double BLSSS::find_posterior_mode() {
BinomialLogitUnNormalizedLogPosterior logpost(m_, pri_.get());
const Selector &inc(m_->coef().inc());
Vector beta(m_->included_coefficients());
int dim = beta.size();
if (dim == 0) {
return negative_infinity();
// TODO: This logic prohibits an empty model. Better to return
// the actual value of the un-normalized posterior, which in
// this case would just be the likelihood portion.
} else {
Vector gradient(dim);
Matrix hessian(dim, dim);
double logf;
std::string error_message;
bool ok = max_nd2_careful(beta,
gradient,
hessian,
logf,
Target(logpost),
dTarget(logpost),
d2Target(logpost),
1e-5,
error_message);
if (ok) {
m_->set_included_coefficients(beta, inc);
return logf;
} else {
return negative_infinity();
}
}
}
MultivariateKalmanStorage(int observation_dim, int state_dim,
bool store_state_moments)
: KalmanStateStorage(store_state_moments ? state_dim : 0),
kalman_gain_(state_dim, observation_dim),
forecast_precision_(observation_dim),
forecast_precision_log_determinant_(negative_infinity()),
forecast_error_(observation_dim) {}
double SSLM::adjusted_observation(int t) const {
if (is_missing_observation(t)) {
return negative_infinity();
}
return dat()[t]->latent_data_value()
- observation_model_->predict(dat()[t]->x());
}
double BM::Loglike(const Vector &probvec, Vec &g, Mat &h, uint nd)const{
if (probvec.size() != 1) {
report_error("Wrong size argument.");
}
double p = probvec[0];
if (p < 0 || p > 1) {
return negative_infinity();
}
double logp = log(p);
double logp2 = log(1-p);
double ntrials = n_ * suf()->nobs();
double success = n_*suf()->sum();
double fail = ntrials - success;
double ans = success * logp + fail * logp2;
if(nd>0){
double q = 1-p;
g[0] = (success - p*ntrials)/(p*q);
if(nd>1){
h(0,0) = -1*(success/(p*p) + fail/(q*q));
}
}
return ans;
}
double ExponentialModel::Loglike(const Vector &lambda_vector, Vector &g,
Matrix &h, uint nd) const {
if (lambda_vector.size() != 1) {
report_error("Wrong size argument.");
}
double lam = lambda_vector[0];
double ans = 0;
if (lam <= 0) {
ans = negative_infinity();
if (nd > 0) {
g[0] = std::max(fabs(lam), .10);
if (nd > 1) {
h(0, 0) = -1;
}
}
return ans;
}
double n = suf()->n();
double sum = suf()->sum();
ans = n * log(lam) - lam * sum;
if (nd > 0) {
g[0] = n / lam - sum;
if (nd > 1) {
h(0, 0) = -n / (lam * lam);
}
}
return ans;
}
/*======================================================================*/
double dtriangle(double x, double x0, double x1, double xm,
bool logscale){
double m0, m1, y, ans;
if(x1<x0){
std::ostringstream err;
err << "error in dtriangle: called with" << std::endl
<< "x0 = " << x0 << std::endl
<< "x1 = " << x1 << std::endl
<< "xm = " << xm << std::endl
<< "logscale = " << logscale << std::endl
<< "x0 must be less than x1";
throw_exception<std::runtime_error>(err.str());
}
if(x0==x1) return x0;
if(x<x0 || x> x1) return (logscale ? negative_infinity() : 0);
if(xm< x0 || xm>x1) xm=(x0+x1)/2.0;
y = 2.0/(x1-x0);
m0 = y/(xm-x0);
m1= y/(xm-x1);
ans = (x<xm ? m0*(x-x0) : m1*(x-x1));
return (logscale? log(ans): ans);
}
double BetaPosteriorSampler::logpri()const {
double mean = model_->mean();
double sample_size = model_->sample_size();
if (mean <= 0 || sample_size <= 0) {
return negative_infinity();
}
return mean_prior_->logp(mean) + sample_size_prior_->logp(sample_size);
}
double WishartModel::Loglike(const Vector &sumsq_triangle_nu,
Vector &g, uint nd)const{
const double log2 = 0.69314718055994529;
const double logpi = 1.1447298858494002;
int k=dim();
SpdParams Sumsq_arg(dim());
Vector::const_iterator it = Sumsq_arg.unvectorize(sumsq_triangle_nu, true);
double nu = *it;
const SpdMatrix &SS(Sumsq_arg.var());
