apop_mle.c File Reference

Data Structures

• struct grad_params
• struct infostruct
• struct apop_model_for_infomatrix_struct

Typedefs

• typedef double(* apop_fn_with_params )(apop_data *, apop_model *)
• typedef void(* apop_df_with_void )(const gsl_vector *beta, void *d, gsl_vector *gradient)
• typedef void(* apop_fdf_with_void )(const gsl_vector *beta, void *d, double *f, gsl_vector *df)

Functions

• void apop_estimate_parameter_t_tests (apop_model *est)
• apop_mle_settings * apop_mle_settings_init (apop_mle_settings in)
• apop_mle_settings * apop_mle_settings_alloc (apop_model *parent)
• void * apop_mle_settings_copy (apop_mle_settings *in)
• void apop_mle_settings_free (apop_mle_settings *in)
• gsl_vector * apop_numerical_gradient (apop_data *data, apop_model *model, double delta)
• apop_data * apop_model_hessian (apop_data *data, apop_model *model, double delta)
• apop_data * apop_model_numerical_covariance (apop_data *data, apop_model *model, double delta)
• apop_model * apop_maximum_likelihood (apop_data *data, apop_model dist)
• apop_model * apop_estimate_restart (apop_model *e, apop_model *copy, char *starting_pt, double boundary)

Variables

• double default_delta = 1e-3
• apop_model apop_model_for_infomatrix
• jmp_buf anneal_jump

---

Detailed Description

The MLE functions. Call them with an apop_model.

This file includes a number of distributions and models whose parameters one would estimate using maximum likelihood techniques.

It has (more-or-less) a single public function: apop_maximum_likelihood, and you don't even need to use that one, because the apop_estimate function defaults to using it if there is no model-specific estimation routine provided.

At the bottom are the maximum likelihood procedures themselves. There are four: Newton-type derivative methods, the no-derivative version, the with-derivative version, and the simulated annealing routine.

---

Function Documentation

void apop_estimate_parameter_t_tests

(

apop_model *

est

)

For many, it is a knee-jerk reaction to a parameter estimation to test whether each individual parameter differs from zero. This function does that.

Parameters:

est

The apop_estimate, which includes pre-calculated parameter estimates, var-covar matrix, and the original data set.

Returns nothing. At the end of the routine, the est->parameters->matrix includes a set of t-test values: p value, confidence (=1-pval), t statistic, standard deviation, one-tailed Pval, one-tailed confidence.

apop_mle_settings* apop_mle_settings_init

(

apop_mle_settings

in

)

Initialize an apop_mle_settings struct.

apop_data* apop_model_hessian	(	apop_data *	data,
		apop_model *	model,
		double	delta
	)

Numerically estimate the matrix of second derivatives of the parameter values. The math is simply a series of re-evaluations at small differential steps. [Therefore, it may be expensive to do this for a very computationally-intensive model.]

Parameters:

	data	The data at which the model was estimated
	model	The model, with parameters already estimated
	delta	the step size for the differentials. The current default is around 1e-3.

Returns:

The matrix of estimated second derivatives at the given data and parameter values.

This function uses the Designated initializers syntax for inputs.

apop_data* apop_model_numerical_covariance	(	apop_data *	data,
		apop_model *	model,
		double	delta
	)

Produce the covariance matrix for the parameters of an estimated model via the derivative of the score function at the parameter. I.e., I find the second derivative via apop_model_hessian , and take the negation of the inverse.

I follow Efron and Hinkley in using the estimated information matrix---the value of the information matrix at the estimated value of the score---not the expected information matrix that is the integral over all possible data. See Pawitan 2001 (who cribbed a little off of Efron and Hinkley) or Klemens 2008 (who directly cribbed off of both) for further details.

Parameters:

	data	The data by which your model was estimated
	model	A model whose parameters have been estimated.
	delta	The differential by which to step for sampling changes. (default currently = 1e-3)

Returns:

A covariance matrix for the data. Also, if model->covariance != NULL, I'll set it to the result as well.

This function uses the Designated initializers syntax for inputs.

---

Variable Documentation

apop_model apop_model_for_infomatrix

Initial value:

 {"Ad hoc model for working out the information matrix.", 
                                                .log_likelihood = apop_fn_for_infomatrix}