘lzma’}: The compression algorithm to use.
**kwargsdict: Extra parameters passed to gzip.open(), bz2.open(), or lzma.open().

static load(path: str, decompress: Literal['gzip', 'bz2', 'lzma'] = 'gzip') → FitResult[source]#

Load a previously saved fit result.

Parameters:

pathstr: The file path of previously saved fit result.
decompress{‘gzip’, ‘bz2’, ‘lzma’}: The decompression algorithm used to load the fit result.

Returns:

FitResult: The loaded fit result.

class MLEResult(minuit: Minuit, helper: Helper)[source]#

Bases: FitResult

Result of maximum likelihood fit.

Attributes

`aic`	Akaike information criterion with sample size correction.
`bic`	Bayesian information criterion.
`deviance`	Deviance of the model at MLE.
`dof`	Degree of freedom.
`gof`	Goodness of fit p-value.
`mle`	MLE and error of parameters.
`ndata`	Data points number.
`plot`	Result plotter.
`status`	Fit status of Minuit.

Methods

`boot`([n, seed, parallel, n_parallel, ...])	Preform parametric bootstrap.
`ci`([cl, params, fn, method, rtol, parallel])	Calculate confidence intervals.
`covar`([params, fn, method, parallel])	Calculate covariance matrix.
`eiso`(emin_rest, emax_rest, z, duration, cl, ...)	Calculate the isotropic emission energy of model.
`flux`(emin, emax[, energy, cl, method, ...])	Calculate the flux of model.
`load`(path[, decompress])	Load a previously saved fit result.
`lumin`(emin_rest, emax_rest, z, cl, method, ...)	Calculate the luminosity of model.
`save`(path[, compress])	Save the fit result to a file.
`summary`([file])	Print the summary of fit result.

property plot: MLEResultPlotter#: Result plotter.

boot(n: int = 10000, seed: int | None = None, parallel: bool = True, n_parallel: int | None = None, progress: bool = True, update_rate: int = 50)[source]#

Preform parametric bootstrap.

Parameters:

nint, optional: Number of parametric bootstraps based on the MLE. The default is 10000.
seedint, optional: The seed of random number generator used in parametric bootstrap.
parallelbool, optional: Whether to run simulation fit in parallel. The default is True.
n_parallelint, optional: Number of parallel processes to use when parallel is True. Defaults to jax.local_device_count().
progressbool, optional: Whether to display progress bar. The default is True.
update_rateint, optional: The update rate of progress bar. The default is 50.

covar(params: str | Sequence[str] | None = None, fn: dict[str, Callable] | None = None, method: Literal['hess', 'boot'] = 'hess', parallel: bool = True) → ParamsCovar[source]#

Calculate covariance matrix.

Parameters:

paramsstr or sequence of str, optional

Parameters to calculate covariance matrix. If not specified, calculate for parameters of interest.

fndict

A dict containing functions to calculate the covariance matrix. The keys are the names of the function results, and the values are the functions whose input is a dict of model parameters.

method{‘hess’, ‘boot’}, optional

Method used to calculate covariance. Available options are:

'hess': inverse of Hessian matrix from Minuit

'boot': calculate covariance based on bootstrap samples, MLEResult.boot() must be called before using this method.

The default is 'hess'.

parallelbool, optional

Whether to evaluate fn in parallel when method is 'boot'. The default is True.

Returns:

ParamsCovar: The covariance matrix.

ci(cl: float | int = 1, params: str | Iterable[str] | None = None, fn: dict[str, Callable] | None = None, method: Literal['profile', 'boot'] = 'profile', rtol: float | dict[str, float] = 1e-06, parallel: bool = True) → ConfidenceInterval[source]#

Calculate confidence intervals.

