Computes the Posterior of the hyperparameters theta. More...

#include <PostTheta.h>

Public Member Functions
	PostTheta (int ns, int nt, int nb, int no, MatrixXd B, Vect y, Vect theta_prior, Vect mu_initial, string likelihood, Vect extraCoeffVecLik, string solver_type, const bool constr, const MatrixXd Dxy, const bool validate, const Vect w)
	constructor for regression model (no random effects).

	PostTheta (int ns, int nt, int nb, int no, SpMat Ax, Vect y, SpMat c0, SpMat g1, SpMat g2, Vect theta_prior, Vect mu_initial, string likelihood, Vect extraCoeffVecLik, string solver_type, int dim_spatial_domain, string manifold, const bool constr, const MatrixXd Dx, const MatrixXd Dxy, const bool validate, const Vect w)
	constructor for spatial model (order 2).

	PostTheta (int ns, int nt, int nb, int no, SpMat Ax, Vect y, SpMat c0, SpMat g1, SpMat g2, SpMat g3, SpMat M0, SpMat M1, SpMat M2, Vect theta_prior, Vect mu_initial, string likelihood, Vect extraCoeffVecLik, string solver_type, int dim_spatial_domain, string manifold, const bool constr, const MatrixXd Dx, const MatrixXd Dxy, const bool validate, const Vect w)
	constructor for spatial temporal model.

	PostTheta (int ns, int nt, int nss, int nb, int no, SpMat Ax, Vect y, SpMat c0, SpMat g1, SpMat g2, SpMat g3, SpMat M0, SpMat M1, SpMat M2, Vect theta_prior_param, Vect mu_initial, string likelihood, Vect extraCoeffVecLik, string solver_type, int dim_spatial_domain, string manifold, const bool constr, const MatrixXd Dx, const MatrixXd Dxy, const bool validate, const Vect w)
	constructor for spatial temporal model w/ add. spatial field

double	operator() (Vect &theta, Vect &grad)
	structure required by BFGS solver, requires : theta, gradient theta

double	compute_error_bfgs (Vect &theta)

void	computeG (Vect &theta)
	overwriting G every time, not explicitly listed, better way to do this? needs to be stored after every iteration for smart hessian ...

int	get_fct_count ()

void	convert_theta2interpret (Vect &theta, Vect &theta_interpret)

void	convert_interpret2theta (Vect &theta_interpret, Vect &theta)

void	convert_theta2interpret_spatTemp (double lgamE, double lgamS, double lgamT, double &sigU, double &ranS, double &ranT)
	convert hyperparameters theta from the model parametrisation to the interpretable parametrisation ie. from log(gamma_E, gamma_s, gamma_t) to log(sigma.u, rangeS, rangeT)

void	convert_interpret2theta_spatTemp (double sigU, double ranS, double ranT, double &lgamE, double &lgamS, double &lgamT)
	convert hyperparameters theta from the interpretable parametrisation to the model parametrisation ie. from log(sigma.u, rangeS, rangeT) to log(gamma_E, gamma_s, gamma_t)

void	convert_interpret2theta_spat (double lranS, double lsigU, double &lgamS, double &lgamE)
	convert hyperparameters theta from the interpretable parametrisation to the model parametrisation ie. from log(rangeS, sigma.u) to log(gamma_s, gamma_E) for spatial model order 2

void	convert_theta2interpret_spat (double lgamS, double lgamE, double &lranS, double &lsigU)
	convert hyperparameters theta from the interpretable parametrisation to the model parametrisation ie. from log(rangeS, sigma.u) to log(gamma_s, gamma_E) for spatial model order 2

void	get_mu (Vect &theta, Vect &mu_)
	get conditional mean mu for theta – Gaussian case.

Vect	get_grad ()
	returns current gradient of theta.

void	get_Qprior (Vect theta, SpMat &Qprior)

MatrixXd	get_Covariance (Vect theta, double eps)
	Compute Covariance matrix of hyperparameters theta, at theta.

MatrixXd	get_Cov_interpret_param (Vect interpret_theta, double eps)

double	f_eval (Vect &theta)

void	get_marginals_f (Vect &theta, Vect &mu, Vect &vars)
	Compute the marginal variances of the latent parameters at theta. Using selected inversion procedure.

void	get_fullFact_marginals_f (Vect &theta, SpMat &Qinv)
	Compute the marginal variances of the latent parameters at theta. Using selected inversion procedure.

void	compute_fullInverseQ (Vect &theta, MatrixXd &Qinv)

MatrixXd	hess_eval (Vect theta, double eps)
	computes the hessian at theta using second order finite difference. Is used be get_Covariance.

