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main.py
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"""Performing sbi on simulated and real data."""
from sbi.inference import SNPE, simulate_for_sbi
from sbi.utils import RestrictionEstimator, BoxUniform
import torch
import copy
import numpy as np
from utils import session_simple
from utils.session_simple import Session, per_neuron_trial_spikes
import pickle
import pandas as pd
from tqdm import tqdm
import func_timeout
import nest
# %% Simulation
def simulate_neuron(sim_params, neuron_params, simulate_voltage=False):
"""Simulate the firing rate of a neuron using the nest simulator."""
# Set parameters
sigma = abs(sim_params['std_I'])
mu = sim_params['mu_I']
# Simulation
nest.set_verbosity("M_WARNING")
nest.ResetKernel()
nest.rng_seed = sim_params['seed']
nest.resolution = sim_params['sim_res']
# Neuron
neurons = nest.Create("iaf_psc_exp", 1,
params=neuron_params)
# Noise
noise = nest.Create("noise_generator")
noise.set({"mean": mu, "std": sigma,
"dt": sim_params['dt_noise']})
# Spike Detector
spikedetector = nest.Create("spike_recorder")
# Connections
nest.Connect(noise, neurons)
# Run without recording
nest.Simulate(sim_params['dry_simtime'])
# Connect spike & voltage recorder
nest.Connect(neurons, spikedetector)
if simulate_voltage:
vm = nest.Create('voltmeter')
nest.SetStatus(vm, {'interval': 1})
nest.Connect(vm, neurons)
# Run the simulation
nest.Simulate(sim_params['simtime'])
# Get Voltage Data
if simulate_voltage:
dmm = vm.get()
Vms = dmm['events']['V_m']
single_mem = np.array(Vms)
else:
single_mem = []
# Get Spike Data
dSD = spikedetector.get("events")
ts_n = dSD["times"]
single_ts = np.array(ts_n)
return single_ts, single_mem
def compute_isi_stats(single_ts):
"""Calculate moments of isi distribution."""
if len(single_ts) < 3:
std = 0
mu = 0
elif len(single_ts) > 75:
std = 0
mu = 0
else:
isi = np.diff(single_ts)
log_isi = np.log2(isi)
mu = np.mean(log_isi)
std = np.std(log_isi)
isi_stats = [std, mu]
return isi_stats
def recover_voltages_from_params(sim_params, neuron_params, in_params):
"""Simulate neurons to measure voltage stats from input params."""
# Create array
curr_sim_params = copy.deepcopy(sim_params)
curr_sim_params['mu_I'] = in_params[1]
curr_sim_params['std_I'] = in_params[0]
curr_sim_params['simtime'] = 5_000
curr_sim_params['seed'] = np.random.randint(1, 50000)
ts, voltage = simulate_neuron(curr_sim_params,
neuron_params,
simulate_voltage=True)
mean_mem = np.mean(voltage)
std_mem = np.std(voltage)
isi = np.diff(ts)
isi_mean = np.mean(isi)
isi_std = np.std(isi)
voltage_stats = np.array([std_mem, mean_mem])
isi_stats = np.array([isi_std, isi_mean])
return voltage_stats, isi_stats
class sbi_simulator:
"""SBI simulator class."""
def __init__(self, sbi_params, sim_params, neuron_params):
"""Init."""
self.sbi_params = sbi_params
self.sim_params = sim_params
self.neuron_params = neuron_params
def __call__(self, theta):
"""Run simulation."""
theta = np.array(theta)[0]
new_sim_params = copy.deepcopy(self.sim_params)
new_sim_params['std_I'] = theta[0]
new_sim_params['mu_I'] = theta[1]
new_sim_params['seed'] = np.random.randint(1, 50000)
neuron_params = copy.deepcopy(self.neuron_params)
# Firing
ts, _ = simulate_neuron(new_sim_params, neuron_params)
# Stats
isi_stats = compute_isi_stats(ts)
isi_stats.append(len(ts))
# Valid trial
if isi_stats[1] == 0:
observation = np.full(len(isi_stats), np.nan)
else:
observation = np.array(isi_stats)
observation = np.array([observation.astype('float32')])
return torch.tensor(observation)
def create_prior(sbi_params):
"""Create prior to be used for sbi."""
low = []
high = []
for prior_param in ['std', 'mu']:
bounds_name = 'prior_bounds_' + prior_param
low.append(sbi_params[bounds_name][0])
high.append(sbi_params[bounds_name][1])
prior = BoxUniform(low=torch.asarray(low),
high=torch.asarray(high))
return prior
def create_posterior(sbi_params, sim_params, neuron_params):
"""Create posterior via simulation based inference."""