Parameters:

clfloat or int, optional

Confidence level for the confidence interval. If 0 < cl < 1, the value is interpreted as the confidence level. If cl >= 1, it is interpreted as the number of standard deviations. For example, cl=1 produces a 1-sigma or 68.3% confidence interval. The default is 1.

paramsstr or sequence of str, optional

Parameters to calculate confidence intervals. If not specified, calculate for parameters of interest.

fndict, optional

A dict containing functions to calculate the confidence intervals. The keys are the names of the function results, and the values are the functions whose input is a dict of model parameters.

method{‘profile’, ‘boot’}, optional

Method for calculating confidence intervals. Available options are:

'profile': use Minos algorithm of Minuit to find the confidence intervals based on the profile likelihood

'boot': use parametric bootstrap method to calculate the confidence intervals. MLEResult.boot() must be called before using this method.

The default is 'profile'.

rtolfloat, or dict of float, optional

The relative tolerance in determining the value of composite parameters and fn when method is 'profile'. The default is 1e-6.

parallelbool, optional

Whether to evaluate fn in parallel when method is 'boot'. The default is True.

Returns:

ConfidenceInterval: The confidence intervals.

flux(emin: float | int, emax: float | int, energy: bool = True, cl: float | int = 1, method: Literal['profile', 'boot'] = 'profile', ngrid: int = 1000, comps: bool = False, log: bool = True, params: dict[str, float | int] | None = None) → MLEFlux[source]#

Calculate the flux of model.

Warning

The flux is calculated by trapezoidal rule, and is accurate only if enough numbers of energy grids are used.

Parameters:

eminfloat or int

Minimum value of energy range, in units of keV.

emaxfloat or int

Maximum value of energy range, in units of keV.

energybool, optional

When True, calculate energy flux in units of erg cm⁻² s⁻¹; otherwise calculate photon flux in units of ph cm⁻² s⁻¹. The default is True.

clfloat or int, optional

Confidence level for the confidence interval. If 0 < cl < 1, the value is interpreted as the confidence level. If cl >= 1, it is interpreted as the number of standard deviations. For example, cl=1 produces a 1-sigma or 68.3% confidence interval. The default is 1.

method{‘profile’, ‘boot’}, optional

Method for calculating confidence intervals. Available options are:

'profile': use Minos algorithm of Minuit to find the confidence intervals based on the profile likelihood

'boot': use parametric bootstrap method to calculate the confidence intervals. MLEResult.boot() must be called before using this method.

The default is 'profile'.

ngridint, optional

The energy grid number to use in integration. The default is 1000.

Returns:

MLEFlux: The flux of the model.

Other Parameters:

compsbool, optional: Whether to return the result of each component. The default is False.
logbool, optional: Whether to use logarithmically regular energy grid. The default is True.
paramsdict, optional: Parameters dict to overwrite the fitted parameters.

lumin(emin_rest: float | int, emax_rest: float | int, z: float | int, cl: float | int = 1, method: Literal['profile', 'boot']='profile', ngrid: int = 1000, comps: bool = False, log: bool = True, params: dict[str, float | int] | None=None, cosmo: LambdaCDM = FlatLambdaCDM(name='Planck18', H0=<Quantity 67.66 km / (Mpc s)>, Om0=0.30966, Tcmb0=<Quantity 2.7255 K>, Neff=3.046, m_nu=<Quantity [0., 0., 0.06] eV>, Ob0=0.04897)) → MLELumin[source]#

Calculate the luminosity of model.

Warning

The luminosity is calculated by trapezoidal rule, and is accurate only if enough numbers of energy grids are used.

Parameters:

emin_restfloat or int

Minimum value of rest-frame energy range, in units of keV.

emax_restfloat or int

Maximum value of rest-frame energy range, in units of keV.

zfloat or int

Redshift of the source.

clfloat or int, optional

Confidence level for the confidence interval. If 0 < cl < 1, the value is interpreted as the confidence level. If cl >= 1, it is interpreted as the number of standard deviations. For example, cl=1 produces a 1-sigma or 68.3% confidence interval. The default is 1.

method{‘profile’, ‘boot’}, optional

Method for calculating confidence intervals. Available options are:

'profile': use Minos algorithm of Minuit to find the confidence intervals based on the profile likelihood

'boot': use parametric bootstrap method to calculate the confidence intervals. MLEResult.boot() must be called before using this method.