MatrixXd	hess_eval_interpret_theta (Vect interpret_theta, double eps)

void	check_pos_def (MatrixXd &hess)
	check if Hessian positive definite (matrix assumed to be dense & small since dim(theta) small)

double	eval_post_theta (Vect &theta, Vect &mu)
	Core function. Evaluate posterior of theta. mu are latent parameters.

void	eval_log_gaussian_prior_hp (Vect &theta_param, Vect &theta_prior_param, double &log_prior)
	evaluate log prior of the hyperparameters using original theta value

void	eval_log_pc_prior_hp (double &log_sum, Vect &lambda, Vect &theta_interpret)
	evaluate log prior using PC prior

void	update_mean_constr (const MatrixXd &D, Vect &e, Vect &sol, MatrixXd &V, MatrixXd &W, MatrixXd &U, Vect &updated_sol)

void	eval_log_dens_constr (Vect &x, Vect &mu, SpMat &Q, double &log_det_Q, const MatrixXd &D, MatrixXd &W, double &val_log_dens)

void	eval_log_prior_lat (Vect &theta, Vect &mu, double &val)
	evaluate log prior of random effects

void	eval_likelihood (Vect &theta, Vect &mu, double &log_det, double &val)
	compute log likelihood : log_det tauno and value -thetayTy

void	construct_Q_spatial (Vect &theta, SpMat &Qs)
	spatial model : SPDE discretisation – matrix construction

void	construct_Q_spat_temp (Vect &theta, SpMat &Qst)
	spatial temporal model : SPDE discretisation. DEMF(1,2,1) model.

void	construct_Qprior (Vect &theta, SpMat &Qx)

void	construct_Q (Vect &theta, Vect &mu, SpMat &Q)
	construct precision matrix. Calls spatial, spatial-temporal, etc.

void	construct_b (Vect &theta, Vect &rhs)
	Assemble right-handside.

void	eval_denominator (Vect &theta, double &val, SpMat &Q, Vect &rhs, Vect &mu)
	Evaluate denominator: conditional probability of Qx\|y.

double	cond_LogPriorLat (SpMat &Qprior, Vect &x)
	evaluate Gaussian log prior (without log determinant!!), mean assumed to be zero

double	cond_LogPoisLik (Vect &eta)
	evaluate log Poisson likelihood

double	cond_negLogPoisLik (Vect &eta)
	evaluate negative log Poisson likelihood

Vect	grad_cond_negLogPoisLik (Vect &eta)
	evaluate analytical negative gradient log Poisson likelihood

Vect	diagHess_cond_negLogPoisLik (Vect &eta)
	evaluate analytical negative diagonal Hessian of log Poisson likelihood

double	cond_negLogPois (SpMat &Qprior, Vect &x)
	evaluate negative condiational log Poisson + Gaussian prior

void	link_f_sigmoid (Vect &x, Vect &sigmoidX)
	link function. vectorized evaluation of sigmoid function for each entry

double	cond_negLogBinomLik (Vect &eta)
	evaluate negative log Binomial likelihood

double	cond_negLogBinom (SpMat &Qprior, Vect &x)
	evaluate negative condiational log Poisson + Gaussian prior

double	cond_negLogDist (SpMat &Qprior, Vect &x, function< double(Vect &, Vect &)> lik_func)
	evaluate negative condiational log likelihood + Gaussian prior

void	FD_gradient (Vect &eta, Vect &grad)
	compute finite difference gradient. 1st order central difference. currently stepsize h fixed.

void	FD_diag_hessian (Vect &eta, Vect &diag_hess)
	compute finite difference diagonal of hessian. 2nd order central difference. currently stepsize h fixed.

void	NewtonIter (Vect &theta, Vect &x, SpMat &Q, double &log_det)
	Newton iteration to find optimum of conditional distribution latent parameters of prior & likelihood.

void	record_times (std::string file_name, int iter_count, double t_Ftheta_ext, double t_thread_nom, double t_priorHyp, double t_priorLat, double t_priorLatAMat, double t_priorLatChol, double t_likel, double t_thread_denom, double t_condLat, double t_condLatAMat, double t_condLatChol, double t_condLatSolve)

	~PostTheta ()
	class destructor. Frees memory allocated by PostTheta class.