# Create simulator
simulator = sbi_simulator(sbi_params,
sim_params, neuron_params)
# Create Prior
prior = create_prior(sbi_params)
restriction_estimator = RestrictionEstimator(prior=prior)
proposals = [prior]
num_rounds = sbi_params['prior_nr_rounds']
for i in range(num_rounds):
# Run sbi
theta, x = simulate_for_sbi(simulator, proposals[-1],
sbi_params['prior_nr_sims'],
num_workers=sbi_params['nr_workers'],
show_progress_bar=True)
restriction_estimator.append_simulations(theta, x)
restriction_estimator.train()
restricted_prior = restriction_estimator.restrict_prior()
proposals.append(restricted_prior)
# Main simulation
theta, x = simulate_for_sbi(simulator,
proposals[-1],
sbi_params['nr_train_sims'],
num_workers=sbi_params['nr_workers'])
restriction_estimator.append_simulations(theta, x)
# Get all simulations
all_theta, all_x, _ = restriction_estimator.get_simulations()
# Simulate
prior_samples, prior_obs = \
simulate_for_sbi(simulator, proposals[-1],
sbi_params['validation_samples'],
num_workers=sbi_params['nr_workers'],
show_progress_bar=False)
# Train posterior
inference = SNPE(prior=prior)
inference.append_simulations(all_theta, all_x).train()
posterior = inference.build_posterior()
return posterior, simulator, prior_samples, prior_obs
def sample_posterior(sbi_params, posterior, obs):
"""Sample the posterior with the observations from data."""
sample_obs = posterior.sample((sbi_params['nr_posterior_samples'],),
x=obs, show_progress_bars=False)
return sample_obs
def run_w_timeout(f, args):
"""Timeout a function if it takes too long."""
try:
return func_timeout.func_timeout(2, f, args=args)
except func_timeout.FunctionTimedOut:
pass
return []
def get_max_likelihood_from_posterior(sbi_params, posterior, isi_stats):
"""Sample the posterior and then pick likeliest parameters."""
obs = isi_stats
c_posterior = copy.deepcopy(posterior)
c_posterior.set_default_x(obs)
# Run with timeout in case there are some unsupported observations
# These are given input parameters 0.5, 0.5 and can be filtered out
f = sample_posterior
args = (sbi_params,
c_posterior,
obs)
temp_samples = run_w_timeout(f, args)
if len(temp_samples) == 0:
rec_params = np.array([0.5, 0.5], dtype='float32')
else:
prob = c_posterior.log_prob(temp_samples)
top_prob = np.argmax(prob)
rec_params = temp_samples[top_prob].numpy()
return rec_params
def get_stats_from_obs(sbi_params, sim_params, neuron_params,
posterior, isi_stats):
"""Get all relevant stats."""
in_params = get_max_likelihood_from_posterior(sbi_params, posterior,
isi_stats)
voltage_stats, isi_stats = recover_voltages_from_params(sim_params,
neuron_params,
in_params)
return in_params, voltage_stats, isi_stats
def create_trial_dataset(sim_params, data_params):
"""Create trial data set from all selected sessions."""
