// Simulate a WeeklyCyclePoissonProcess by thinning
PointProcess WP::simulate(RNG &rng, const DateTime &t0, const DateTime &t1,
std::function<Data *()> mark_generator) const {
PointProcess ans(t0, t1);
double max_rate = 0;
for (int d = 0; d < 7; ++d) {
for (int h = 0; h < 24; ++h) {
max_rate = std::max(max_rate, event_rate(DayNames(d), h));
}
}
double duration = t1 - t0;
int number_of_candidate_events = rpois_mt(rng, max_rate * duration);
Vector times(number_of_candidate_events);
for (int i = 0; i < number_of_candidate_events; ++i) {
times[i] = runif_mt(rng, 0, duration);
}
times.sort();
for (int i = 0; i < times.size(); ++i) {
DateTime cand = t0 + times[i];
double prob = event_rate(cand) / max_rate;
if (runif_mt(rng, 0, 1) < prob) {
Data *mark = mark_generator();
if (mark) {
ans.add_event(cand, Ptr<Data>(mark));
} else {
ans.add_event(cand);
}
}
}
return ans;
}
// Args:
// rng: The random number generator.
// binary_inputs: The value of the inputs to the terminal layer (i.e. the
// outputs from the final hidden layer). These will be updated by the
// imputation.
// logprob: On input this is a vector giving the marginal (un-logged)
// probability that each input node is active. These values will be
// over-written by their logarithms.
// logprob_complement: On input this is any vector with size matching
// logprob. On output its elements contain log(1 - exp(logprob)).
//
// Effects:
// The latent data for the terminal layer is imputed, and the sufficient
// statistics for the latent regression model in the terminal layer are
// updated to included the imputed data.
void GFFPS::impute_terminal_layer_inputs(
RNG &rng,
double response,
std::vector<bool> &binary_inputs,
Vector &logprob,
Vector &logprob_complement) {
for (int i = 0; i < logprob.size(); ++i) {
logprob_complement[i] = log(1 - logprob[i]);
logprob[i] = log(logprob[i]);
}
Vector terminal_layer_inputs(binary_inputs.size());
Nnet::to_numeric(binary_inputs, terminal_layer_inputs);
double logp_original = terminal_inputs_log_full_conditional(
response, terminal_layer_inputs, logprob, logprob_complement);
for (int i = 0; i < terminal_layer_inputs.size(); ++i) {
terminal_layer_inputs[i] = 1 - terminal_layer_inputs[i];
double logp = terminal_inputs_log_full_conditional(
response, terminal_layer_inputs, logprob, logprob_complement);
double log_input_prob = logp - lse2(logp, logp_original);
double logu = log(runif_mt(rng));
if (logu < log_input_prob) {
logp_original = logp;
} else {
terminal_layer_inputs[i] = 1 - terminal_layer_inputs[i];
}
}
model_->terminal_layer()->suf()->add_mixture_data(
response, terminal_layer_inputs, 1.0);
Nnet::to_binary(terminal_layer_inputs, binary_inputs);
}
//----------------------------------------------------------------------
// univariate slice sampling to set each element
void CS::draw_one() {
double oldr = R_(i_, j_);
double logp_star = logp(R_(i_, j_));
double u = logp_star - rexp_mt(rng(), 1);
find_limits();
if (lo_ >= hi_) {
set_r(0);
return;
}
// const double eps(100*std::numeric_limits<double>::epsilon());
const double eps(1e-6);
check_limits(oldr, eps);
while (1) {
double cand = runif_mt(rng(), lo_, hi_);
double logp_cand = logp(cand);
if (logp_cand > u) { // found something inside slice
set_r(cand);
return;
} else { // contract slice
if (cand > oldr) {
hi_ = cand;
} else {
lo_ = cand;
}
}
if (fabs(hi_ - lo_) < eps) {
set_r(hi_);
return;
}
}
}
double rtriangle_mt(RNG & rng, double x0, double x1, double xm){
/* simulates from the noncentral triangle distribution on the
interval (x0, x1) with a break at xm. If xm < x0 || xm > x1 then
xm is taken to be the midpoint of the interval.