Private Attributes
int	MPI_size

int	MPI_rank

int	threads_level1

int	threads_level2

int	ns

int	nt

int	nss

int	nb

int	no

int	nst

int	nu

int	n

size_t	nnz_Qst

size_t	nnz_Qs

int	dim_th

int	dim_spatial_domain

string	manifold

int	dim_grad_loop

int	num_solvers

Solver *	solverQ

Solver *	solverQst

int	threadID_solverQst

int	threadID_solverQ

string	likelihood

Vect	extraCoeffVecLik

string	solver_type

std::string	prior

int	fct_count

int	iter_count

int	iter_acc

Vect	y

Vect	theta_prior_param

Vector3i	dimList

SpMat	Ax

MatrixXd	B

SpMat	c0

SpMat	g1

SpMat	g2

SpMat	g3

SpMat	M0

SpMat	M1

SpMat	M2

SpMat	Qb

SpMat	Qu

SpMat	Qst

SpMat	Qs

SpMat	Qx

SpMat	Qxy

double	yTy

Vect	BTy

Vect	AxTy

SpMat	AxTAx

Vect	mu_initial

Vect	mu

Vect	mu_midpoint

MatrixXd	mu_matrix

Vect	t_grad

double	min_f_theta

double	w_sum

int	no_f_eval

ArrayXi	task_to_rank_list_grad

MatrixXd	G

const bool	constr

const MatrixXd	Dx

const MatrixXd	Dxy

const bool	validate

const Vect	w

bool	printed_eps_flag = false

double	t_priorLatChol

double	t_condLatChol

double	t_condLatSolve

double	t_bfgs_iter

Detailed Description

Computes the Posterior of the hyperparameters theta.

Computes the posterior of theta for a given theta and its gradient using a central finite difference approximation. Can additionally compute an approximation to the Hessian.

Constructor & Destructor Documentation

◆ PostTheta() [1/4]

PostTheta::PostTheta	(	int	ns,
		int	nt,
		int	nb,
		int	no,
		MatrixXd	B,
		Vect	y,
		Vect	theta_prior,
		Vect	mu_initial,
		string	likelihood,
		Vect	extraCoeffVecLik,
		string	solver_type,
		const bool	constr,
		const MatrixXd	Dxy,
		const bool	validate,
		const Vect	w
	)

constructor for regression model (no random effects).

Parameters

[in]	ns_	number of spatial grid points per time step.
[in]	nt_	number of temporal time steps.
[in]	nb_	number of fixed effects.
[in]	no_	number of observations.
[in]	B_	covariate matrix.
[in]	y_	vector with observations.

Note: B = B_ or is its own copy?

◆ PostTheta() [2/4]

PostTheta::PostTheta	(	int	ns,
		int	nt,
		int	nb,
		int	no,
		SpMat	Ax,
		Vect	y,
		SpMat	c0,
		SpMat	g1,
		SpMat	g2,
		Vect	theta_prior,
		Vect	mu_initial,
		string	likelihood,
		Vect	extraCoeffVecLik,
		string	solver_type,
		int	dim_spatial_domain,
		string	manifold,
		const bool	constr,
		const MatrixXd	Dx,
		const MatrixXd	Dxy,
		const bool	validate,
		const Vect	w
	)

constructor for spatial model (order 2).

Parameters

[in]	ns_	number of spatial grid points per time step.
[in]	nt_	number of temporal time steps.
[in]	nb_	number of fixed effects.
[in]	no_	number of observations.
[in]	Ax_	covariate matrix.
[in]	y_	vector with observations.
[in]	c0_	diagonalised mass matrix.
[in]	g1_	stiffness matrix.
[in]	g2_	defined as : g1 * c0^-1 * g1

◆ PostTheta() [3/4]

PostTheta::PostTheta	(	int	ns,
		int	nt,
		int	nb,
		int	no,
		SpMat	Ax,
		Vect	y,
		SpMat	c0,
		SpMat	g1,
		SpMat	g2,
		SpMat	g3,
		SpMat	M0,
		SpMat	M1,
		SpMat	M2,
		Vect	theta_prior,
		Vect	mu_initial,
		string	likelihood,
		Vect	extraCoeffVecLik,
		string	solver_type,
		int	dim_spatial_domain,
		string	manifold,
		const bool	constr,
		const MatrixXd	Dx,
		const MatrixXd	Dxy,
		const bool	validate,
		const Vect	w
	)

constructor for spatial temporal model.

constructor for spatial model (order 2).

