void gammaexpo(){
printf("gamma/exponential\n");
apop_model *gamma = apop_model_set_parameters(apop_gamma, 1, 0.4);
apop_model *drawfrom = apop_model_set_parameters(apop_exponential, 0.4);
int draw_ct = 120;
apop_data *draws = apop_model_draws(drawfrom, draw_ct);
apop_model *gammaup = apop_update(draws, gamma, apop_exponential);
apop_model_show(gammaup);
gamma->more = apop_gamma;
gamma->log_likelihood = fake_ll;
Apop_settings_add_group(gamma, apop_mcmc, .burnin=.1, .periods=1e5,
.proposal=apop_model_set_parameters(apop_normal, 1, .001));
apop_model *upd = apop_update(draws, gamma, apop_exponential);
apop_model *gammaed = apop_estimate(upd->data, apop_gamma);
apop_model_show(gammaed);
deciles(gammaed, gammaup, 3);
Apop_settings_add_group(gamma, apop_mcmc, .burnin=.1, .periods=1e5,
.proposal=apop_model_set_parameters(apop_normal, 1, .01));
gamma->log_likelihood = NULL;
apop_model *upd_r = apop_update(draws, gamma, apop_exponential);
apop_model *gammafied2 = apop_estimate(apop_data_pmf_expand(upd_r->data, 2000), apop_gamma);
deciles(gammafied2, gammaup, 5);
}
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);
}
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);
}
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(){
apop_model_print (
apop_estimate(
apop_update(
apop_model_draws(
apop_model_mixture(
apop_model_set_parameters(apop_poisson, 2.8),
apop_model_set_parameters(apop_poisson, 2.0),
apop_model_set_parameters(apop_poisson, 1.3)
),
1e4
),
truncate_model(
apop_model_set_parameters(apop_normal, 2, 1),
0
),
apop_poisson
)->data,
apop_normal
)
, NULL);
}