*/
double y, m0, m1, a0, u;
if(x1 < x0) {
std::ostringstream err;
err << "error in rtriangle_mt: called with" << std::endl
<< "x0 = " << x0 << std::endl
<< "x1 = " << x1 << std::endl
<< "xm = " << xm << std::endl
<< "x0 must be less than x1";
throw_exception<std::runtime_error>(err.str());
}
else if(x0 == x1) return x0;
if(xm < x0 || xm > x1) xm=(x0 + x1)/2.0;
y = 2.0/(x1-x0);
m0 = y/(xm-x0);
m1= y/(xm-x1);
a0 = 0.5*y*(xm-x0);
u=runif_mt(rng,0,1);
double ans =0;
if(u<a0) ans = x0 + sqrt(2*u/m0); /* area of left right triangle */
else if(u>=a0) ans = x1-sqrt(-2.0*(1-u)/m1); /* area of right right triangle */
else throw_exception<std::runtime_error>("an unknown error occurred in rtriangle_mt");
return ans;
}
// Find the upper and lower limits of a slice containing x for a
// potentially multimodal distribution. Uses Neal's (2003 Annals of
// Statistics) doubling algorithm.
bool SSS::find_limits_unbounded(double x){
hi_ = x + suggested_dx_;
lo_ = x - suggested_dx_;
logphi_ = logf_(hi_);
logplo_ = logf_(lo_);
if(unimodal_){
find_limits_unbounded_unimodal(x);
return true;
}else{
int doubling_count = 0;
while(!done_doubling()){
double u = runif_mt(rng(), -1, 1);
if(u>0) double_hi(x);
else double_lo(x);
if (++doubling_count > 100) {
// The slice has been doubled 100 times. This is almost
// certainly beecause of an error in the target distribution
// or a crazy starting value.
return false;
}
}
}
check_upper_limit(x);
check_lower_limit(x);
return true;
}
//----------------------------------------------------------------------
void BLCSSS::rwm_draw_chunk(int chunk){
clock_t start = clock();
const Selector &inc(m_->coef().inc());
int nvars = inc.nvars();
Vec full_nonzero_beta = m_->beta(); // only nonzero components
// Compute information matrix for proposal distribution. For
// efficiency, also compute the log-posterior of the current beta.
Vec mu(inc.select(pri_->mu()));
Spd siginv(inc.select(pri_->siginv()));
double original_logpost = dmvn(full_nonzero_beta, mu, siginv, 0, true);
const std::vector<Ptr<BinomialRegressionData> > &data(m_->dat());
int nobs = data.size();
int full_chunk_size = compute_chunk_size();
int chunk_start = chunk * full_chunk_size;
int elements_remaining = nvars - chunk_start;
int this_chunk_size = std::min(elements_remaining, full_chunk_size);
Selector chunk_selector(nvars, false);
for(int i = chunk_start; i< chunk_start + this_chunk_size; ++i) {
chunk_selector.add(i);
}
Spd proposal_ivar = chunk_selector.select(siginv);
for(int i = 0; i < nobs; ++i){
Vec x = inc.select(data[i]->x());
double eta = x.dot(full_nonzero_beta);
double prob = plogis(eta);
double weight = prob * (1-prob);
VectorView x_chunk(x, chunk_start, this_chunk_size);
// Only upper triangle is accessed. Need to reflect at end of loop.
proposal_ivar.add_outer(x_chunk, weight, false);
int yi = data[i]->y();
int ni = data[i]->n();
original_logpost += dbinom(yi, ni, prob, true);
}
proposal_ivar.reflect();
VectorView beta_chunk(full_nonzero_beta, chunk_start, this_chunk_size);
if(tdf_ > 0){
beta_chunk = rmvt_ivar_mt(
rng(), beta_chunk, proposal_ivar / rwm_variance_scale_factor_, tdf_);
}else{
beta_chunk = rmvn_ivar_mt(
rng(), beta_chunk, proposal_ivar / rwm_variance_scale_factor_);
}
double logpost = dmvn(full_nonzero_beta, mu, siginv, 0, true);
Vec full_beta(inc.expand(full_nonzero_beta));
logpost += m_->log_likelihood(full_beta, 0, 0, false);
double log_alpha = logpost - original_logpost;
double logu = log(runif_mt(rng()));
++rwm_chunk_attempts_;
if(logu < log_alpha){
m_->set_beta(full_nonzero_beta);
++rwm_chunk_successes_;
}
clock_t end = clock();
rwm_chunk_times_ += double(end - start) / CLOCKS_PER_SEC;
}
void SliceSampler::find_limits(){
if(unimodal){
while(phi > pstar) doubling(true);
while(plo > pstar) doubling(false);
}else{
while(phi > pstar || plo > pstar){
double tmp = runif_mt(rng(), -1,1);
doubling(tmp>0);}}}
//----------------------------------------------------------------------
void BLCSSS::rwm_draw_chunk(int chunk){
const Selector &inc(m_->coef().inc());
int nvars = inc.nvars();
Vector full_nonzero_beta = m_->included_coefficients();
// Compute information matrix for proposal distribution. For
// efficiency, also compute the log-posterior of the current beta.