Parameters

[in]	ns_	number of spatial grid points per time step.
[in]	nt_	number of temporal time steps.
[in]	nb_	number of fixed effects.
[in]	no_	number of observations.
[in]	Ax_	covariate matrix.
[in]	y_	vector with observations.
[in]	c0_	diagonalised mass matrix space.
[in]	g1_	stiffness matrix space.
[in]	g2_	defined as : g1 * c0^-1 * g1
[in]	g3_	defined as : g1 * (c0^-1 * g1)^2
[in]	M0_	diagonalised mass matrix time.
[in]	M1_	diagonal matrix with diag(0.5, 0, ..., 0, 0.5) -> account for boundary
[in]	M2_	stiffness matrix time.
[in]	theta_prior	prior hyperparameters
[in]	solver_type	linear solver: currently PARDISO, BTA
[in]	dim_spatial_domain	dimension spatial field 1D/2D ...
[in]	manifold	plane: "", "sphere", can add more later
[in]	constr	constraints, mainly sum-to-zero

◆ PostTheta() [4/4]

PostTheta::PostTheta	(	int	ns,
		int	nt,
		int	nss,
		int	nb,
		int	no,
		SpMat	Ax,
		Vect	y,
		SpMat	c0,
		SpMat	g1,
		SpMat	g2,
		SpMat	g3,
		SpMat	M0,
		SpMat	M1,
		SpMat	M2,
		Vect	theta_prior_param,
		Vect	mu_initial,
		string	likelihood,
		Vect	extraCoeffVecLik,
		string	solver_type,
		int	dim_spatial_domain,
		string	manifold,
		const bool	constr,
		const MatrixXd	Dx,
		const MatrixXd	Dxy,
		const bool	validate,
		const Vect	w
	)

constructor for spatial temporal model w/ add. spatial field

constructor for both spatial models (order 2).

Parameters

[in]	ns_	number of spatial grid points per time step.
[in]	nt_	number of temporal time steps.
[in]	nss_	number of spatial grid points in add. spatial field
[in]	nb_	number of fixed effects.
[in]	no_	number of observations.
[in]	Ax_	covariate matrix.
[in]	y_	vector with observations.
[in]	c0_	diagonalised mass matrix space.
[in]	g1_	stiffness matrix space.
[in]	g2_	defined as : g1 * c0^-1 * g1
[in]	g3_	defined as : g1 * (c0^-1 * g1)^2
[in]	M0_	diagonalised mass matrix time.
[in]	M1_	diagonal matrix with diag(0.5, 0, ..., 0, 0.5) -> account for boundary
[in]	M2_	stiffness matrix time.

Member Function Documentation

◆ check_pos_def()

void PostTheta::check_pos_def ( MatrixXd & hess )

check if Hessian positive definite (matrix assumed to be dense & small since dim(theta) small)

Parameters

[in,out] updates hessian to only the diagonal entries if not positive definite.

◆ cond_LogPoisLik()

double PostTheta::cond_LogPoisLik ( Vect & eta )

evaluate log Poisson likelihood

Parameters

[in]	eta	Vector. linear predictor eta = A*x
[out]	f_val	double. evaluated log density

◆ cond_LogPriorLat()

double PostTheta::cond_LogPriorLat	(	SpMat &	Qprior,
		Vect &	x
	)

evaluate Gaussian log prior (without log determinant!!), mean assumed to be zero

Parameters

[in]	Qprior	precision matrix
[in]	x	current x vector
[out]	f_val	evaluated log density

◆ cond_negLogBinom()

double PostTheta::cond_negLogBinom	(	SpMat &	Qprior,
		Vect &	x
	)

evaluate negative condiational log Poisson + Gaussian prior

Parameters

[in]	extraCoeffVecLik	Vector. ntrials.
[in]	Qprior	SpMat. precision matrix.
[in]	x	Vector. current vector x.
[out]	f_val	double. evaluated negative log density

◆ cond_negLogBinomLik()

double PostTheta::cond_negLogBinomLik ( Vect & eta )

evaluate negative log Binomial likelihood

Parameters

[in]	extraCoeffVecLik	Vector. ntrials.
[in]	eta	Vector. linear predictor eta = A*x.
[out]	f_val	double. evaluated negative log density.

◆ cond_negLogDist()

double PostTheta::cond_negLogDist	(	SpMat &	Qprior,
		Vect &	x,
		function< double(Vect &, Vect &)>	lik_func
	)

evaluate negative condiational log likelihood + Gaussian prior

Parameters

[in]	extraCoeffVecLik	Vector.
[in]	Qprior	SpMat. precision matrix.
[in]	x	Vector. current vector x.
[in]	lik_func	function. defines the likelihood
[out]	f_val	double. evaluated negative log density

◆ cond_negLogPois()

double PostTheta::cond_negLogPois	(	SpMat &	Qprior,
		Vect &	x
	)

evaluate negative condiational log Poisson + Gaussian prior

Parameters

[in]	Qprior	SpMat. precision matrix.
[in]	x	Vector. current vector x.
[out]	f_val	double. evaluated negative log density

◆ cond_negLogPoisLik()

double PostTheta::cond_negLogPoisLik ( Vect & eta )

evaluate negative log Poisson likelihood

Parameters

[in]	eta	Vector. linear predictor eta = A*x
[out]	f_val	double. evaluated negative log density

◆ construct_b()

void PostTheta::construct_b	(	Vect &	theta,
		Vect &	rhs
	)

Assemble right-handside.

