void betabinom(){
apop_model *beta = apop_model_set_parameters(apop_beta, 10, 5);
apop_model *drawfrom = apop_model_copy(apop_multinomial);
drawfrom->parameters = apop_data_falloc((2), 30, .4);
drawfrom->dsize = 2;
int draw_ct = 80;
apop_data *draws = apop_model_draws(drawfrom, draw_ct);
apop_model *betaup = apop_update(draws, beta, apop_binomial);
apop_model_show(betaup);
beta->more = apop_beta;
beta->log_likelihood = fake_ll;
apop_model *bi = apop_model_fix_params(apop_model_set_parameters(apop_binomial, 30, NAN));
apop_model *upd = apop_update(draws, beta, bi);
apop_model *betaed = apop_estimate(upd->data, apop_beta);
deciles(betaed, betaup, 1);
beta->log_likelihood = NULL;
apop_model *upd_r = apop_update(draws, beta, bi);
betaed = apop_estimate(apop_data_pmf_expand(upd_r->data, 2000), apop_beta);
deciles(betaed, betaup, 1);
apop_data *d2 = apop_model_draws(upd, draw_ct*2);
apop_model *d2m = apop_estimate(d2, apop_beta);
deciles(d2m, betaup, 1);
}
void gammafish(){
printf("gamma/poisson\n");
apop_model *gamma = apop_model_set_parameters(apop_gamma, 1.5, 2.2);
apop_model *drawfrom = apop_model_set_parameters(apop_poisson, 3.1);
int draw_ct = 90;
apop_data *draws = apop_model_draws(drawfrom, draw_ct);
apop_model *gammaup = apop_update(draws, gamma, apop_poisson);
apop_model_show(gammaup);
gamma->more = apop_gamma;
gamma->log_likelihood = fake_ll;
apop_model *proposal = apop_model_fix_params(apop_model_set_parameters(apop_normal, NAN, 1));
proposal->parameters = apop_data_falloc((1), .9);
//apop_data_set(apop_settings_get(gamma, apop_mcmc, proposal)->parameters, .val=.9);
Apop_settings_add_group(gamma, apop_mcmc, .burnin=.1, .periods=1e4, .proposal=proposal);
apop_model *upd = apop_update(draws, gamma, apop_poisson);
apop_model *gammafied = apop_estimate(upd->data, apop_gamma);
deciles(gammafied, gammaup, 5);
//Apop_settings_add_group(beta, apop_mcmc, .burnin=.4, .periods=1e4);
gamma->log_likelihood = NULL;
apop_model *upd_r = apop_update(draws, gamma, apop_poisson);
apop_model *gammafied2 = apop_estimate(apop_data_pmf_expand(upd_r->data, 2000), apop_gamma);
deciles(gammafied2, gammaup, 5);
deciles(gammafied, gammafied2, 5);
}
int main(){
gsl_rng *r = apop_rng_alloc(2468);
double binom_start = 0.6;
double beta_start_a = 0.3;
double beta_start_b = 0.5;
int i, draws = 1500;
double n = 4000;
//First, the easy estimation using the conjugate distribution table.
apop_model *bin = apop_model_set_parameters(apop_binomial, n, binom_start);
apop_model *beta = apop_model_set_parameters(apop_beta, beta_start_a, beta_start_b);
apop_model *updated = apop_update(.prior= beta, .likelihood=bin,.rng=r);
//Now estimate via Gibbs sampling.
//Requires a one-parameter binomial, with n fixed,
//and a data set of n data points with the right p.
apop_model *bcopy = apop_model_set_parameters(apop_binomial, n, GSL_NAN);
apop_data *bin_draws = apop_data_fill(apop_data_alloc(1,2), n*(1-binom_start), n*binom_start);
bin = apop_model_fix_params(bcopy);
apop_model_add_group(beta, apop_update, .burnin=.1, .periods=1e4);
apop_model *out_h = apop_update(bin_draws, beta, bin, NULL);
//We now have a histogram of values for p. What's the closest beta
//distribution?