The default is 'profile'.

ngridint, optional

The energy grid number to use in integration. The default is 1000.

Returns:

MLELumin: The luminosity of the model.

Other Parameters:

compsbool, optional: Whether to return the result of each component. The default is False.
logbool, optional: Whether to use logarithmically regular energy grid. The default is True.
paramsdict, optional: Parameters dict to overwrite the fitted parameters.
cosmoLambdaCDM, optional: Cosmology model used to calculate luminosity. The default is Planck18.

eiso(emin_rest: float | int, emax_rest: float | int, z: float | int, duration: float | int, cl: float | int = 1, method: Literal['profile', 'boot']='profile', ngrid: int = 1000, comps: bool = False, log: bool = True, params: dict[str, float | int] | None=None, cosmo: LambdaCDM = FlatLambdaCDM(name='Planck18', H0=<Quantity 67.66 km / (Mpc s)>, Om0=0.30966, Tcmb0=<Quantity 2.7255 K>, Neff=3.046, m_nu=<Quantity [0., 0., 0.06] eV>, Ob0=0.04897)) → MLEEiso[source]#

Calculate the isotropic emission energy of model.

Warning

The \(E_\mathrm{iso}\) is calculated by trapezoidal rule, and is accurate only if enough numbers of energy grids are used.

Parameters:

emin_restfloat or int

Minimum value of rest-frame energy range, in units of keV.

emax_restfloat or int

Maximum value of rest-frame energy range, in units of keV.

zfloat or int

Redshift of the source.

durationfloat or int

Observed duration of the source, in units of seconds.

clfloat or int, optional

Confidence level for the confidence interval. If 0 < cl < 1, the value is interpreted as the confidence level. If cl >= 1, it is interpreted as the number of standard deviations. For example, cl=1 produces a 1-sigma or 68.3% confidence interval. The default is 1.

method{‘profile’, ‘boot’}, optional

Method for calculating confidence intervals. Available options are:

'profile': use Minos algorithm of Minuit to find the confidence intervals based on the profile likelihood

'boot': use parametric bootstrap method to calculate the confidence intervals. MLEResult.boot() must be called before using this method

The default is 'profile'.

ngridint, optional

The energy grid number to use in integration. The default is 1000.

Returns:

MLEEiso: The isotropic emission energy of the model.

Other Parameters:

compsbool, optional: Whether to return the result of each component. The default is False.
logbool, optional: Whether to use logarithmically regular energy grid. The default is True.
paramsdict, optional: Parameters dict to overwrite the fitted parameters.
cosmoLambdaCDM, optional: Cosmology model used to calculate luminosity. The default is Planck18.

property gof: dict[str, float]#: Goodness of fit p-value.

property mle: dict[str, tuple[float, float]]#: MLE and error of parameters.

property deviance: dict[str, float]#: Deviance of the model at MLE.

property aic: float#: Akaike information criterion with sample size correction.

property bic: float#: Bayesian information criterion.

property status: FMin#: Fit status of Minuit.

class PosteriorResult(helper: Helper, idata: InferenceData, ml_optimize: Callable, sampler_state: Any = None)[source]#

Bases: FitResult

Result obtained from Bayesian fit.

Attributes

`deviance`	Mean and median of model deviance.
`divergence`	Number of divergent samples.
`dof`	Degree of freedom.
`ess`	Effective MCMC sample size.
`gof`	Goodness of fit p-value.
`idata`	ArviZ InferenceData.
`lnZ`	Log model evidence and error.
`loo`	Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO-CV).
`mean`	Mean of parameter samples.
`median`	Median of parameter samples.
`mle`	MLE parameters.
`ndata`	Data points number.
`plot`	Result plotter.
`reff`	Relative MCMC efficiency.
`rhat`	Computes split R-hat over MCMC chains.
`sampler_state`	The sampler state at the end of the sampling phase.
`std`	Standard deviation of parameter samples.
`waic`	The widely applicable information criterion (WAIC).

