# This prior is not exactly the same as the true parameter
prior_dict = {'c': dists.Normal(loc=8e-11,scale=2e-11),
'm': dists.Normal(loc = 1.5, scale = 1e-1),
'a0':dists.Gamma(1/2, 2), # Chi squared with k=1
"v":dists.Gamma(1/2,2)} # This is chi squared with k=1
# # This prior is significantly different from the true parameters
# prior_dict = {'c': dists.Normal(loc=8e-11,scale=1e-11),
# 'm': dists.Normal(loc = 1.5, scale = 5e-1),
# 'a0':dists.Gamma(1/2, 2), # Chi squared with k=1
# "v":dists.Gamma(1/2,2)} # This is chi squared with k=1
my_prior = dists.StructDist(prior_dict)
# Run the smc2 inference
fk_smc2 = ssp.SMC2(ssm_cls=ParisLaw, data=data, prior=my_prior, init_Nx=8000)#, ar_to_increase_Nx=0.1)
alg_smc2 = particles.SMC(fk=fk_smc2, N=10000, store_history=True, verbose=True)
alg_smc2.run()
alg_smc2.true_model = true_model # Save the true model so it can be used in post processing
alg_smc2.true_states = true_states # Save the true states so RUL's can be calculated
# Save the result
with open('run_20201010a.pkl', 'wb') as f:
dill.dump(alg_smc2, f)
# Load the previously computed data
with open('run_20201010a.pkl', 'rb') as f:
alg_smc2 = dill.load(f)
# algorithms
N = 10**3 # re-run with N= 10^4 for the second CDF plots
fks = {}
fk_opts = {
'ssm_cls': state_space_models.StochVolLeverage,
'prior': prior,
'data': data,
'init_Nx': 100,
'smc_options': {
'qmc': False
},
'ar_to_increase_Nx': 0.1,
'wastefree': False,
'len_chain': 6
}
fks['smc2'] = ssp.SMC2(**fk_opts)
fk_opts['smc_options']['qmc'] = True
fks['smc2_qmc'] = ssp.SMC2(**fk_opts)
fk_opts['ssm_cls'] = state_space_models.StochVol
fks['smc2_sv'] = ssp.SMC2(**fk_opts)
# runs
runs = particles.multiSMC(fk=fks,
N=N,
collect=[Moments(mom_func=qtiles)],
verbose=True,
nprocs=0,
nruns=25)
# plots
#######
data=data,
prior=my_prior,
Nx=200,
niter=1000)
pg.run() # may take several seconds...
plt.plot(pg.chain.theta['mu'])
plt.xlabel('iter')
plt.ylabel('mu')
plt.figure()
plt.hist(pg.chain.theta['mu'][20:], 50)
plt.xlabel('mu')
import particles
from particles import smc_samplers as ssp
fk_smc2 = ssp.SMC2(ssm_cls=StochVol,
data=data,
prior=my_prior,
init_Nx=50,
ar_to_increase_Nx=0.1)
alg_smc2 = particles.SMC(fk=fk_smc2, N=500)
alg_smc2.run()
plt.figure()
plt.scatter(alg_smc2.X.theta['mu'], alg_smc2.X.theta['rho'])
plt.xlabel('mu')
plt.ylabel('rho')
plt.show()