Parameters

[in]	theta	current theta vector
[in,out]	rhs	right-handside /todo Could compute Ax^T*y once, and only multiply with appropriate exp_theta.

◆ construct_Q()

void PostTheta::construct_Q	(	Vect &	theta,
		Vect &	mu,
		SpMat &	Q
	)

construct precision matrix. Calls spatial, spatial-temporal, etc.

Parameters

[in]	theta	current theta vector
[in]	mu	mode latent parameters
[in,out]	Q	fills precision matrix

◆ construct_Q_spat_temp()

void PostTheta::construct_Q_spat_temp	(	Vect &	theta,
		SpMat &	Qst
	)

spatial temporal model : SPDE discretisation. DEMF(1,2,1) model.

Parameters

[in]	theta	current theta vector
[in,out]	Qst	fills spatial-temporal precision matrix

◆ construct_Q_spatial()

void PostTheta::construct_Q_spatial	(	Vect &	theta,
		SpMat &	Qs
	)

spatial model : SPDE discretisation – matrix construction

Parameters

[in]	theta	current theta vector
[in,out]	Qs	fills spatial precision matrix

◆ convert_interpret2theta_spat()

void PostTheta::convert_interpret2theta_spat	(	double	lranS,
		double	lsigU,
		double &	lgamS,
		double &	lgamE
	)

convert hyperparameters theta from the interpretable parametrisation to the model parametrisation ie. from log(rangeS, sigma.u) to log(gamma_s, gamma_E) for spatial model order 2

Parameters

[in]	log(ranS)	spatial range
[in]	log(sigma.u)	precision of random effects
[in,out]	log(gamma_s)
[in,out]	log(gamma_E)

◆ convert_interpret2theta_spatTemp()

void PostTheta::convert_interpret2theta_spatTemp	(	double	sigU,
		double	ranS,
		double	ranT,
		double &	lgamE,
		double &	lgamS,
		double &	lgamT
	)

convert hyperparameters theta from the interpretable parametrisation to the model parametrisation ie. from log(sigma.u, rangeS, rangeT) to log(gamma_E, gamma_s, gamma_t)

Parameters

[in]	log(sigma.u)	precision of random effects
[in]	log(ranS)	spatial range
[in]	log(ranT)	temporal range
[in,out]	log(gamma_E)
[in,out]	log(gamma_s)
[in,out]	log(gamma_t)

◆ convert_theta2interpret_spat()

void PostTheta::convert_theta2interpret_spat	(	double	lgamS,
		double	lgamE,
		double &	lranS,
		double &	lsigU
	)

convert hyperparameters theta from the interpretable parametrisation to the model parametrisation ie. from log(rangeS, sigma.u) to log(gamma_s, gamma_E) for spatial model order 2

Parameters

[in]	log(gamma_s)
[in]	log(gamma_E)
[in,out]	log(ranS)	spatial range
[in,out]	log(sigma.u)	precision of random effects

◆ convert_theta2interpret_spatTemp()

void PostTheta::convert_theta2interpret_spatTemp	(	double	lgamE,
		double	lgamS,
		double	lgamT,
		double &	sigU,
		double &	ranS,
		double &	ranT
	)

convert hyperparameters theta from the model parametrisation to the interpretable parametrisation ie. from log(gamma_E, gamma_s, gamma_t) to log(sigma.u, rangeS, rangeT)

Parameters

[in]	log(gamma_E)
[in]	log(gamma_s)
[in]	log(gamma_t)
[in,out]	log(sigma.u)	precision of random effects
[in,out]	log(ranS)	spatial range
[in,out]	log(ranT)	temporal range

◆ diagHess_cond_negLogPoisLik()

Vect PostTheta::diagHess_cond_negLogPoisLik ( Vect & eta )

evaluate analytical negative diagonal Hessian of log Poisson likelihood

Parameters

[in]	eta	Vector. linear predictor eta = A*x
[out]	diagHess	Vect. diagonal of Hessian (off-diagonal entries are zero)

◆ eval_denominator()

void PostTheta::eval_denominator	(	Vect &	theta,
		double &	val,
		SpMat &	Q,
		Vect &	rhs,
		Vect &	mu
	)

Evaluate denominator: conditional probability of Qx|y.