Methods

`ci`([cl, params, fn, hdi, parallel])	Calculate credible intervals.
`covar`([params, fn, parallel])	Calculate the covariance matrix.
`eiso`(emin_rest, emax_rest, z, duration, cl, ...)	Calculate the isotropic emission energy of model.
`flux`(emin, emax[, cl, energy, ngrid, hdi, ...])	Calculate the flux of model.
`load`(path[, decompress])	Load a previously saved fit result.
`lumin`(emin_rest, emax_rest, z, cl, ngrid, ...)	Calculate the luminosity of model.
`ppc`([n, seed, parallel, n_parallel, ...])	Perform posterior predictive check.
`save`(path[, compress])	Save the fit result to a file.
`summary`([file])	Print the summary of fit result.

property plot: PosteriorResultPlotter#: Result plotter.

covar(params: str | Iterable[str] | None = None, fn: dict[str, Callable] | None = None, parallel: bool = True) → ParamsCovar[source]#

Calculate the covariance matrix.

Parameters:

paramsstr or sequence of str, optional: Parameters to calculate covariance matrix. If not specified, calculate for all parameters.
fndict, optional: A dict containing functions to calculate the covariance matrix. The keys are the names of the function results, and the values are the functions whose input is a dict of model parameters.
parallelbool, optional: Whether to use parallel computation for fn. The default is True.

Returns:

ParamsCovar: The covariance matrix.

ci(cl: float | int = 1, params: str | Iterable[str] | None = None, fn: dict[str, Callable] | None = None, hdi: bool = False, parallel: bool = True) → CredibleInterval[source]#

Calculate credible intervals.

Parameters:

clfloat or int, optional: The credible level of samples within the credible interval. If 0 < cl < 1, the value is interpreted as the probability mass. If cl >= 1, it is interpreted as the number of standard deviations. For example, cl=1 produces a 1-sigma or 68.3% credible interval. The default is 1.
paramsstr or sequence of str, optional: Parameters to calculate confidence intervals. If not specified, calculate for parameters of interest.
fndict, optional: A dict containing functions to calculate the confidence intervals. The keys are the names of the function results, and the values are the functions whose input is a dict of model parameters.
hdibool, optional: Whether to return the highest density interval. The default is False, which means an equal tailed interval is returned.
parallelbool, optional: Whether to use parallel computation for fn. The default is True.

Returns:

CredibleInterval: The credible interval.

Calculate the flux of model.

Warning

The flux is calculated by trapezoidal rule, and is accurate only if enough numbers of energy grids are used.

Parameters:

eminfloat or int: Minimum value of energy range, in units of keV.
emaxfloat or int: Maximum value of energy range, in units of keV.
clfloat or int, optional: The credible level of samples within the credible interval. If 0 < cl < 1, the value is interpreted as the probability mass. If cl >= 1, it is interpreted as the number of standard deviations. For example, cl=1 produces a 1-sigma or 68.3% credible interval. The default is 1.
energybool, optional: When True, calculate energy flux in units of erg cm⁻² s⁻¹; otherwise calculate photon flux in units of ph cm⁻² s⁻¹. The default is True.
ngridint, optional: The energy grid number to use in integration. The default is 1000.

Returns:

PosteriorFlux: The flux of the model.