Vector mu(inc.select(pri_->mu()));
SpdMatrix siginv(inc.select(pri_->siginv()));
double original_logpost = dmvn(full_nonzero_beta, mu, siginv, 0, true);
const std::vector<Ptr<BinomialRegressionData> > &data(m_->dat());
int nobs = data.size();
int full_chunk_size = compute_chunk_size(max_rwm_chunk_size_);
int chunk_start = chunk * full_chunk_size;
int elements_remaining = nvars - chunk_start;
int this_chunk_size = std::min(elements_remaining, full_chunk_size);
Selector chunk_selector(nvars, false);
for(int i = chunk_start; i< chunk_start + this_chunk_size; ++i) {
chunk_selector.add(i);
}
SpdMatrix proposal_ivar = chunk_selector.select(siginv);
for(int i = 0; i < nobs; ++i){
Vector x = inc.select(data[i]->x());
double eta = x.dot(full_nonzero_beta);
double prob = plogis(eta);
double weight = prob * (1-prob);
VectorView x_chunk(x, chunk_start, this_chunk_size);
// Only upper triangle is accessed. Need to reflect at end of loop.
proposal_ivar.add_outer(x_chunk, weight, false);
original_logpost += dbinom(data[i]->y(), data[i]->n(), prob, true);
}
proposal_ivar.reflect();
VectorView beta_chunk(full_nonzero_beta, chunk_start, this_chunk_size);
if(tdf_ > 0){
beta_chunk = rmvt_ivar_mt(
rng(), beta_chunk, proposal_ivar / rwm_variance_scale_factor_, tdf_);
}else{
beta_chunk = rmvn_ivar_mt(
rng(), beta_chunk, proposal_ivar / rwm_variance_scale_factor_);
}
double logpost = dmvn(full_nonzero_beta, mu, siginv, 0, true);
Vector full_beta(inc.expand(full_nonzero_beta));
logpost += m_->log_likelihood(full_beta, 0, 0, false);
double log_alpha = logpost - original_logpost;
double logu = log(runif_mt(rng()));
if (logu < log_alpha) {
m_->set_included_coefficients(full_nonzero_beta);
move_accounting_.record_acceptance("rwm_chunk");
} else {
move_accounting_.record_rejection("rwm_chunk");
}
}
double BLSSS::mcmc_one_flip(Selector &mod, uint which_var, double logp_old) {
mod.flip(which_var);
double logp_new = log_model_prob(mod);
double u = runif_mt(rng(), 0,1);
if(log(u) > logp_new - logp_old) {
mod.flip(which_var); // reject draw
return logp_old;
}
return logp_new;
}
double Tn2Sampler::draw(RNG &rng){
double u= runif_mt(rng, 0, cdf.back());
IT pos = std::lower_bound(cdf.begin(), cdf.end(), u);
uint k = pos - cdf.begin();
// draw from the doubly truncated exponential distribution
double lo = knots[k];
double hi = knots[k+1];
double lam = -1*dlogf[k];
double cand;
if(lam==0){
cand = runif_mt(rng, lo, hi);
}else{
cand = rtrun_exp_mt(rng, lam, lo, hi);
}
double target = f(cand);
double logu = hull(cand, k) - rexp_mt(rng, 1);
if(logu < target) return cand;
add_point(cand);
return draw(rng);
}
double rig_mt(RNG & rng, double mu, double lambda){
double y = rnorm_mt(rng);
y = y * y;
double mu2 = mu * mu;
double muy = mu * y;
double mu2lam = .5 * mu/lambda;
double x = mu + muy * mu2lam
- mu2lam * sqrt(muy * (4*lambda + muy));
double z = runif_mt(rng);
if(z > mu/(mu+x)) return mu2/x;
return x;
}
double rtrun_exp_mt(RNG & rng, double lam, double lo, double hi){
// samples a random variable from the exponential distribution with
// rate lam, with support truncated between lo and hi
double Fmax = 1-exp(-lam*(hi-lo));
double u = runif_mt(rng, 0, 1);
double x = lo - log(1-u*Fmax)/lam;
return x;
}
Vector SliceSampler::draw(const Vector &theta) {
last_position_ = theta;
initialize();
find_limits();
Vector candidate;
double logp_candidate = log_p_slice_ - 1;
do {
double lambda = runif_mt(rng(), -lo_, hi_);
candidate = last_position_ + lambda * random_direction_;
logp_candidate = logp_(candidate);
if (logp_candidate < log_p_slice_) contract(lambda, logp_candidate);
} while (logp_candidate < log_p_slice_);
scale_ = hi_ + lo_; // both hi_ and lo_ > 0
return candidate;
}
bool SSS::find_lower_limit(double x){
lo_ = x - suggested_dx_;
logplo_ = logf_(lo_);
int doubling_count = 0;
while(logplo_ >= logp_slice_ || (!unimodal_ && runif_mt(rng()) > .5)){
double_lo(x);
if (++doubling_count > 100) {
// The slice has been doubled over 100 times. This is almost
// certainly because of an error in the implementation of the
// target distribution, or a crazy starting value.
