# Marginal likelihood implementation and measurement uncertainty

**URL:** <https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029>\
**Category:** Questions\
**Created:** [October 28, 2019, 2:07pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029 "2019-10-28T14:07:57Z")\
**Posts on this page:** 13\
**Page:** 1

<div class="post-metadata">

**Author:** ![Bobrepoman](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bobrepoman/32/2255_2.png) [@Bobrepoman](https://discourse.pymc.io/u/Bobrepoman)\
**Post date:** [October 28, 2019, 2:07pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/1 "2019-10-28T14:07:58Z")

</div>

Hey all.

I have been trying to implement GP regression in a similar fashion to the example here [Link](https://docs.pymc.io/notebooks/GP-Marginal.html#Marginal-Likelihood-Implementation)  
and it works fine, but i want to include the measured uncertainties in my y-values in my GP regression. The model i have is:

```
with pm.Model() as model:
ℓ = pm.Uniform('ℓ', lower=np.sqrt(5.0), upper=6.0*50.0*np.sqrt(2.0)) 
η = pm.Uniform('η', lower=0.0, upper=1.0)

cov = η**2 * pm.gp.cov.Exponential(1, ℓ)
gp = pm.gp.Marginal(cov_func=cov).

σ = pm.HalfNormal("σ", sigma=np.sqrt(np.pi/(np.pi-2)))

y_ = gp.marginal_likelihood("y", X=X, y=y, noise=σ)

mp = pm.find_MAP()

```

My question is if it is possible to include measurement uncertainties either by using weights (1/yerr^2) or like this example [Link 2](https://stackoverflow.com/questions/49414416/including-measurement-uncertainties-in-pymc3) by subtracting the observed error?

My goal is to get a model where the standard deviation of the predictive mean approaches the measurement uncertainty near data points.

---

<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [October 31, 2019, 2:33pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/2 "2019-10-31T14:33:02Z")

</div>

No sure I understand, is the the measured uncertainties known? If so you can build a latent GP and use that as the mu and plugin your measure uncertainties as sigma to a Gaussian

---

<div class="post-metadata">

**Author:** ![Bobrepoman](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bobrepoman/32/2255_2.png) [@Bobrepoman](https://discourse.pymc.io/u/Bobrepoman)\
**Post date:** [October 31, 2019, 10:56pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/3 "2019-10-31T22:56:28Z")

</div>

I have data points with known measurement uncertainties.

I know that the data i have is the sum of a function f(x) and a Gaussian white noise process with zero mean and variance equal to 1. I also know the specific covariance function for f(x) (a CAR(1) model).

I could definitely write up the the likelihood function as a Gaussian let me try that.

---

<div class="post-metadata">

**Author:** ![Bobrepoman](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bobrepoman/32/2255_2.png) [@Bobrepoman](https://discourse.pymc.io/u/Bobrepoman)\
**Post date:** [November 1, 2019, 1:08am UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/4 "2019-11-01T01:08:17Z")

</div>

Okay so i have tried to use the latent variable method with a normal likelihood and it seems to work great! Thanks a bunch for the help. One of the things i noticed is the sampling time has increased from 3 min to 48 min going from the marginal likelihood method, my guess is that is because it now has to sample f\_rotated as well. Here is my approach:

```
with pm.Model() as model:
ℓ = pm.Uniform('ℓ', lower=np.sqrt(5.0), upper=6.0*50.0*np.sqrt(2.0))
η = pm.Uniform('η', lower=0.0, upper=1.0)

cov = η**2 * pm.gp.cov.Exponential(1, ℓ)
gp = pm.gp.Latent(cov_func=cov)

f = gp.prior("f", X=X)

y_ = pm.Normal("y", mu=f, sd=yerr, observed=y)
trace = pm.sample(2000) #The NUTS sampling 

```

Say i wanted to include a “noise boost” parameter to the likelihood how would i go about that? I have tried to include it as a parameter and multiply it with yerr

```
k = pm.Uniform('k', lower=1.0, upper=2.0)
y_ = pm.Normal("y", mu=f, sd=k*yerr, observed=y)

```

But in that case i get an ValueError because i am setting an array element with a sequence. Mathematically i am thinking something like the following:  
 ![likelihoodfunction](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/0/07fe16865cdc5b29cc650f458eec358ad67da80d.png)

---

<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [November 1, 2019, 7:49am UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/5 "2019-11-01T07:49:14Z")

</div>

Glad you make it work! Yes it is likely slower because there are more optimization in marginal.