Other Parameters:

hdibool, optional: Whether to return the highest density interval. The default is False, which means an equal tailed interval is returned.
compsbool, optional: Whether to return the result of each component. The default is False.
logbool, optional: Whether to use logarithmically regular energy grid. The default is True.
paramsdict, optional: Parameters dict to overwrite the fitted parameters. Ignored when method is 'profile'.

lumin(emin_rest: float | int, emax_rest: float | int, z: float | int, cl: float | int = 1, ngrid: int = 1000, hdi: bool = False, comps: bool = False, log: bool = True, params: dict[str, float | int] | None=None, cosmo: LambdaCDM = FlatLambdaCDM(name='Planck18', H0=<Quantity 67.66 km / (Mpc s)>, Om0=0.30966, Tcmb0=<Quantity 2.7255 K>, Neff=3.046, m_nu=<Quantity [0., 0., 0.06] eV>, Ob0=0.04897)) → PosteriorLumin[source]#

Calculate the luminosity of model.

Warning

The luminosity is calculated by trapezoidal rule, and is accurate only if enough numbers of energy grids are used.

Parameters:

emin_restfloat or int: Minimum value of rest-frame energy range, in units of keV.
emax_restfloat or int: Maximum value of rest-frame energy range, in units of keV.
zfloat or int: Redshift of the source.
clfloat or int, optional: The credible level of samples within the credible interval. If 0 < cl < 1, the value is interpreted as the probability mass. If cl >= 1, it is interpreted as the number of standard deviations. For example, cl=1 produces a 1-sigma or 68.3% credible interval. The default is 1.
ngridint, optional: The energy grid number to use in integration. The default is 1000.

Returns:

PosteriorLumin: The luminosity of the model.

Other Parameters:

hdibool, optional: Whether to return the highest density interval. The default is False, which means an equal tailed interval is returned.
compsbool, optional: Whether to return the result of each component. The default is False.
logbool, optional: Whether to use logarithmically regular energy grid. The default is True.
paramsdict, optional: Parameters dict to overwrite the fitted parameters. Ignored when method is 'profile'.
cosmoLambdaCDM, optional: Cosmology model used to calculate luminosity. The default is Planck18.

eiso(emin_rest: float | int, emax_rest: float | int, z: float | int, duration: float | int, cl: float | int = 1, ngrid: int = 1000, hdi: bool = False, comps: bool = False, log: bool = True, params: dict[str, float | int] | None=None, cosmo: LambdaCDM = FlatLambdaCDM(name='Planck18', H0=<Quantity 67.66 km / (Mpc s)>, Om0=0.30966, Tcmb0=<Quantity 2.7255 K>, Neff=3.046, m_nu=<Quantity [0., 0., 0.06] eV>, Ob0=0.04897)) → PosteriorEiso[source]#

Calculate the isotropic emission energy of model.

Warning

The \(E_\mathrm{iso}\) is calculated by trapezoidal rule, and is accurate only if enough numbers of energy grids are used.

Parameters:

emin_restfloat or int: Minimum value of rest-frame energy range, in units of keV.
emax_restfloat or int: Maximum value of rest-frame energy range, in units of keV.
zfloat or int: Redshift of the source.
durationfloat or int: Observed duration of the source, in units of seconds.
clfloat or int, optional: The credible level of samples within the credible interval. If 0 < cl < 1, the value is interpreted as the probability mass. If cl >= 1, it is interpreted as the number of standard deviations. For example, cl=1 produces a 1-sigma or 68.3% credible interval. The default is 1.
ngridint, optional: The energy grid number to use in integration. The default is 1000.

Returns:

PosteriorEiso: The isotropic emission energy of the model.

Other Parameters:

hdibool, optional: Whether to return the highest density interval. The default is False, which means an equal tailed interval is returned.
compsbool, optional: Whether to return the result of each component. The default is False.
logbool, optional: Whether to use logarithmically regular energy grid. The default is True.
paramsdict, optional: Parameters dict to overwrite the fitted parameters. Ignored when method is 'profile'.
cosmoLambdaCDM, optional: Cosmology model used to calculate luminosity. The default is Planck18.

ppc(n: int = 10000, seed: int | None = None, parallel: bool = True, n_parallel: int | None = None, progress: bool = True, update_rate: int = 50)[source]#

Perform posterior predictive check.

