def simulator(n, numTrials):
modelLikelihoods = dict()
posteriors = dict()
actualD = random.uniform(dFloat[0], dFloat[parameterGridDimension - 1])
actualTheta = np.random.uniform(thetaFloat[0], thetaFloat[parameterGridDimension - 1])
actualSigma = np.random.uniform(sigmaFloat[0], sigmaFloat[parameterGridDimension - 1])
trueD.append(actualD)
trueTheta.append(actualTheta)
trueSigma.append(actualSigma)
numModels = len(parameters)
for perm in parameters:
modelLikelihoods[tuple(perm)] = 0
posteriors[tuple(perm)] = 1.0 / numModels
trialConditions = []
for i in xrange(numTrials):
value_list = []
for i in xrange(nItems):
itemValue = random.choice(potential_values)
value_list.append(itemValue)
trialConditions.append(value_list)
# Run the simulation using known parameter values
RT, choice, fixItem, fixTime, fixRDV, uninterruptedLastFixTime, lst_of_item_values_dict = \
run_simulations(nItems, numTrials, trialConditions, actualD, actualTheta, actualSigma)
print("Computing Model " + str(n + 1) + ":" + str((actualD, actualTheta, actualSigma)))
for trial in xrange(numTrials):
print(trial)
trialChoice = choice[trial]
leftValue = lst_of_item_values_dict[0][trial]
rightValue = lst_of_item_values_dict[1][trial]
itemFixation = fixItem[trial]
timeOfFixations = fixTime[trial]
for perm in parameters:
trialdScaled, trialthetaScaled, trialsigmaScaled = tuple(perm)
triald = trialdScaled / 1000.
trialtheta = trialthetaScaled / 1000.
trialsigma = trialsigmaScaled / 1000.
likelihood = get_trial_likelihood(trialChoice, leftValue, rightValue, itemFixation, timeOfFixations, \
triald, trialtheta, trialsigma)
modelLikelihoods[tuple(perm)] = likelihood
# Get the denominator for normalizing the posteriors.
denominator = 0
for perm in parameters:
denominator += posteriors[tuple(perm)] * modelLikelihoods[tuple(perm)]
if denominator == 0:
continue
# Calculate the posteriors after this trial.
for perm in parameters:
prior = posteriors[tuple(perm)]
posteriors[tuple(perm)] = modelLikelihoods[tuple(perm)] * prior / denominator
optimalValues = max(posteriors.iteritems(), key=operator.itemgetter(1))[0]
optimald, optimaltheta, optimalsigma = optimalValues
return optimalValues
def main():
# Parameters
parameters = np.vstack(np.meshgrid(d, theta, sigma)).reshape(3,-1).T
numModels = len(parameters)
for perm in parameters:
modelLikelihoods[tuple(perm)] = 0
# We will assume a uniform prior over all models.
posteriors[tuple(perm)] = 1.0 / numModels
# Creates the item values to be used in the simulation
trialConditions = []
for i in range(numTrials):
value_list = []
for i in range(nItems):
itemValue = random.choice(potential_values)
value_list.append(itemValue)
trialConditions.append(value_list)
# Run the simulation using known parameter values
RT, choice, fixItem, fixTime, fixRDV, uninterruptedLastFixTime, lst_of_item_values_dict = \
run_simulations(nItems, numTrials, trialConditions, actuald, actualTheta, actualSigma)
for trial in xrange(numTrials):
print(trial)
trialChoice = choice[trial]
leftValue = lst_of_item_values_dict[0][trial]
rightValue = lst_of_item_values_dict[1][trial]
itemFixation = fixItem[trial]
timeOfFixations = fixTime[trial]
den = 0
for perm in parameters:
triald, trialtheta, trialsigma = tuple(perm)
likelihood = get_trial_likelihood(trialChoice, leftValue, rightValue, itemFixation, timeOfFixations,
triald, trialtheta, trialsigma)
modelLikelihoods[tuple(perm)] += np.log(likelihood)
prior = posteriors[tuple(perm)]
posteriors[tuple(perm)] = prior * likelihood
denominator = np.sum(posteriors.values())
if denominator != 0:
for perm in parameters:
posteriors[tuple(perm)] = posteriors[tuple(perm)] / denominator
# Marginalizing over the 3 parameters to plot separate posteriors.
for i in range(parameterGridDimension):
ds[d[i]] = 0
thetas[theta[i]] = 0
sigmas[sigma[i]] = 0
for perm in parameters:
x = perm[0] # d
y = perm[1] # theta
z = perm[2] # sigma
post = posteriors[tuple(perm)]
ds[x] += post
thetas[y] += post
sigmas[z] += post
def main():
# Generates all the permutation of models given a list for d, theta and sigma
parameters = np.vstack(np.meshgrid(d, theta, sigma)).reshape(3,-1).T
numModels = len(parameters)
# Initialize the likelihood and posteriors.
# - Posteriors are set to a uniform distribution
# - Likelihoods are set to 0.
for perm in parameters:
modelLikelihoods[tuple(perm)] = 0
# We will assume a uniform prior over all models.
posteriors[tuple(perm)] = 1.0 / numModels
# Creates the item values to be used in the simulation
trialConditions = []
for i in xrange(numTrials):
value_list = []
for i in xrange(nItems):
itemValue = random.choice(potential_values)
value_list.append(itemValue)
trialConditions.append(value_list)
# Run the simulation using known parameter values
RT, choice, fixItem, fixTime, fixRDV, uninterruptedLastFixTime, lst_of_item_values_dict = \
run_simulations(nItems, numTrials, trialConditions, actuald, actualTheta, actualSigma)
# Extract the data from the above simulation
for trial in xrange(numTrials):
print(trial)
trialChoice = choice[trial]
leftValue = lst_of_item_values_dict[0][trial]
rightValue = lst_of_item_values_dict[1][trial]
itemFixation = fixItem[trial]
timeOfFixations = fixTime[trial]
# Get the likelihood for each model and update the model likelihoods
for perm in parameters:
triald, trialtheta, trialsigma = tuple(perm)
likelihood = get_trial_likelihood(trialChoice, leftValue, rightValue, itemFixation, timeOfFixations,
triald, trialtheta, trialsigma)
modelLikelihoods[tuple(perm)] = likelihood
# Get the denominator for normalizing the posteriors.
denominator = 0
for perm in parameters:
denominator += posteriors[tuple(perm)] * modelLikelihoods[tuple(perm)]
if denominator == 0:
continue
# Calculate the posteriors after this trial.
for perm in parameters:
# The new prior is the previous posterior because that is the prior information we have.
# At the very start this will simply be the uniform distribution.
prior = posteriors[tuple(perm)]
posteriors[tuple(perm)] = modelLikelihoods[tuple(perm)] * prior / denominator
print("Done with Computation of Posteriors!")
# Marginalizing over the 3 parameters to plot separate posteriors.
for i in range(parameterGridDimension):
ds[d[i]] = 0
thetas[theta[i]] = 0
sigmas[sigma[i]] = 0
for perm in parameters:
x = perm[0] # d
y = perm[1] # theta
z = perm[2] # sigma
post = posteriors[tuple(perm)]
ds[x] += post
thetas[y] += post
sigmas[z] += post