Parameters

[in]	theta	current theta vector
[in,out]	log_det	fill log determinant of conditional distribution of denominator
[in,out]	val	fill value with muQmu
[in,out]	Q	construct precision matrix
[in,out]	rhs	construct right-handside
[in,out]	mu	insert mean of latent parameters

◆ eval_likelihood()

void PostTheta::eval_likelihood	(	Vect &	theta,
		Vect &	mu,
		double &	log_det,
		double &	val
	)

compute log likelihood : log_det tau*no and value -theta*yTy

Parameters

[in]	theta	current theta vector
[in,out]	log_det	inserts log determinant of log likelihood.
[in,out]	val	inserts the value of -theta*yTy

◆ eval_log_gaussian_prior_hp()

void PostTheta::eval_log_gaussian_prior_hp	(	Vect &	theta_param,
		Vect &	theta_prior_param,
		double &	log_prior
	)

evaluate log prior of the hyperparameters using original theta value

Parameters

[in]	thetai	current theta_i value
[in]	thetai_original	original theta_i value
[in,out]	log	prior is being updated.

variance / precision of 1 : no normalising constant. computed through -0.5 * (theta_i* - theta_i)*(theta_i*-theta_i)

◆ eval_log_pc_prior_hp()

void PostTheta::eval_log_pc_prior_hp	(	double &	log_sum,
		Vect &	lambda,
		Vect &	theta_interpret
	)

evaluate log prior using PC prior

Parameters

[in,out]	log	sum
[in]	lambda	: parameters for penalised complexity prior
[in]	theta_interpret	current theta value in interpretable scale

complicated prior. check appropriate references for details.

◆ eval_log_prior_lat()

void PostTheta::eval_log_prior_lat	(	Vect &	theta,
		Vect &	mu,
		double &	val
	)

evaluate log prior of random effects

Parameters

[in]	theta	current theta vector
[in,out]	log_det	inserts log determinant.

Todo: construct spatial matrix (at the moment this is happening twice. FIX)

◆ eval_post_theta()

double PostTheta::eval_post_theta	(	Vect &	theta,
		Vect &	mu
	)

Core function. Evaluate posterior of theta. mu are latent parameters.

Parameters

[in]	theta	hyperparameter vector
[in,out]	mu	vector of the conditional mean

Returns: f(theta) value

◆ FD_diag_hessian()

void PostTheta::FD_diag_hessian	(	Vect &	eta,
		Vect &	diag_hess
	)

compute finite difference diagonal of hessian. 2nd order central difference. currently stepsize h fixed.

Parameters

[in]	extraCoeffVecLik	Vector.
[in]	eta	Vector. linear predictor eta = A*x.
[in]	lik_func	function. defines the likelihood
[in,out]	diag_hess	Vector. diagonal of Hessian.

◆ FD_gradient()

void PostTheta::FD_gradient	(	Vect &	eta,
		Vect &	grad
	)

compute finite difference gradient. 1st order central difference. currently stepsize h fixed.

Parameters

[in]	extraCoeffVecLik	Vector.
[in]	eta	Vector. linear predictor eta = A*x.
[in]	lik_func	function. defines the likelihood
[in,out]	grad	Vector. gradient.

◆ get_Covariance()

MatrixXd PostTheta::get_Covariance	(	Vect	theta,
		double	eps
	)

Compute Covariance matrix of hyperparameters theta, at theta.

computes the hessian of f(theta) using a second order finite difference stencil and then inverts the hessian. Gaussian assumption.

Parameters

[in] theta hyperparameter Vector

Returns: cov covariance matrix of the hyperparameters

◆ get_fullFact_marginals_f()

void PostTheta::get_fullFact_marginals_f	(	Vect &	theta,
		SpMat &	Qinv
	)

Compute the marginal variances of the latent parameters at theta. Using selected inversion procedure.

Parameters

[in]	Vector	theta.
[in,out]	Vector	with selected inverse for all non-zero entries of Q.

◆ get_grad()

Vect PostTheta::get_grad ( )

returns current gradient of theta.

Returns: gradient_theta

◆ get_marginals_f()

void PostTheta::get_marginals_f	(	Vect &	theta,
		Vect &	mu,
		Vect &	vars
	)

Compute the marginal variances of the latent parameters at theta. Using selected inversion procedure.

