def anlPrior1():
pois = ss.poisson
pois4 = {}
fib3 = {}
for i in range(101):
pois4[i] = 0
fib3[i] = 0
for i in range(101):
prob = pois.pmf(i,4)
pois4[i] = prob
if i < 5:
fib3[fib1(3*i)] = prob
fib3 = stocPy.norm(fib3)
p = pois.cdf(3,4)
print sum(pois4.values())
print sorted(fib3.items())
print sum(fib3.values())
l2 = {}
for v1, p1 in fib3.items():
poisCur = {}
for i in range(101):
prob = pois.pmf(i,v1)
if math.isnan(prob):
prob = 0
print v1, i
poisCur[i] = prob
#print v1, v2, p1, p2
for v2, p2 in poisCur.items():
try:
l2[v1+v2] += p1*p2
except:
l2[v1+v2] = p1*p2
l2 = stocPy.norm(l2)
print sorted(l2.items())
print sum(l2.values())
l = {}
for k,v in l2.items():
l[k] = v * (1-p)
try:
l[6] += p
except:
l[6] = p
print sum(l.values())
plotDict(l, 2000)
def anlLik(plot=True, trans=True, twoDim = True):
rng = 15
pois = ss.poisson
pois4 = {}
for i in range(rng):
pois4[i] = pois.pmf(i, 4)
lik = {}
for r, pr in pois4.items():
for p, pp in pois4.items():
if r > 4:
l = 6
else:
l = fib0(3*r) + p
pl = pois.pmf(6, l)
if r > 4 and trans: #2nd poisson not evaluated
prob = pr*pl
else:
prob = pr*pp*pl
if r == 0 and p == 0:
prob = 0
if twoDim:
lik[(r,p)] = prob
else:
try:
lik[r] += prob
except:
lik[r] = prob
if plot:
if twoDim:
Xs2, Ys2 = np.meshgrid(range(rng),range(rng))
print len(Xs2), len(Ys2)
Zs2 = []
for i in range(len(Xs2)):
Zs2.append([])
for j in range(len(Ys2)):
Zs2[i].append(lik[Xs2[i][j], Ys2[i][j]])
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(Xs2, Ys2, Zs2, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=0)
plt.xlabel("pois1", size=20)
plt.ylabel("pois2", size=20)
ax.set_zlabel("Trace likelihood", size=20)
plt.title("Trace likelihood when ignoring trans-dimensionality", size=20)
else:
Xs = []
Ys = []
lik = stocPy.norm(lik)
[(Xs.append(x), Ys.append(y)) for x,y in sorted(lik.items())]
plt.plot(Xs, Ys, 'D')
plt.xlabel("pois1", size=20)
plt.ylabel("Probability", size=20)
plt.title("Posterior implied by ignoring trans-dimensionality", size=22)
plt.show()
return lik
def getMixExpMovement(d, depths, weights = None):
if not weights:
weights = [1.0 for i in range(len(depths))]
weights = stocPy.norm(weights)
mix = 0
for i in range(len(depths)):
mix += weights[i] * getExpMovement(d, depths[i])
return mix
def anlPost(data, ps, prior = ss.uniform(0,20).pdf):
probs = {}
for p in ps:
val = prior(p)
if val > 0:
ep = math.exp(-float(p))
for d in data:
val *= float(p)**float(d) * ep / math.factorial(float(d))
probs[p] = val
probs = stocPy.norm(probs)
return probs
def getPost(model, start, end, inc, aprox=True, show = True, fn=None, rfn = None, data=None):
xs = []
ys = []
if rfn:
with open(rfn,'r') as f:
xs, ys = cPickle.load(f)
else:
for m in np.arange(start, end+inc, inc):
xs.append(m)
if aprox:
ys.append(getLikAprox(model, m, data=data))
else:
ys.append(getLikExact(model, m))
if aprox and (model < 5 or model == 9):
ys = stocPy.norm(ys)
else:
print ys
corr = 1500
print [math.e**(y + corr) for y in ys]
ys = stocPy.norm([math.e**(y + corr) for y in ys])
def anlPrior():
pois = ss.poisson
pois4 = {}
fib3 = {}
for i in range(101):
pois4[i] = 0
fib3[i] = 0
for i in range(101):
prob = pois.pmf(i,4)
pois4[i] = prob
if i < 5:
fib3[fib0(3*i)] = prob
fib3 = stocPy.norm(fib3)
p = pois.cdf(3,4)
print sum(pois4.values())
print sorted(fib3.items())
print sum(fib3.values())
l2 = {}
for v1, p1 in pois4.items():
for v2, p2 in fib3.items():
try:
l2[v1+v2] += p1*p2
except:
l2[v1+v2] = p1*p2
print sum(l2.values())
l = {}
for k,v in l2.items():
l[k] = v * (1-p)
try:
l[6] += p
except:
l[6] = p
print sum(l.values())
plotDict(l, 2000)
def getPost(start, end, inc, show = True, fn=None, rfn = None):
xs = []
ys = []
if rfn:
with open(rfn,'r') as f:
xs, ys = cPickle.load(f)
else:
for m in np.arange(start, end+inc, inc):
xs.append(m)
ys.append(ss.norm.pdf(9, m, math.sqrt(2)) * ss.norm.pdf(8, m, math.sqrt(2)) * ss.norm.pdf(m, 1, math.sqrt(5)))
ys = stocPy.norm(ys)
if show:
plt.plot(xs,ys, linewidth=3)
plt.ylabel("Probability", size=20)
plt.xlabel("x", size=20)
plt.title("True Posterior for MarsagliaMean model", size=30)
plt.show()
if fn:
with open(fn,'w') as f:
cPickle.dump((xs,ys),f)
return dict(zip(xs, ys))
def anlPost(disp=True, rep=1, cond=6, size=21):
pois = ss.poisson
pois4 = {}
for i in range(size):
prob = pois.pmf(i,4)
pois4[i] = prob
rs = {}
for r in range(size):
pr = pois4[r]
l = {}
if r > 4:
l[6] = 1
else:
f = fib0(3*r)
for k,v in pois4.items():
l[k+f] = v
assert(abs(sum(l.values()) - 1) < 0.0001)
for val,prob in l.items():
#print r, val, pois.pmf(6,val), prob
condProb = 1
for i in range(rep):
condProb *= pois.pmf(cond,val)
pl = condProb * prob
if math.isnan(pl):
pl = 0
try:
rs[r] += pl*pr
except:
rs[r] = pl*pr
rs = stocPy.norm(rs)
if disp:
print sorted(rs.items())
print sum(rs.values())
plotDict(rs)
return rs
def getPost(ds, a, fn=None):
crp = stocPy.CRP(a)
parts = allParts(ds)
post = {}
for p in range(len(parts)):
part = parts[p]
ll = crp.logpmf(part)
if p % 1000 == 0:
print p, part, ll,
sys.stdout.flush()
for cl in part:
ll += getLL(cl, fn)
try:
post[len(part)].append(ll)
except:
post[len(part)] = [ll]
if p % 1000 == 0:
print ll
sys.stdout.flush()
post = dict([(k, sum(map(lambda x: math.e**x, v))) for (k, v) in post.items()])
print post
post = stocPy.norm(post)
return post