# Loading Data
areas = data_params['areas_to_fit']
# Initialize a list to store rows
rows = []
# Iterate over areas
for area in areas:
sessions = session_simple.select_sessions(dataset='ChangeDetectionConflict',
area=area,
min_units=0,
min_performance=None,
filter_performance=False,
exclude_muscimol=True,
exclude_opto=True)
# Iterate over sessions
for sn, c_session in sessions.iterrows():
print(f"Loading trials from session number {sn}")
# Setting session parameters
c_data_params = copy.deepcopy(data_params)
animal_id = c_session['animal_id']
session_id = c_session['session_id']
c_data_params['area'] = area
c_session = Session(dataset=data_params['dataset'],
animal_id=animal_id,
session_id=session_id,
subfolder='')
c_session.load_data(load_lfp=False, use_newtrials=False)
trial_numbers = c_session.select_trials()
sel_trial_ind = np.isin(c_session.trial_data['trialNum'],
trial_numbers)
c_trial_data = c_session.trial_data.loc[sel_trial_ind, :]
# Trial times
sec_pre = sim_params['simtime']/1000
sec_post = \
(sim_params['simtime'] + data_params['skip_transient'])/1000
trial_times = c_session.get_aligned_times(trial_numbers,
time_before_in_s=sec_pre,
time_after_in_s=sec_post,
event='stimChange')
# Selecting neurons
neuron_index = c_session.select_units(area=c_data_params['area'],
layer=None,
min_isolation_distance=10)
spikes = c_session.spike_time_stamps[neuron_index]
neuron_ts = per_neuron_trial_spikes(c_data_params, spikes,
trial_times, neuron_index)
# Iterate over the rows in session.trial_data (each trial)
for trial_idx, trial_row in tqdm(c_trial_data.iterrows()):
for neuron_idx in range(len(neuron_index)):
# Make a copy of the trial_row (Series)
new_row = trial_row.copy()
neuron_id = neuron_index[neuron_idx]
# Append neuron-specific information
new_row['spikes_pre'] = \
neuron_ts[neuron_idx][trial_idx][0]
new_row['spikes_transient'] = \
neuron_ts[neuron_idx][trial_idx][1]
new_row['spikes_post'] = \
neuron_ts[neuron_idx][trial_idx][2]
new_row['animal_id'] = animal_id
new_row['session_id'] = session_id
new_row['neuron_id'] = neuron_id
new_row['unique_nidx'] = \
f"{session_id}_{animal_id}__{neuron_id}"
new_row['unique_tidx'] = \
f"{session_id}_{animal_id}_{trial_idx}"
new_row['area'] = area
rows.append(new_row)
# Convert the list of Series to a DataFrame
df = pd.DataFrame(rows).reset_index(drop=True)
return df
def perform_inference(sbi_params, sim_params,
data_params, neuron_params,
posterior, trial_dataset):
"""Infer parameters from all trials pre and post stimulus change."""
# Perform inference
# trials_to_fit = trial_dataset[trial_dataset['fit_trial']]
# trials_to_fit.reset_index(drop=True, inplace=True)
nr_trials = len(trial_dataset)
for t_nr in tqdm(range(nr_trials)):
c_trial = trial_dataset.loc[t_nr]
# Test pre and post
if c_trial['fit_trial']:
# Perform Inference Pre
isi_mu_pre = c_trial['log_isi_mu_pre']
isi_std_pre = c_trial['log_isi_std_pre']
spikes_pre = c_trial['nr_spikes_pre']
isi_stats_pre = [isi_std_pre, isi_mu_pre]
isi_stats_pre.append(spikes_pre)
in_stats, voltage_stats, isi_stats = \
get_stats_from_obs(sbi_params,
sim_params,
neuron_params,
posterior,
isi_stats_pre)
# Saving
# Inputs
trial_dataset.at[t_nr, 'input_std_pre'] = in_stats[0]
trial_dataset.at[t_nr, 'input_mu_pre'] = in_stats[1]
# Voltages
trial_dataset.at[t_nr, 'voltages_std_pre'] = voltage_stats[0]
trial_dataset.at[t_nr, 'voltages_mu_pre'] = voltage_stats[1]
# ISI
trial_dataset.at[t_nr, 'rec_isi_std_pre'] = isi_stats[0]
trial_dataset.at[t_nr, 'rec_isi_mu_pre'] = isi_stats[1]
# Perform Inference Post
isi_mu_post = c_trial['log_isi_mu_post']
isi_std_post = c_trial['log_isi_std_post']
spikes_post = c_trial['nr_spikes_post']
isi_stats_post = [isi_std_post, isi_mu_post]
isi_stats_post.append(spikes_post)
in_stats, voltage_stats, isi_stats = \
get_stats_from_obs(sbi_params,
sim_params,
neuron_params,
posterior,
isi_stats_post)
# Saving
# Inputs
trial_dataset.at[t_nr, 'input_std_post'] = in_stats[0]
trial_dataset.at[t_nr, 'input_mu_post'] = in_stats[1]
# Voltages
trial_dataset.at[t_nr, 'voltages_std_post'] = voltage_stats[0]
trial_dataset.at[t_nr, 'voltages_mu_post'] = voltage_stats[1]
# ISI
trial_dataset.at[t_nr, 'rec_isi_std_post'] = isi_stats[0]
trial_dataset.at[t_nr, 'rec_isi_mu_post'] = isi_stats[1]
return trial_dataset
def prior_val(sbi_params, sim_params, neuron_params,
posterior, prior_samples, prior_obs):
"""Validate the parameter recovery of parameters sampled from the prior."""