`k*yerr` is a scalar multiple by a array so it should work… what is the full error message?

---

<div class="post-metadata">

**Author:** ![Bobrepoman](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bobrepoman/32/2255_2.png) [@Bobrepoman](https://discourse.pymc.io/u/Bobrepoman)\
**Post date:** [November 1, 2019, 1:52pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/6 "2019-11-01T13:52:18Z")

</div>

The full error is

```
ValueError Traceback (most recent call last)
<ipython-input-5-f8e03522a0bb> in <module>
 37 k = pm.Uniform('k', lower=1.0, upper=2.0)#pm.HalfNormal("σ", 
 sigma=np.sqrt(np.pi/(np.pi-2)))#pm.HalfCauchy("σ", beta=0.5)
 38 
---> 39 y_ = pm.Normal("y", mu=f, sd=k*yerr, observed=y)
 40 #mp = pm.find_MAP() #The Maximum A Posteriori values
 41 trace = pm.sample(2000) #The NUTS sampling

~\Anaconda3\lib\site-packages\pymc3\distributions\distribution.py in __new__ (cls, name, *args, **kwargs)
 43 raise TypeError("observed needs to be data but got: {}".format(type(data)))
 44 total_size = kwargs.pop('total_size', None)
---> 45 dist = cls.dist(*args, **kwargs)
 46 return model.Var(name, dist, data, total_size)
 47 else:

~\Anaconda3\lib\site-packages\pymc3\distributions\distribution.py in dist(cls, *args, **kwargs)
 54 def dist(cls, *args, **kwargs):
 55 dist = object. __new__ (cls)
---> 56 dist. __init__ (*args, **kwargs)
 57 return dist
 58 

~\Anaconda3\lib\site-packages\pymc3\distributions\continuous.py in __init__ (self, mu, sigma, tau, sd, **kwargs)
463 if sd is not None:
464 sigma = sd
--> 465 tau, sigma = get_tau_sigma(tau=tau, sigma=sigma)
466 self.sigma = self.sd = tt.as_tensor_variable(sigma)
467 self.tau = tt.as_tensor_variable(tau)

~\Anaconda3\lib\site-packages\pymc3\distributions\continuous.py in get_tau_sigma(tau, sigma)
128 sigma = 1. * sigma
129 
--> 130 return floatX(tau), floatX(sigma)
131 
132 

~\Anaconda3\lib\site-packages\pymc3\theanof.py in floatX(X)
 63 """
 64 try:
---> 65 return X.astype(theano.config.floatX)
 66 except AttributeError:
 67 # Scalar passed

ValueError: setting an array element with a sequence.