Parameters:

nint, optional: The number of posterior predictions. The default is 10000.
seedint, optional: The seed of random number generator used in posterior predictions.
parallelbool, optional: Whether to run simulation fit in parallel. The default is True.
n_parallelint, optional: Number of parallel processes to use when parallel is True. Defaults to jax.local_device_count().
progressbool, optional: Whether to display progress bar. The default is True.
update_rateint, optional: The update rate of progress bar. The default is 50.

property gof: dict[str, float]#: Goodness of fit p-value.

property mle: dict[str, tuple[float, float]]#: MLE parameters.

property idata: InferenceData#: ArviZ InferenceData.

property sampler_state: Any#: The sampler state at the end of the sampling phase.

property mean: dict[str, float]#: Mean of parameter samples.

property std: dict[str, float]#: Standard deviation of parameter samples.

property median: dict[str, float]#: Median of parameter samples.

property deviance: dict#: Mean and median of model deviance.

property reff: float#: Relative MCMC efficiency.

property ess: dict[str, int]#: Effective MCMC sample size.

property rhat: dict[str, float]#

Computes split R-hat over MCMC chains.

In general, only fully trust the sample if R-hat is less than 1.01. In the early workflow, R-hat below 1.1 is often sufficient. See [1] for more information.

References

[1]

https://arxiv.org/abs/1903.08008

property divergence: int#: Number of divergent samples.

property waic: ELPDData#

The widely applicable information criterion (WAIC).

Estimates the expected log point-wise predictive density (elpd) using WAIC. Also calculates the WAIC’s standard error and the effective number of parameters. See [1] and [2] for more information.

References

[1]

https://arxiv.org/abs/1507.04544

[2]

https://arxiv.org/abs/1004.2316

property loo: ELPDData#

Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO-CV).

Estimates the expected log point-wise predictive density (elpd) using PSIS-LOO-CV. Also calculates LOO’s standard error and the effective number of parameters. For more information, see [1], [2] and [3].

References

[1]

https://avehtari.github.io/modelselection/CV-FAQ.html

[2]

https://arxiv.org/abs/1507.04544

[3]

https://arxiv.org/abs/1507.02646

property lnZ: tuple[float, float]#: Log model evidence and error.

class ParamsCovar(names: tuple[str, ...], matrix: CovarMatrix)[source]#

Bases: NamedTuple

Covariance matrix of the model parameters.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

names: tuple[str, ...]#: Parameter names.

matrix: Matrix#: Covariance matrix.

class ConfidenceInterval(mle: dict[str, float], se: dict[str, float], intervals: dict[str, tuple[float, float]], errors: dict[str, tuple[float, float]], cl: float, method: str, status: dict)[source]#

Bases: NamedTuple

Confidence interval result.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

mle: dict[str, float]#: The maximum likelihood estimation.

se: dict[str, float]#: The standard errors of the MLE, calculated from Hessian matrix.

intervals: dict[str, tuple[float, float]]#: The confidence intervals.

errors: dict[str, tuple[float, float]]#: The confidence intervals in error form.

cl: float#: The confidence level.

method: str#: Method used to calculate the confidence interval.

status: dict#: Status of the calculation progress.

class MLEFlux(emin: float, emax: float, energy: bool, mle: dict[str, Q] | dict[str, dict[str, Q]], se: dict[str, Q] | dict[str, dict[str, Q]], intervals: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], errors: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], cl: float, method: str, status: dict)[source]#

Bases: NamedTuple

The flux of the MLE model.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

emin: float#: Minimum value of energy range.

emax: float#: Maximum value of energy range.

energy: bool#: Whether the flux is in energy flux. False for photon flux.

mle: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The maximum likelihood estimation of flux.

se: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The standard errors of MLE, calculated from Hessian matrix.

intervals: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The confidence intervals of the model flux.

errors: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The confidence intervals of the model flux in error form.

cl: float#: The confidence level.