nr_samples = sbi_params['validation_samples']
prior_I_samples = np.array(prior_samples[0:nr_samples])
prior_isi = np.array(prior_obs[0:nr_samples])
real_I = []
rec_I = []
spikes = []
for sample in tqdm(range(len(prior_I_samples))):
# Simulate real_I
c_real_I = prior_I_samples[sample]
c_real_isi = prior_isi[sample]
if c_real_isi[0] > 0:
c_spikes = c_real_isi[2]
x = np.array([c_real_isi])
posterior.set_default_x(x)
temp_samples = \
posterior.sample((sbi_params['nr_posterior_samples'],),
show_progress_bars=False)
prob = posterior.log_prob(temp_samples)
top_prob = np.argmax(prob)
c_rec_I = temp_samples[top_prob].numpy()
# Append everything to list
real_I.append(c_real_I)
rec_I.append(c_rec_I)
spikes.append(c_spikes)
spikes = np.array(spikes)
real_I = np.array(real_I)
rec_I = np.array(rec_I)
diff_I = real_I - rec_I
# Results
results_validation = {
'real_I': real_I,
'rec_I': rec_I,
'spikes': spikes,
'diff_I': diff_I}
return results_validation
def compute_full_isi_stats(single_ts):
"""Calculate moments of isi distribution."""
nr_spikes = len(single_ts)
if nr_spikes < 3:
std = 0
mu = 0
log_std = 0
log_mu = 0
cv = 0
else:
isi = np.diff(single_ts)
std = np.std(isi)
mu = np.mean(isi)
stats = compute_isi_stats(single_ts)
log_std = stats[0]
log_mu = stats[1]
cv = std/mu
return pd.Series([nr_spikes, std, mu, log_std, log_mu, cv])
def add_isi_stats(trial_dataset):
"""Add pre and post ISI stats for each trial in dataset."""
# Add isi stats pre
columns_pre = ['nr_spikes_pre', 'isi_std_pre',
'isi_mu_pre', 'log_isi_std_pre',
'log_isi_mu_pre', 'cv_pre']
trial_dataset[columns_pre] = \
trial_dataset['spikes_pre'].apply(compute_full_isi_stats)
# Add isi stats post
columns_post = ['nr_spikes_post', 'isi_std_post',
'isi_mu_post', 'log_isi_std_post',
'log_isi_mu_post', 'cv_post']
trial_dataset[columns_post] = \
trial_dataset['spikes_post'].apply(compute_full_isi_stats)
# Add difference isi_stats
trial_dataset['isi_std_diff'] = \
trial_dataset['isi_std_post'] - trial_dataset['isi_std_pre']
trial_dataset['isi_mu_diff'] = \
trial_dataset['isi_mu_post'] - trial_dataset['isi_mu_pre']
return trial_dataset
def identify_bursts(spike_train):
"""Identify bursting ISI in single spike train."""
if len(spike_train) < 5:
burstyness = 0
else:
isi = np.diff(spike_train)
mean_isi = np.mean(isi)
low_isi = isi[isi < mean_isi]
ML = np.mean(low_isi)
# Burstyness
burst_isi = low_isi[low_isi < ML]
nr_bursts = len(burst_isi)
burstyness = nr_bursts/len(isi)
return burstyness
def add_burstyness_measure(df):
"""Compute the burst measure for each trial period."""
nr_trials = len(df)
for pre_post in ["pre", "post"]:
burstyness_list = []
for n in range(nr_trials):
test_train = df[f'spikes_{pre_post}'].iloc[n]
burstyness = identify_bursts(test_train)
burstyness_list.append(burstyness)
df[f'burst_{pre_post}'] = burstyness_list
return df
def add_change_scores_to_fit_trials(df):
"""Add change scores for fit trials."""