Parameters

[in]	Vector	theta.
[in,out]	Vector	with marginals of f.

◆ get_mu()

void PostTheta::get_mu	(	Vect &	theta,
		Vect &	mu_
	)

get conditional mean mu for theta – Gaussian case.

Parameters

[in]	theta	hyperparameter vector
[in,out]	mu_	vector of the conditional mean

◆ grad_cond_negLogPoisLik()

Vect PostTheta::grad_cond_negLogPoisLik ( Vect & eta )

evaluate analytical negative gradient log Poisson likelihood

Parameters

[in]	eta	Vector. linear predictor eta = A*x
[out]	grad	Vect. gradient.

◆ hess_eval()

MatrixXd PostTheta::hess_eval	(	Vect	theta,
		double	eps
	)

computes the hessian at theta using second order finite difference. Is used be get_Covariance.

Parameters

[in] theta hyperparameter vector

Returns: Dense Matrix with Hessian.

Todo: not yet parallelised ....

◆ link_f_sigmoid()

void PostTheta::link_f_sigmoid	(	Vect &	x,
		Vect &	sigmoidX
	)

link function. vectorized evaluation of sigmoid function for each entry

Parameters

[in]	x	Vector. current vector x.
[in,out]	sigmoidX	Vector. sigmoid(x) element-wise.

◆ NewtonIter()

void PostTheta::NewtonIter	(	Vect &	theta,
		Vect &	x,
		SpMat &	Q,
		double &	log_det
	)

Newton iteration to find optimum of conditional distribution latent parameters of prior & likelihood.

Parameters

[in]	theta	hyperparameters. can be an empty vector.
[in,out]	x	latent parameters. contains initial guess of mode on entry and found mode on exit.
[in,out]	Q	SpMat. precision matrix.
[in,out]	x	log det of Q.

◆ operator()()

double PostTheta::operator()	(	Vect &	theta,
		Vect &	grad
	)

structure required by BFGS solver, requires : theta, gradient theta

Note: Gradient call is already parallelised using nested OpenMP. --> there are l1 threads (usually 8, one for each function evaluation), that themselves then split into another e.g. 8 threads, when calling PARDISO to factorise the system. --> somehow introduce additional parallelism to compute f(theta), possible to do in parallel

Member Data Documentation

◆ Ax

SpMat PostTheta::Ax

private

sparse matrix of size no x (nu+nb). Projects observation locations onto FEM mesh and includes covariates at the end.

◆ AxTAx

SpMat PostTheta::AxTAx

private

conmpute t(Ax)*Ax once. spat/spat temp model

◆ AxTy

Vect PostTheta::AxTy

private

compute t(Ax)*y once. spat/spat temp model

◆ B

MatrixXd PostTheta::B

private

if space (-time) model included in last columns of Ax. For regression only B exists.

◆ BTy

Vect PostTheta::BTy

private

compute t(B)*y once. regression model only

◆ c0

SpMat PostTheta::c0

private

Diagonal mass matrix spatial part.

◆ constr

const bool PostTheta::constr

private

true if there is a sum to zero constraint

◆ dim_grad_loop

int PostTheta::dim_grad_loop

private

dimension of gradient loop

◆ dim_th

int PostTheta::dim_th

private

dimension of hyperparameter vector theta

◆ Dx

const MatrixXd PostTheta::Dx

private

constraint vector, sum to zero constraint

◆ Dxy

const MatrixXd PostTheta::Dxy

private

constraint vector, sum to zero constraint

◆ fct_count

int PostTheta::fct_count

private

count total number of function evaluations

◆ G

MatrixXd PostTheta::G

private

orthonormal basis for finite difference stencil is Identity if smart gradient disabled

◆ g1

SpMat PostTheta::g1

private

stiffness matrix space.

◆ g2

SpMat PostTheta::g2

private

defined as : g1 * c0^-1 * g1

◆ g3

SpMat PostTheta::g3

private

defined as : g1 * (c0^-1 * g1)^2.

◆ iter_count

int PostTheta::iter_count

private

count total number of operator() call

◆ likelihood

string PostTheta::likelihood

private

assumed likelihood of the observations

◆ M0

SpMat PostTheta::M0

private

diagonalised mass matrix time.

◆ M1

SpMat PostTheta::M1

private

diagonal matrix with diag(0.5, 0, ..., 0, 0.5) -> account for boundary

◆ M2

SpMat PostTheta::M2

private

stiffness matrix time.