if(nu <k) return negative_infinity();
double ldSS = 0;
bool ok=true;
ldSS = SS.logdet(ok);
if(!ok) return negative_infinity();
double n = suf()->n();
double sumldw = suf()->sumldw();
const SpdMatrix &sumW(suf()->sumW());
double tab = traceAB(SS, sumW);
double tmp1(0), tmp2(0);
for(int i = 1; i<=k; ++i){
double tmp = .5*(nu-i+1);
tmp1+= lgamma(tmp);
if(nd>0) tmp2+= digamma(tmp);
}
double ans = .5*( n*(-nu*k*log2 - .5*k*(k-1)*logpi -2*tmp1 + nu*ldSS)
+(nu-k-1)*sumldw - tab);
if(nd>0){
double dnu = .5*( n*(-k*log2 - tmp2+ldSS) + sumldw);
SpdMatrix SSinv(SS.inv());
int m=0;
for(int i=0; i<k; ++i){
for(int j=0; j<=i; ++j){
g[m] = .5*n*nu * (i==j? SSinv(i,i) : 2*SSinv(i,j));
g[m] -= .5*(i==j ? sumW(i,i) : 2* sumW(i,j));
++m; }}
g[m] = dnu;
}
return ans;
}
double pig(double x, double mu, double lambda, bool logscale){
if(x <= 0) return logscale ? negative_infinity() : 0;
if(mu <= 0) throw_exception<std::runtime_error>("mu <= 0 in pig");
if(lambda <= 0) throw_exception<std::runtime_error>("lambda <= 0 in pig");
double rlx = sqrt(lambda/x);
double xmu = x/mu;
double ans = pnorm(rlx * (xmu -1)) + exp(2*lambda/mu) * pnorm(-rlx*(xmu + 1));
return logscale ? log(ans) : ans;
}
double dig(double x, double mu, double lambda, bool logscale){
const double log_two_pi(1.83787706640935);
if(x <= 0) return logscale ? negative_infinity() : 0;
if(mu <= 0) throw_exception<std::runtime_error>("mu <= 0 in dig");
if(lambda <= 0) throw_exception<std::runtime_error>("lambda <= 0 in dig");
double ans = -lambda * pow(x-mu, 2)/(2 * mu * mu * x);
ans += .5 * (log(lambda) - log_two_pi - 3 * log(x));
return logscale ? ans : exp(ans);
}
//======================================================================
// One 'week' of data, which may or may not contain an observed
// monthly total.
FineNowcastingData::FineNowcastingData(
const Vec &x,
double coarse_observation,
bool coarse_observation_observed,
bool contains_end,
double fraction_of_value_in_initial_period)
: x_(new RegressionData(negative_infinity(), x)),
coarse_observation_(coarse_observation),
coarse_observation_observed_(coarse_observation_observed),
contains_end_(contains_end),
fraction_in_initial_period_(fraction_of_value_in_initial_period)
{}
double Bspline::knot(int i) const {
if (knots_.empty()) {
return negative_infinity();
} else {
if (i <= 0) {
return knots_[0];
} else if (i >= knots_.size()) {
return knots_.back();
} else {
return knots_[i];
}
}
}
double beta_log_likelihood(double a, double b, const BetaSuf &suf){
if (a <= 0 || b <= 0) {
return negative_infinity();
}
double n = suf.n();
double sumlog = suf.sumlog();
double sumlogc = suf.sumlogc();
double ans = n*(lgamma(a + b) - lgamma(a)-lgamma(b));
ans += (a-1)*sumlog + (b-1)*sumlogc;
return ans;
}
double ExponentialModel::Logp(double x, double &g, double &h, uint nd) const {
double lam = this->lam();
if (lam <= 0) {
return negative_infinity();
}
double ans = x < 0 ? negative_infinity() : log(lam) - lam * x;
if (nd > 0) {
if (lam > 0) {
g = 1.0 / lam - x;
} else {
g = 1.0;
}
if (nd > 1) {
if (lam > 0) {
h = -1.0 / (lam * lam);
} else {
h = -1.0;
}
}
}
return ans;
}
double PRSS::find_posterior_mode() {
const Selector &included(model_->inc());
d2TargetFunPointerAdapter logpost(
boost::bind(&PoissonRegressionModel::log_likelihood, model_,
_1, _2, _3, _4),
boost::bind(&MvnBase::logp_given_inclusion, slab_prior_.get(),
_1, _2, _3, included, _4));
Vector beta = model_->included_coefficients();
int dim = beta.size();
if (dim == 0) {
return negative_infinity();
// TODO: This logic prohibits an empty model. Better to return
// the actual value of the un-normalized log posterior, which in
// this case would just be the likelihood portion.