apop_data *d = apop_data_alloc(0, draws, 1);
for(i=0; i < draws; i ++)
apop_draw(apop_data_ptr(d, i, 0), r, out_h);
apop_model *out_beta = apop_estimate(d, apop_beta);
//Finally, we can compare the conjugate and Gibbs results:
apop_vector_normalize(updated->parameters->vector);
apop_vector_normalize(out_beta->parameters->vector);
double error = apop_vector_distance(updated->parameters->vector, out_beta->parameters->vector, .metric='m');
double updated_size = apop_vector_sum(updated->parameters->vector);
Apop_assert(error/updated_size < 0.01, "The error is %g, which is too big.", error/updated_size);
}
int main(){
gsl_rng *r = apop_rng_alloc(10);
size_t i, ct = 5e4;
//set up the model & params
apop_data *d = apop_data_alloc(ct,2);
apop_data *params = apop_data_alloc(2,2,2);
apop_data_fill(params, 8, 1, 0.5,
2, 0.5, 1);
apop_model *pvm = apop_model_copy(apop_multivariate_normal);
pvm->parameters = apop_data_copy(params);
//make random draws from the multivar. normal
//this `pull a row view, fill its data element' form works for rows but not cols.
for(i=0; i< ct; i++){
Apop_row(d, i, onerow);
apop_draw(onerow->data, r, pvm);
}
//set up and estimate a model with fixed covariance matrix but free means
gsl_vector_set_all(pvm->parameters->vector, GSL_NAN);
apop_model *mep1 = apop_model_fix_params(pvm);
apop_model *e1 = apop_estimate(d, *mep1);
//compare results
printf("original params: ");
apop_vector_show(params->vector);
printf("estimated params: ");
apop_vector_show(e1->parameters->vector);
}
int main(){
size_t ct = 5e4;
//set up the model & params
apop_data *params = apop_data_falloc((2,2,2), 8, 1, 0.5,
2, 0.5, 1);
apop_model *pvm = apop_model_copy(apop_multivariate_normal);
pvm->parameters = apop_data_copy(params);
pvm->dsize = 2;
apop_data *d = apop_model_draws(pvm, ct);
//set up and estimate a model with fixed covariance matrix but free means
gsl_vector_set_all(pvm->parameters->vector, GSL_NAN);
apop_model *mep1 = apop_model_fix_params(pvm);
apop_model *e1 = apop_estimate(d, mep1);
//compare results
printf("original params: ");
apop_vector_print(params->vector);
printf("estimated params: ");
apop_vector_print(e1->parameters->vector);
assert(apop_vector_distance(params->vector, e1->parameters->vector)<1e-2);
}
static void wishart_estimate(apop_data *d, apop_model *m){
Nullcheck_m(m, );
//apop_data_set(m->parameters, 0, -1, d->matrix->size1);
//Start with cov matrix via mean of inputs; df=NaN
apop_data_set(m->parameters, 0, -1, GSL_NAN);
apop_data *summ=apop_data_summarize(d);
Apop_col_t(summ, "mean", means);
gsl_vector *t = m->parameters->vector; //mask this while unpacking
m->parameters->vector=NULL;
apop_data_unpack(means, m->parameters);
m->parameters->vector=t;
//Estimate a model with fixed cov matrix and blank (NaN) df.
apop_model *modified_wish = apop_model_copy(m);
modified_wish->log_likelihood = fixed_wishart_ll;
apop_model *fixed_wish = apop_model_fix_params(modified_wish);
apop_model *est_via_fix = apop_estimate(d, fixed_wish);
//copy df from fixed version to the real thing; clean up.
t->data[0] = apop_data_get(est_via_fix->parameters, 0, -1);
gsl_matrix_scale(m->parameters->matrix, 1./t->data[0]);
apop_data_free(summ);
apop_model_free(modified_wish);
apop_model_free(fixed_wish);
}
/* amodel apop_wishart The Wishart distribution, which is currently somewhat untested.
Here's the likelihood function. \f$p\f$ is the dimension of the data and covariance
matrix, \f$n\f$ is the degrees of freedom, \f$\mathbf{V}\f$ is the \f$p\times p\f$
matrix of Wishart parameters, and \f${\mathbf{W}}\f$ is the \f$p\times p\f$ matrix whose