# Inputs
df['input_mu_diff'] = df['input_mu_post'] - df['input_mu_pre']
df['input_std_diff'] = df['input_std_post'] - df['input_std_pre']
# Voltages
df['voltages_mu_diff'] = df['voltages_mu_post'] - df['voltages_mu_pre']
df['voltages_std_diff'] = df['voltages_std_post'] - df['voltages_std_pre']
return df
def add_condition_labels(df):
"""Add condition labels (modality & intensity) to df."""
# Modality
df['modality'] = np.zeros(len(df))
aud = df['trialType'] == 'Y'
vis = df['trialType'] == 'X'
aud_vis = df['trialType'] == 'C'
catch = df['trialType'] == 'P'
df.loc[aud, 'modality'] = 'auditory'
df.loc[vis, 'modality'] = 'visual'
df.loc[aud_vis, 'modality'] = 'audio-visual'
df.loc[catch, 'modality'] = 'catch'
df['condition'] = np.zeros(len(df))
AC = df['audioFreqChangeNorm']
VC = df['visualOriChangeNorm']
no_change = (AC == 1) & (VC == 1)
thresh = ((AC == 2) & (VC == 1)) | ((AC == 1) & (VC == 2)) |\
((AC == 2) & (VC == 2)) | ((AC == 2) & (VC == 2))
maximum = ((AC == 3) & (VC == 1)) | ((AC == 1) & (VC == 3)) |\
((AC == 3) & (VC == 3)) | ((AC == 3) & (VC == 3))
both = ((AC == 3) & (VC == 2)) | ((AC == 2) & (VC == 3))
df.loc[no_change, 'condition'] = 'no_change'
df.loc[thresh, 'condition'] = 'thresh'
df.loc[maximum, 'condition'] = 'max'
df.loc[both, 'condition'] = 'mix'
return df
def filter_and_flag_trials(sim_params, data_params, trial_dataset):
"""Flag trials for fitting."""
# Good Spikes
min_cutoff = (sim_params['simtime']/1000) * \
data_params['min_fr_in_trial']
max_cutoff = (sim_params['simtime']/1000) * \
data_params['max_fr_in_trial']
good_spikes_pre = \
(trial_dataset['nr_spikes_pre'] > min_cutoff) & \
(trial_dataset['nr_spikes_pre'] < max_cutoff)
good_spikes_post = \
(trial_dataset['nr_spikes_post'] > min_cutoff) & \
(trial_dataset['nr_spikes_post'] < max_cutoff)
trial_dataset['good_spikes'] = good_spikes_pre & good_spikes_post
# Good trial
trial_dataset['fit_trial'] = \
trial_dataset['good_spikes']
return trial_dataset
def save_thing(name, thing, save_folder, plot_folder):
"""Save something results."""
for folder in [save_folder, plot_folder]:
# Validation
f_name = folder + "/" + name + ".pkl"
with open(f_name, "wb") as handle:
pickle.dump(thing, handle)
def load_or_create_posterior(run_params, sbi_params, sim_params,
data_params, neuron_params,
plot_params, save_folder,
data_folder):
"""Load or create posterior and sample prior parameters for validation."""
if run_params['fresh_posterior']:
posterior, simulator, prior_samples, prior_obs = \
create_posterior(sbi_params, sim_params, neuron_params)
save_thing('posterior', posterior, save_folder, data_folder)
save_thing('simulator', simulator, save_folder, data_folder)
save_thing('prior_obs', prior_obs, save_folder, data_folder)
save_thing('prior_samples', prior_samples, save_folder, data_folder)
else:
try:
# Simulator
file_name = data_folder + '/simulator.pkl'
unpickle_sim = open(file_name, 'rb')
simulator = pickle.load(unpickle_sim)
# Posterior
file_name = data_folder + '/posterior.pkl'
unpickle_post = open(file_name, 'rb')
posterior = pickle.load(unpickle_post)
# Prior_obs
file_name = data_folder + '/prior_obs.pkl'
unpickle_df = open(file_name, 'rb')
prior_obs = pickle.load(unpickle_df)
# Prior_samples
file_name = data_folder + '/prior_samples.pkl'
unpickle_df = open(file_name, 'rb')
prior_samples = pickle.load(unpickle_df)
except FileNotFoundError:
print("""Did not find posterior ... Creating new one.""")
posterior, simulator, prior_samples, prior_obs = \
create_posterior(sbi_params, sim_params, neuron_params)
save_thing('prior_obs', prior_obs, save_folder, data_folder)
save_thing('prior_samples', prior_samples, save_folder, data_folder)
save_thing('posterior', posterior, save_folder, data_folder)
save_thing('simulator', simulator, save_folder, data_folder)
else:
print("Loading previous Posterior, Simulator & Prior")
return posterior, simulator, prior_samples, prior_obs
def load_or_create_trial_dataset(run_params, sbi_params, sim_params,
data_params, neuron_params,
plot_params, save_folder,
data_folder):
"""Load or create trial dataset."""