}
Vector gradient(dim);
Spd hessian(dim);
double logf;
std::string error_message;
bool ok = max_nd2_careful(beta,
gradient,
hessian,
logf,
Target(logpost),
dTarget(logpost),
d2Target(logpost),
1e-5,
error_message);
if (ok) {
model_->set_included_coefficients(beta, included);
return logf;
} else {
return negative_infinity();
}
}
//----------------------------------------------------------------------
// Omits a factor of (2*pi)^{N/2} \exp{-.5 * (N - 1) * s^2 } from
// the integrated likelihood.
double ProbitBartPosteriorSampler::log_integrated_probit_likelihood(
const Bart::ProbitSufficientStatistics &suf) const {
double n = suf.sample_size();
if (n <= 0) {
return negative_infinity();
}
double ybar = suf.sum() / n; // handle n == 0;
double prior_variance = mean_prior_variance();
double ivar = n + (1.0 / prior_variance);
double posterior_variance = 1.0 / ivar;
double posterior_mean = suf.sum() / ivar;
double ans = log(posterior_variance / prior_variance)
- n * square(ybar)
+ square(posterior_mean) / posterior_variance;
return .5 * ans;
}
double ZGS::log_prior(double sigsq, double *d1, double *d2) const {
if (sigsq <= 0.0) {
return negative_infinity();
}
double a = precision_prior_->alpha();
double b = precision_prior_->beta();
// The log prior is the gamma density plus a jacobian term:
// log(abs(d(siginv) / d(sigsq))).
if (d1) {
double sig4 = sigsq * sigsq;
*d1 += -(a + 1) / sigsq + b / sig4;
if (d2) {
double sig6 = sigsq * sig4;
*d2 += (a + 1) / sig4 - 2 * b / sig6;
}
}
return dgamma(1 / sigsq, a, b, true) - 2 * log(sigsq);
}
double PoissonModel::Loglike(const Vector &lambda_vector,
Vec &g, Mat &h, uint nd)const{
if (lambda_vector.size() != 1) {
report_error("Wrong size argument.");
}
double lam = lambda_vector[0];
if (lam < 0) {
return negative_infinity();
}
Ptr<PoissonSuf> s = suf();
double sm = s->sum();
double n = s->n();
double ans = sm*log(lam) - n*lam - s->lognc();
if(nd>0){
g[0] = sm/lam-n;
if(nd>1) h(0,0) = -sm/(lam*lam);
}
return ans;
}
double GaussianBartPosteriorSampler::log_integrated_gaussian_likelihood(
const Bart::GaussianBartSufficientStatistics &suf) const {
double n = suf.n();
if (n < 5) {
return negative_infinity();
}
double prior_variance = mean_prior_variance();
double sigsq = model_->sigsq();
double ybar = suf.ybar();
double sample_variance = suf.sample_var();
double ivar = (n / sigsq) + (1.0 / prior_variance);
double posterior_variance = 1.0 / ivar;
double posterior_mean = (n * ybar / sigsq) / ivar;
double ans = -n * (log_2_pi + log(sigsq)) +
log(posterior_variance / prior_variance) -
(n - 1) * sample_variance / sigsq - n * square(ybar) / sigsq +
square(posterior_mean) / posterior_variance;
return .5 * ans;
}
double BM::Loglike(const Vector &ab, Vec &g, Mat &h, uint nd) const{
if (ab.size() != 2) {
report_error("Wrong size argument.");
}
double alpha = ab[0];
double beta = ab[1];
if (alpha <= 0 || beta <= 0) {
if (nd > 0) {
g[0] = (alpha <= 0) ? 1.0 : 0.0;
g[1] = (beta <= 0) ? 1.0 : 0.0;
if (nd > 1) {
h = 0.0;
h.diag() = -1.0;
}
}
return negative_infinity();
}
double n = suf()->n();
double sumlog = suf()->sumlog();
double sumlogc = suf()->sumlogc();
double ans = n*(lgamma(alpha + beta) - lgamma(alpha)-lgamma(beta));
ans += (alpha-1)*sumlog + (beta-1)*sumlogc;
if(nd>0){
double psisum = digamma(alpha + beta);
g[0] = n*(psisum-digamma(alpha)) + sumlog;
g[1] = n*(psisum-digamma(beta)) + sumlogc;
if(nd>1){
double trisum = trigamma(alpha+beta);
h(0,0) = n*(trisum - trigamma(alpha));
h(0,1) = h(1,0) = n*trisum;
h(1,1) = n*(trisum - trigamma(beta));}}
return ans;
}
double ArPosteriorSampler::logpri()const{
bool ok = model_->check_stationary(model_->phi());
if(!ok) return negative_infinity();
return siginv_prior_->logp(1.0 / model_->sigsq());
}
double GFFPS::logpri() const {
report_error("Not yet implemented");
return negative_infinity();
}
void LiuWestParticleFilter::update(RNG &rng,
const Data &observation,
int observation_time) {
//====== Step 1
// Compute the means and variances to be used in the kernel density
// estimate.
