likelihoodprofiler package

Submodules

likelihoodprofiler.get_endpoint module

likelihoodprofiler.get_endpoint.get_endpoint(theta_init, theta_num, loss_func, method, direction='right', loss_crit=0.0, scale=[], theta_bounds=[], scan_bound=None, scan_tol=0.001, loss_tol=0.001, local_alg=28, **kwargs)

Calculates right or left endpoint of CI for parameter component. It is a wripper of get_right_endpoint functions for selection of direction and using different transformations for faster optimization.

Parameters

  • theta_init (Array[Float64]) – starting values of parameter vector \(\Theta\). The starting values is not necessary to be the optimum values for loss_func but it the value of loss_func must be lower than loss_crit.

  • theta_num (Int) – number \(n\) of vector component to compute confidence interval \(\Theta^n\).

  • loss_func (Function) – loss function \(\Lambda\left(\Theta\right)\) the profile of which is analyzed. Usually we use log-likelihood for profile analysis in form \(\Lambda( \theta ) = - 2 ln\left( L(\Theta) \right)\).

  • method (String) – computational method to evaluate interval endpoint. Currently the following methods are implemented: "CICO_ONE_PASS", "LIN_EXTRAPOL", "QUADR_EXTRAPOL".

  • direction (String) – "right" or "left" endpoint to estimate.

  • loss_crit (Float64) – critical level of loss function. The endpoint of CI for selected parameter is the value at which profile likelihood meets the value of loss_crit.

  • scale (String) – vector of scale transformations for each component. Possible values: "direct", "log", "logit". This option can make optimization much more faster, especially for wide theta_bounds. The default value is "direct" (no transformation) for all components.

  • theta_bounds (Array[Array[Float64,Float64]]) – vector of bounds for each component in format \((left_border, right_border)\). This bounds define the ranges for possible parameter values. The defaults are the non-limited values taking into account the scale, i.e. \((0, Inf)\) for "log" scale.

  • scan_bounds (Array[Float64,Float64]) – vector of scan bound for theta_num component. It must be within the theta_bounds for the scanned component. The defaults are (-9., 9.) for transformed values, i.e. :math:`(1e-9, 1e9) for "log" scale.

  • scan_tol (Float64) – Absolute tolerance of scanned component (stop criterion).

  • loss_tol (Float64) – Absolute tolerance of loss_func at loss_crit (stop criterion). Restriction. Currently is not effective for nlopt.CICO_ONE_PASS methods because of limitation in nlopt.LN_AUGLAG interface.

  • local_alg (Function) – algorithm of optimization. Currently the local derivation free algorithms form NLOPT pack were tested. The methods: nlopt.LN_NELDERMEAD, nlopt.LN_COBYLA, nlopt.LN_PRAXIS show good results. Methods: nlopt.LN_BOBYQA, nlopt.LN_SBPLX, nlopt.LN_NEWUOA is not recommended.

  • **kwargs (Any) – the additional keyword arguments passed to get_right_endpoint for specific method.

Returns

object storing confidence endpoint and profile points found on fly.

Return type

class EndPoint

likelihoodprofiler.get_interval module

class likelihoodprofiler.get_interval.ParamInterval(input, loss_init, method, result)

Bases: object

Structure storing result of parameter interval calculation

Parameters
plot()
class likelihoodprofiler.get_interval.ParamIntervalInput(theta_init, theta_num, loss_func, loss_crit, scale, theta_bounds, scan_bounds, scan_tol, loss_tol, local_alg, fitter_options)

Bases: object

Calculates right or left endpoint of CI for parameter component. It is a wripper of get_right_endpoint functions for selection of direction and using different transformations for faster optimization.

Parameters

  • theta_init (Array[Float64]) – initial parameters vector

  • theta_num (Int) – number of the parameter for analysis

  • loss_func (Function) – loss function

  • loss_crit (Float64) – loss function maximum value, “identifiability level

  • scale (Array[String]) –

  • theta_bounds (Array[[Float64, Float64]]) – search bounds for id parameter

  • scan_bounds (Float64) –

  • scan_tol (Float64) – fitting tolerance for local optimizer (default - 1e-3)

  • loss_tol (Float64) – constraints tolerance

  • local_alg (Function) – local fitting algorithm (default - LN_NELDERMEAD)

  • fitter_options (Any) –

likelihoodprofiler.get_interval.get_interval(theta_init, theta_num, loss_func, method, loss_crit=0.0, scale=[], theta_bounds=[], scan_bounds=None, scan_tol=0.001, loss_tol=0.001, local_alg=28, **kwargs)

Computes confidence interval for single component theta_num of parameter vector and loss_func according to loss_crit level.