method: str#: Method used to calculate the confidence interval.

status: dict#: Status of the calculation progress.

class MLELumin(emin_rest: float, emax_rest: float, z: float, cosmo: LambdaCDM, mle: dict[str, Q] | dict[str, dict[str, Q]], se: dict[str, Q] | dict[str, dict[str, Q]], intervals: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], errors: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], cl: float, method: str, status: str)[source]#

Bases: NamedTuple

The luminosity of the MLE model.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

emin_rest: float#: Minimum value of rest-frame energy range.

emax_rest: float#: Maximum value of rest-frame energy range.

z: float#: Redshift of the source.

cosmo: LambdaCDM#: Cosmology model used to calculate luminosity.

mle: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The maximum likelihood estimation of luminosity.

se: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The standard errors of MLE, calculated from Hessian matrix.

intervals: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The confidence intervals of the model luminosity.

errors: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The confidence intervals of the model luminosity in error form.

cl: float#: The confidence level.

method: str#: Method used to calculate the confidence interval.

status: str#: Status of the calculation progress.

class MLEEiso(emin_rest: float, emax_rest: float, z: float, duration: float, cosmo: LambdaCDM, mle: dict[str, Q] | dict[str, dict[str, Q]], se: dict[str, Q] | dict[str, dict[str, Q]], intervals: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], errors: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], cl: float, method: str, status: str)[source]#

Bases: NamedTuple

The isotropic emission energy of the MLE model.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

emin_rest: float#: Minimum value of rest-frame energy range.

emax_rest: float#: Maximum value of rest-frame energy range.

z: float#: Redshift of the source.

duration: float#: Observed duration of the source.

cosmo: LambdaCDM#: Cosmology model used to calculate Eiso.

mle: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The maximum likelihood estimation of Eiso.

se: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The standard errors of MLE, calculated from Hessian matrix.

intervals: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The confidence intervals of the model Eiso.

errors: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The confidence intervals of the model Eiso in error form.

cl: float#: The confidence level.

method: str#: Method used to calculate the confidence interval.

status: str#: Status of the calculation progress.

class BootstrapResult(mle: dict, data: dict, models: dict, params: dict, deviance: dict, p_value: dict, n: int, n_valid: int, seed: int)[source]#

Bases: NamedTuple

Parametric bootstrap result.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

mle: dict#: The maximum likelihood estimation.

data: dict#: Simulation data based on MLE.

models: dict#: Bootstrap models.

params: dict#: Bootstrap parameters.

deviance: dict#: Bootstrap deviance.

p_value: dict#: Model fitness \(p\)-value.

n: int#: Numbers of bootstrap.

n_valid: int#: Numbers of valid bootstrap.

seed: int#: Seed of random number generator used in simulation.

class CredibleInterval(median: dict[str, float], intervals: dict[str, tuple[float, float]], errors: dict[str, tuple[float, float]], cl: float, method: str, dist: dict[str, JAXArray])[source]#

Bases: NamedTuple

Credible interval result.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

median: dict[str, float]#: Median of the posterior distribution.

intervals: dict[str, tuple[float, float]]#: The credible intervals.

errors: dict[str, tuple[float, float]]#: The credible intervals in error form.

cl: float#: The credible level.

method: str#: Highest Density Interval (HDI), or equal tailed interval (ETI).

dist: dict[str, Array]#: Posterior distribution.

class PosteriorFlux(emin: float, emax: float, energy: bool, mean: dict[str, Q] | dict[str, dict[str, Q]], std: dict[str, Q] | dict[str, dict[str, Q]], median: dict[str, Q] | dict[str, dict[str, Q]], intervals: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], errors: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], cl: float, method: str, dist: dict[str, Q] | dict[str, dict[str, Q]])[source]#

Bases: NamedTuple

Posterior flux.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

emin: float#: Minimum value of energy range.

emax: float#: Maximum value of energy range.

energy: bool#: Whether the flux is in energy flux. False for photon flux.