std::vector<Vector> predicted_state_mean;
predicted_state_mean.reserve(number_of_particles());
MvnSuf suf(parameter_particles_[0].size());
for (int i = 0; i < number_of_particles(); ++i) {
suf.update_raw(parameter_particles_[i]);
predicted_state_mean.push_back(hmm_->predicted_state_mean(
state_particles_[i], observation_time, parameter_particles_[i]));
}
Vector parameter_mean = suf.ybar();
Vector kernel_weights(number_of_particles());
double max_log_weight = negative_infinity();
std::vector<Vector> predicted_parameter_mean(number_of_particles());
double particle_weight = sqrt(1 - square(kernel_scale_factor_));
for (int i = 0; i < number_of_particles(); ++i) {
predicted_parameter_mean[i] =
particle_weight * parameter_particles_[i]
+ (1 - particle_weight) * parameter_mean;
kernel_weights[i] = log_weights_[i] + hmm_->log_observation_density(
observation,
predicted_state_mean[i],
observation_time,
predicted_parameter_mean[i]);
if (!std::isfinite(kernel_weights[i])) {
kernel_weights[i] = negative_infinity();
}
max_log_weight = std::max<double>(max_log_weight, kernel_weights[i]);
}
double total_weight = 0;
for (int i = 0; i < number_of_particles(); ++i) {
double weight = exp(kernel_weights[i] - max_log_weight);
if (!std::isfinite(weight)) {
weight = 0;
}
total_weight += weight;
kernel_weights[i] = weight;
}
kernel_weights /= total_weight;
SpdMatrix sample_variance = suf.sample_var();
if (sample_variance.rank() < sample_variance.nrow()) {
////////////////
// Refresh the parameter distribution.
////////////////
}
Cholesky sample_variance_cholesky(sample_variance);
if (!sample_variance_cholesky.is_pos_def()) {
report_error("Sample variance is not positive definite.");
}
Matrix variance_cholesky =
kernel_scale_factor_ * sample_variance_cholesky.getL();
//===== Step 2:
// Propose new values of state and parameters, and update the weights.
//
// Space is needed for the new proposals, because sampling and updating is
// done with replacement.
std::vector<Vector> new_state_particles(number_of_particles());
Vector new_log_weights(number_of_particles());
for (int i = 0; i < number_of_particles(); ++i) {
int particle = rmulti_mt(rng, kernel_weights);
Vector parameter_proposal =
rmvn_L_mt(rng, predicted_parameter_mean[particle], variance_cholesky);
try {
Vector state_proposal = hmm_->simulate_transition(
rng, state_particles_[particle], observation_time - 1, parameter_proposal);
parameter_particles_[i] = parameter_proposal;
new_state_particles[i] = state_proposal;
new_log_weights[i] =
hmm_->log_observation_density(observation,
state_proposal,
observation_time,
parameter_proposal)
- hmm_->log_observation_density(observation,
predicted_state_mean[particle],
observation_time,
predicted_parameter_mean[particle]);
if (!std::isfinite(new_log_weights[i])) {
new_log_weights[i] = negative_infinity();
}
} catch (...) {
// If we're here it means the parameter proposal was an illegal value.
// Stuff the new_state_particles[i] entry with the right-sized garbage,
// and set the weight to zero (i.e. set the log weight to negative
// infinity).
new_state_particles[i] = state_particles_[i];
new_log_weights[i] = negative_infinity();
}
}
std::swap(new_state_particles, state_particles_);
std::swap(new_log_weights, log_weights_);
}