Parameters

  • theta_init (Array[Float64]) – starting values of parameter vector \(\Theta\). The starting values is not necessary to be the optimum values for loss_func but it the value of loss_func must be lower than loss_crit.

  • theta_num (Int) – number n of vector component to compute confidence interval \(\Theta^n\).

  • loss_func (Function) – loss function \(\Lambda\left(\theta\right)\) the profile of which is analyzed. Usually we use log-likelihood for profile analysis in form \(\Lambda( \theta ) = - 2 ln\left( L(\theta) \right)\).

  • method (String) – computational method to evaluate interval endpoint. Currently the following methods are implemented: CICO_ONE_PASS, LIN_EXTRAPOL, QUADR_EXTRAPOL.

  • loss_crit (Float64) – critical level of loss function. The endpoint of CI for selected parameter is the value at which profile likelihood meets the value of loss_crit.

  • scale (String) – vector of scale transformations for each component. Possible values: "direct", "log", "logit". This option can make optimization much more faster, especially for wide theta_bounds. The default value is "direct" (no transformation) for all components.

  • theta_bounds (Array[Array[Float64,Float64]]) – vector of bounds for each component in format \((left_border, right_border)\). This bounds define the ranges for possible parameter values. The defaults are the non-limited values taking into account the scale, i.e. \((0, Inf)\) for "log" scale.

  • scan_bounds (Array[Float64,Float64]) – vector of scan bound for theta_num component. It must be within the theta_bounds for the scanned component. The defaults are (-9., 9.) for transformed values, i.e. :math:`(1e-9, 1e9) for "log" scale.

  • scan_tol (Float64) – Absolute tolerance of scanned component (stop criterion).

  • loss_tol (Float64) – Absolute tolerance of loss_func at loss_crit (stop criterion). Restriction. Currently is not effective for nlopt.CICO_ONE_PASS methods because of limitation in nlopt.LN_AUGLAG interface.

  • local_alg (Function) – algorithm of optimization. Currently the local derivation free algorithms form NLOPT pack were tested. The methods: nlopt.LN_NELDERMEAD, nlopt.LN_COBYLA, nlopt.LN_PRAXIS show good results. Methods: nlopt.LN_BOBYQA, nlopt.LN_SBPLX, nlopt.LN_NEWUOA is not recommended.

  • **kwargs (Any) – the additional keyword arguments passed to get_right_endpoint for specific method.

Returns

structure storing all input data and estimated confidence interval.

Return type

ParamInterval

likelihoodprofiler.get_right_endpoint module

likelihoodprofiler.get_right_endpoint.get_right_endpoint(theta_init, theta_num, loss_func, method='CICO_ONE_PASS', theta_bounds=[], scan_bound=9.0, scan_tol=0.001, loss_tol=None, scan_hini=1.0, scan_hmax=inf, local_alg=28, max_iter=100000, ftol_abs=0.001, **kwargs)

Interface for current and future methods for endpoint estimation.

Parameters

  • theta_init (Array[Flaot64]) – theta_init: starting values of parameter vector \(\Theta\). The starting values is not necessary to be the optimum values for loss_func but it the value of loss_func must be lower than loss_crit.

  • theta_num (Int) – number \(n\) of vector component to compute confidence interval \(\Theta^n\).

  • loss_func (Function) – loss function the profile of which is analyzed, see get_interval. In this function loss crit is always equal 0 for code simplification.

  • method (String) – this value is always fixed. Implemented methods are: "CICO_ONE_PASS". It is implemented for easy switching between different implemented and future methods.

  • theta_bounds (Array[Array[Float64, Float64]]) – vector of bounds for each component in format \((left_bound, right_bound)\). This bounds define the ranges for possible parameter values.