mean: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The posterior mean of the flux.

std: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The standard deviation of posterior distribution of flux.

median: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The posterior median of the flux.

intervals: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The credible intervals of the flux.

errors: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The credible intervals of the flux in error form.

cl: float#: The credible level.

method: str#: Highest Density Interval (HDI), or equal tailed interval (ETI).

dist: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: Posterior flux distribution.

class PosteriorLumin(emin_rest: float, emax_rest: float, z: float, cosmo: LambdaCDM, mean: dict[str, Q] | dict[str, dict[str, Q]], std: dict[str, Q] | dict[str, dict[str, Q]], median: dict[str, Q] | dict[str, dict[str, Q]], intervals: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], errors: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], cl: float, method: str, dist: dict[str, Q] | dict[str, dict[str, Q]])[source]#

Bases: NamedTuple

Posterior luminosity.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

emin_rest: float#: Minimum value of rest-frame energy range.

emax_rest: float#: Maximum value of rest-frame energy range.

z: float#: Redshift of the source.

cosmo: LambdaCDM#: Cosmology model used to calculate luminosity.

mean: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The posterior mean of luminosity.

std: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The posterior standard deviation of the luminosity.

median: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The posterior median of the luminosity.

intervals: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The credible intervals of the luminosity.

errors: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The credible intervals of the luminosity in error form.

cl: float#: The credible level.

method: str#: Highest Density Interval (HDI), or equal tailed interval (ETI).

dist: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: Posterior distribution of luminosity.

class PosteriorEiso(emin_rest: float, emax_rest: float, z: float, duration: float, cosmo: LambdaCDM, mean: dict[str, Q] | dict[str, dict[str, Q]], std: dict[str, Q] | dict[str, dict[str, Q]], median: dict[str, Q] | dict[str, dict[str, Q]], intervals: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], errors: dict[str, tuple[Q, Q]] | dict[str, dict[str, tuple[Q, Q]]], cl: float, method: str, dist: dict[str, Q] | dict[str, dict[str, Q]])[source]#

Bases: NamedTuple

Posterior isotropic emission energy.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

emin_rest: float#: Minimum value of rest-frame energy range.

emax_rest: float#: Maximum value of rest-frame energy range.

z: float#: Redshift of the source.

duration: float#: Observed duration of the source.

cosmo: LambdaCDM#: Cosmology model used to calculate Eiso.

mean: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The posterior mean of the Eiso.

std: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The posterior standard deviation of the Eiso.

median: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: The posterior median of the Eiso.

intervals: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The credible intervals of the Eiso.

errors: dict[str, tuple[Quantity, Quantity]] | dict[str, dict[str, tuple[Quantity, Quantity]]]#: The credible intervals of the Eiso in error form.

cl: float#: The credible level.

method: str#: Highest Density Interval (HDI), or equal tailed interval (ETI).

dist: dict[str, Quantity] | dict[str, dict[str, Quantity]]#: Posterior distribution of Eiso.

class PPCResult(params_rep: dict, models_rep: dict, data: dict, params_fit: dict, deviance: dict, models_fit: dict, p_value: dict, n: int, n_valid: int, seed: int)[source]#

Bases: NamedTuple

Posterior predictive check result.

Methods

`count`(value, /)	Return number of occurrences of value.
`index`(value[, start, stop])	Return first index of value.

params_rep: dict#: Posterior of free parameters used to perform ppc.

models_rep: dict#: Models’ values corresponding to params_rep.

data: dict#: Posterior predictive data.

params_fit: dict#: Best fit parameters of posterior predictive data.

deviance: dict#: Deviance of posterior predictive data and best fit models.

models_fit: dict#: Best fit models’ values of posterior predictive data.

p_value: dict#: Posterior predictive \(p\)-value.

n: int#: Numbers of posterior prediction.

n_valid: int#: Numbers of valid ppc.

seed: int#: Seed of random number generator used in simulation.