return false;
}
}
check_lower_limit(x);
return true;
}
void SliceSampler::find_limits() {
if (unimodal_) {
// If the posterior is unimodal then expand each endpoint until it
// is out of the slice.
while (logphi_ > log_p_slice_) doubling(true);
while (logplo_ > log_p_slice_) doubling(false);
} else {
// If the posterior is not known to be unimodal, then randomly
// pick an endpoint and double it until both ends are out of the
// slice. This will sometimes result in unnecessary doubling,
// but this algorithm has the right stationary distribution
// (Neal 2003).
while (logphi_ > log_p_slice_ || logplo_ > log_p_slice_) {
double tmp = runif_mt(rng(), -1, 1);
doubling(tmp > 0);
}
}
}
Vec SliceSampler::draw(const Vec &t){
theta = t;
z = t;
initialize();
pstar = f(theta) - rexp(1);
find_limits();
Vec tstar(theta.size(), 0.0);
double p = pstar -1;
do{
double lam = runif_mt(rng(), -lo, hi);
tstar = theta + lam*z; // randomly chosen point in the slice
p = f(tstar);
if(p<pstar) contract(lam,p);
else theta = tstar;
}while(p < pstar);
scale = hi+lo; // both hi and lo >0
return theta;
}
//----------------------------------------------------------------------
void BLCSSS::draw(){
double u = runif_mt(rng());
clock_t start = clock();
if(u < .333){
++auxmix_tries_;
BinomialLogitSpikeSlabSampler::draw();
clock_t end = clock();
auxmix_times_ += double(end - start) / CLOCKS_PER_SEC;
}else if(u < .6667){
++rwm_tries_;
rwm_draw();
clock_t end = clock();
rwm_times_ += double(end - start) / CLOCKS_PER_SEC;
}else{
++tim_tries_;
tim_draw();
clock_t end = clock();
tim_times_ += double (end - start) / CLOCKS_PER_SEC;
}
}
double SSS::draw(double x){
find_limits(x);
double logp_cand = 0;
int number_of_tries = 0;
do{
double x_cand = runif_mt(rng(), lo_, hi_);
logp_cand = logf_(x_cand);
if(logp_cand < logp_slice_){
contract(x,x_cand, logp_cand);
++number_of_tries;
} else return x_cand;
if(number_of_tries > 100){
ostringstream err;
err << "number of tries exceeded. candidate value is "
<< x_cand << " with logp_cand = " << logp_cand << endl;
handle_error(err.str(), x);
}
}while(logp_cand < logp_slice_);
handle_error("should never get here", x);
return 0;
}
int random_int_mt(RNG & rng, int lo, int hi){
double tmp = runif_mt(rng, lo, hi+1);
return static_cast<int>(std::floor(tmp));
}
double ZIGM::sim(RNG &rng) const {
if (runif_mt(rng) < positive_probability()) {
return gamma_->sim(rng);
}
return 0;
}
double runif(double a, double b){
return runif_mt(BOOM::GlobalRng::rng, a, b);
}
int rmulti_mt(RNG & rng, int lo, int hi){
// draw a random integer between lo and hi with equal probability
double tmp = runif_mt(rng, lo+0.0,hi+1.0);
return (int)floor(tmp);
}
double UM::sim(RNG &rng) const { return runif_mt(rng, lo(), hi()); }
double OrdinalLogitImputer::impute(
RNG &rng, double eta, double lower_cutpoint, double upper_cutpoint) {
return eta + qlogis(runif_mt(
rng, plogis(lower_cutpoint - eta), plogis(upper_cutpoint - eta)));
}