# Create new trial dataset
if run_params['fresh_trial_data']:
print("creating new trial database")
trial_dataset = create_trial_dataset(sim_params, data_params)
trial_dataset = add_isi_stats(trial_dataset)
trial_dataset = add_condition_labels(trial_dataset)
save_thing('trial_data', trial_dataset, save_folder, data_folder)
else:
try:
# Data
file_name = data_folder + '/trial_data.pkl'
unpickle_df = open(file_name, 'rb')
trial_dataset = pickle.load(unpickle_df)
except FileNotFoundError:
print("""Did not find Trial Database ... Creating new one.""")
trial_dataset = create_trial_dataset(sim_params,
data_params)
trial_dataset = add_isi_stats(trial_dataset)
trial_dataset = add_condition_labels(trial_dataset)
save_thing('trial_data', trial_dataset, save_folder, data_folder)
else:
print("loaded already existing trial database")
return trial_dataset
def infer_parameters_for_all_trials(run_params, sbi_params, sim_params,
data_params, neuron_params,
plot_params, save_folder,
data_folder, posterior, trial_dataset):
"""Load or create posterior and sample prior parameters for validation."""
if run_params['fresh_fitting']:
print("Fitting all trials")
fit_trial_dataset = perform_inference(sbi_params,
sim_params,
data_params,
neuron_params,
posterior,
trial_dataset)
fit_trial_dataset = add_change_scores_to_fit_trials(fit_trial_dataset)
save_thing('fit_trial_data', fit_trial_dataset,
save_folder, data_folder)
else:
try:
# Fit Data
file_name = data_folder + '/fit_trial_data.pkl'
unpickle_df = open(file_name, 'rb')
fit_trial_dataset = pickle.load(unpickle_df)
except FileNotFoundError:
print("""Did not find Fitted Trials. Fitting new trials.""")
fit_trial_dataset = perform_inference(sbi_params,
sim_params,
data_params,
neuron_params,
posterior,
trial_dataset)
fit_trial_dataset = \
add_change_scores_to_fit_trials(fit_trial_dataset)
save_thing('fit_trial_data', fit_trial_dataset,
save_folder, data_folder)
else:
print("loaded already existing fit trial database")
def perform_validation(run_params, sbi_params, sim_params,
data_params, neuron_params,
plot_params, save_folder,
data_folder, posterior, prior_samples,
prior_obs):
"""Run validation procedure on prior parameters and observations."""
if run_params['fresh_validation']:
validation_results = prior_val(sbi_params, sim_params,
neuron_params, posterior,
prior_samples, prior_obs)
save_thing('validation_results', validation_results,
save_folder, data_folder)
else:
pass
def main(run_params, sbi_params, sim_params,
data_params, neuron_params,
plot_params, save_folder, data_folder):
"""Perform Sbi."""
# Setting seed
np.random.seed(sim_params['numpy_seed'])
_ = torch.manual_seed(sbi_params['sbi_seed'])
posterior, simulator, prior_samples, prior_obs = \
load_or_create_posterior(run_params, sbi_params, sim_params,
data_params, neuron_params,
plot_params, save_folder,
data_folder)
trial_dataset = \
load_or_create_trial_dataset(run_params, sbi_params, sim_params,
data_params, neuron_params,
plot_params, save_folder,
data_folder)
trial_dataset = \
filter_and_flag_trials(sim_params, data_params, trial_dataset)
infer_parameters_for_all_trials(run_params, sbi_params, sim_params,
data_params, neuron_params,
plot_params, save_folder, data_folder,
posterior, trial_dataset)
perform_validation(run_params, sbi_params, sim_params,
data_params, neuron_params,
plot_params, save_folder,
data_folder, posterior,
prior_samples, prior_obs)