  • scan_bound (Float64) – right scan bound for theta_num component. It must be within the theta_bounds for the scanned component.

  • scan_tol (Float64) – Absolute tolerance of scanned component (stop criterion).

  • loss_tol (Float64) – Absolute tolerance of loss_func at loss_crit (stop criterion). Restriction. Currently is not effective for nlopt.CICO_ONE_PASS methods because of limitation in nlopt.LN_AUGLAG interface.

  • local_alg (Function) – algorithm of optimization. Currently the local derivation free algorithms form NLOPT pack were tested. The methods: nlopt.LN_NELDERMEAD, nlopt.LN_COBYLA, nlopt.LN_PRAXIS show good results. Methods: nlopt.LN_BOBYQA, nlopt.LN_SBPLX, nlopt.LN_NEWUOA is not recommended.

  • **kwargs (Any) – the additional keyword arguments passed to get_right_endpoint for specific method.

Returns

  • Right end point value: Float64.

  • Profile points estimated on fly: Array[ ProfilePoint, 1]

  • Status of sulution: String. One of values: "BORDER_FOUND_BY_SCAN_TOL", "SCAN_BOUND_REACHED".

Return type

Array

likelihoodprofiler.profile module

likelihoodprofiler.profile.profile(theta_init, theta_num, loss_func, skip_optim=False, theta_bounds=None, local_alg=28, ftol_abs=0.001, **kwargs)

Short summary.

theta_initArray[Float64]

starting values of parameter vector \(\Theta\). The starting values is not necessary to be the optimum values for loss_func but it the value of loss_func must be lower than loss_crit.

theta_numInt

number \(n\) of vector component to compute confidence interval \(\Theta^n\).

loss_funcFunction

loss function \(\Lambda\left(\Theta\right)\) the profile of which is analyzed. Usually we use log-likelihood for profile analysis in form \(\Lambda( \theta ) = - 2 ln\left( L(\Theta) \right)\).

skip_optimBool

set True if you need marginal profile, i.e. profile without optimization. Default is False.

theta_bounds :Array[Array[Float64,Float64]]

vector of bounds for each component in format \((left_border, right_border)\). This bounds define the ranges for possible parameter values. The defaults are the non-limited values taking into account the scale, i.e. \((0, Inf)\) for "log" scale.

local_algFunction

algorithm of optimization. Currently the local derivation free algorithms form NLOPT pack were tested. The methods: nlopt.LN_NELDERMEAD, nlopt.LN_COBYLA, nlopt.LN_PRAXIS show good results. Methods: nlopt.LN_BOBYQA, nlopt.LN_SBPLX, nlopt.LN_NEWUOA is not recommended.

ftol_absFloat64

absolute tolerance criterion for profile function.

**kwargsAny

the additional keyword arguments passed to get_right_endpoint for specific method.

Returns

Returns profile function for selected parameter component. Each call of the function starts optimization.

Return type

Function

likelihoodprofiler.structures module

class likelihoodprofiler.structures.EndPoint(value, profilePoints, status, direction, counter, supreme)

Bases: object

Structure storing end point for confidence interval.

Parameters

  • value (Float64 or None # value of endpoint or nothing) –

  • profilePoints (Array[ProfilePoint] # vector of profile points) –

  • status (String # result of analysis) –

  • direction (String # "right" or "left") –

  • counter (Int # number of loss_func() calls to calculate the endpoint) –

  • supreme (Float64 or None # maximal value inside profile interval) –

  • values - "BORDER_FOUND_BY_SCAN_TOL", "BORDER_FOUND_LOSS_TOL", (status) –

  • "MAX_ITER_STOP", "LOSS_ERROR_STOP" ("SCAN_BOUND_REACHED",) –

class likelihoodprofiler.structures.ProfilePoint(value, loss, params, ret, counter)

Bases: object

Structure storing one point from profile function.

Parameters

  • value (Float64 # x value of profile point) –

  • loss (Float64 # y value of profile point (loss function at value)) –

  • params (Array[Float64] # vector of optimal values of loss_func arguments) –

  • ret (String # return value from NLOpt.optimize()) –

  • counter (Int # number of loss_func() calls to calculate the value) –

  • values - -5, 5, 3 (ret) –

Module contents