◆ manifold

string PostTheta::manifold

private

in R^d or on the sphere

◆ min_f_theta

double PostTheta::min_f_theta

private

minimum of function

◆ MPI_rank

int PostTheta::MPI_rank

private

personal mpi rank

◆ MPI_size

int PostTheta::MPI_size

private

number of mpi ranks

◆ mu

Vect PostTheta::mu

private

conditional mean

◆ mu_matrix

MatrixXd PostTheta::mu_matrix

private

store all mu values from previous iteration, dim(mu_matrix) = (n, 2*dim_th+1)

◆ mu_midpoint

Vect PostTheta::mu_midpoint

private

conditional mean, at mid point \theta^k

◆ n

int PostTheta::n

private

total number of unknowns, i.e. ns*nt + nb

◆ nb

int PostTheta::nb

private

number of fixed effects

◆ no

int PostTheta::no

private

number of observations

◆ no_f_eval

int PostTheta::no_f_eval

private

number of function evaluations per iteration

◆ ns

int PostTheta::ns

private

number of spatial grid points per timestep

◆ nss

int PostTheta::nss

private

size of add. spatial field, not def = 0

◆ nst

int PostTheta::nst

private

ns*nt, equal to nu if nss =0

◆ nt

int PostTheta::nt

private

number of temporal time steps

◆ nu

int PostTheta::nu

private

number of random effects, that ns*nu

◆ num_solvers

int PostTheta::num_solvers

private

number of pardiso solvers

◆ prior

std::string PostTheta::prior

private

type of pripr to be used

◆ Qb

SpMat PostTheta::Qb

private

setup indices once. Only prior fixed effects.

◆ Qu

SpMat PostTheta::Qu

private

setup indices once. Only prior random effects

◆ Qx

SpMat PostTheta::Qx

private

setup indices once. Includes Prior RE + FE.

◆ Qxy

SpMat PostTheta::Qxy

private

setup indices for Qxy once.

◆ t_grad

Vect PostTheta::t_grad

private

gradient of theta

◆ theta_prior_param

Vect PostTheta::theta_prior_param

private

vector with prior values. Constructs normal distribution with sd = 1 around these values.

◆ threads_level1

int PostTheta::threads_level1

private

number of threads on first level

◆ w_sum

double PostTheta::w_sum

private

only used if validate is true

◆ y

Vect PostTheta::y

private

vector of observations y. has length no.

◆ yTy

double PostTheta::yTy

private

compute t(y)*y once.

The documentation for this class was generated from the following files:

INLA_main/PostTheta.h
INLA_main/PostTheta.cpp

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PostTheta() [1/4]

◆ PostTheta() [2/4]

◆ PostTheta() [3/4]

◆ PostTheta() [4/4]

Member Function Documentation

◆ check_pos_def()

◆ cond_LogPoisLik()

◆ cond_LogPriorLat()

◆ cond_negLogBinom()

◆ cond_negLogBinomLik()

◆ cond_negLogDist()

◆ cond_negLogPois()

◆ cond_negLogPoisLik()

◆ construct_b()

◆ construct_Q()

◆ construct_Q_spat_temp()

◆ construct_Q_spatial()

◆ convert_interpret2theta_spat()

◆ convert_interpret2theta_spatTemp()

◆ convert_theta2interpret_spat()

◆ convert_theta2interpret_spatTemp()

◆ diagHess_cond_negLogPoisLik()

◆ eval_denominator()

◆ eval_likelihood()

◆ eval_log_gaussian_prior_hp()

◆ eval_log_pc_prior_hp()

◆ eval_log_prior_lat()

◆ eval_post_theta()

◆ FD_diag_hessian()

◆ FD_gradient()

◆ get_Covariance()

◆ get_fullFact_marginals_f()

◆ get_grad()

◆ get_marginals_f()

◆ get_mu()

◆ grad_cond_negLogPoisLik()

◆ hess_eval()

◆ link_f_sigmoid()

◆ NewtonIter()

◆ operator()()

Member Data Documentation

◆ Ax

◆ AxTAx

◆ AxTy

◆ B

◆ BTy

◆ c0

◆ constr

◆ dim_grad_loop

◆ dim_th

◆ Dx

◆ Dxy

◆ fct_count

◆ G

◆ g1

◆ g2

◆ g3

◆ iter_count

◆ likelihood

◆ M0

◆ M1

◆ M2

◆ manifold

◆ min_f_theta

◆ MPI_rank

◆ MPI_size

◆ mu

◆ mu_matrix

◆ mu_midpoint

◆ n

◆ nb

◆ no

◆ no_f_eval

◆ ns

◆ nss

◆ nst