```

Now the interesting thing is that is use

```
sd=yerr*k

```

I get a different error where it is trying to convert the array to a tensor

```
KeyError Traceback (most recent call last)
~\Anaconda3\lib\site-packages\theano\tensor\type.py in dtype_specs(self)
268 'complex64': (complex, 'theano_complex64', 'NPY_COMPLEX64')
--> 269 }[self.dtype]
270 except KeyError:

KeyError: '>f4'

During handling of the above exception, another exception occurred:

TypeError Traceback (most recent call last)
~\Anaconda3\lib\site-packages\theano\tensor\basic.py in constant(x, name, ndim, dtype)
245 try:
--> 246 ttype = TensorType(dtype=x_.dtype, broadcastable=bcastable)
247 if not constant.enable:

~\Anaconda3\lib\site-packages\theano\tensor\type.py in __init__ (self, dtype, broadcastable, name, sparse_grad)
 50 self.broadcastable = tuple(bool(b) for b in broadcastable)
---> 51 self.dtype_specs() # error checking is done there
 52 self.name = name

~\Anaconda3\lib\site-packages\theano\tensor\type.py in dtype_specs(self)
271 raise TypeError("Unsupported dtype for %s: %s"
--> 272 % (self. __class__. __name__ , self.dtype))
273 

TypeError: Unsupported dtype for TensorType: >f4

During handling of the above exception, another exception occurred:

TypeError Traceback (most recent call last)
~\Anaconda3\lib\site-packages\theano\tensor\basic.py in as_tensor_variable(x, name, ndim)
193 try:
--> 194 return constant(x, name=name, ndim=ndim)
195 except TypeError:

~\Anaconda3\lib\site-packages\theano\tensor\basic.py in constant(x, name, ndim, dtype)
265 except Exception:
--> 266 raise TypeError("Could not convert %s to TensorType" % x, type(x))
267 

TypeError: ('Could not convert [0.00485131 0.00487679 0.01067159 0.00494462 0.00560853 0.00562166\n 0.00541271 0.0053869 0.00802224 0.00387515 0.00430117 0.00468504\n 0.00432127 0.00454601 0.00390065 0.00520721 0.00578553 0.00405268\n 0.00448521 0.00422477 0.00439943 0.00501591 0.00491921 0.00525864\n 0.0170183 0.0238815 0.00497915 0.0048724 0.00481433 0.00570282\n 0.02026841 0.00499057 0.00472333 0.00661963 0.00475204 0.00480907\n 0.00482606 0.00537344 0.00541538 0.00564796 0.00554904 0.00553942\n 0.01326797 0.00609176 0.00613547 0.00639062 0.00638895 0.00599033\n 0.00716414] to TensorType', <class 'numpy.ndarray'>)

During handling of the above exception, another exception occurred:

AsTensorError Traceback (most recent call last)
<ipython-input-6-f5c682bfdcff> in <module>
 37 k = pm.Uniform('k', lower=1.0, upper=2.0)#pm.HalfNormal("σ", sigma=np.sqrt(np.pi/(np.pi-2)))#pm.HalfCauchy("σ", beta=0.5)
 38 
---> 39 y_ = pm.Normal("y", mu=f, sd=yerr*k, observed=y)
 40 #mp = pm.find_MAP() #The Maximum A Posteriori values
 41 trace = pm.sample(2000) #The NUTS sampling

~\Anaconda3\lib\site-packages\theano\tensor\var.py in __rmul__ (self, other)
231 
232 def __rmul__ (self, other):
--> 233 return theano.tensor.basic.mul(other, self)
234 
235 def __rdiv__ (self, other):

~\Anaconda3\lib\site-packages\theano\gof\op.py in __call__ (self, *inputs, **kwargs)
613 """
614 return_list = kwargs.pop('return_list', False)
--> 615 node = self.make_node(*inputs, **kwargs)
616 
617 if config.compute_test_value != 'off':

~\Anaconda3\lib\site-packages\theano\tensor\elemwise.py in make_node(self, *inputs)
478 using DimShuffle.
479 """
 --> 480 inputs = list(map(as_tensor_variable, inputs))
481 out_dtypes, out_broadcastables, inputs = self.get_output_info(
482 DimShuffle, *inputs)

~\Anaconda3\lib\site-packages\theano\tensor\basic.py in as_tensor_variable(x, name, ndim)
198 except Exception:
199 str_x = repr(x)
--> 200 raise AsTensorError("Cannot convert %s to TensorType" % str_x, type(x))
201 
202 # this has a different name, because _as_tensor_variable is the

AsTensorError: ('Cannot convert [0.00485131 0.00487679 0.01067159 0.00494462 0.00560853 0.00562166\n 0.00541271 0.0053869 0.00802224 0.00387515 0.00430117 0.00468504\n 0.00432127 0.00454601 0.00390065 0.00520721 0.00578553 0.00405268\n 0.00448521 0.00422477 0.00439943 0.00501591 0.00491921 0.00525864\n 0.0170183 0.0238815 0.00497915 0.0048724 0.00481433 0.00570282\n 0.02026841 0.00499057 0.00472333 0.00661963 0.00475204 0.00480907\n 0.00482606 0.00537344 0.00541538 0.00564796 0.00554904 0.00553942\n 0.01326797 0.00609176 0.00613547 0.00639062 0.00638895 0.00599033\n 0.00716414] to TensorType', <class 'numpy.ndarray'>)
```

---

<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [November 1, 2019, 2:11pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/7 "2019-11-01T14:11:35Z")

</div>

Try casting yerr to a theano.share - there is something funny going on.

---

<div class="post-metadata">

**Author:** ![Bobrepoman](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bobrepoman/32/2255_2.png) [@Bobrepoman](https://discourse.pymc.io/u/Bobrepoman)\
**Post date:** [November 1, 2019, 3:01pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/8 "2019-11-01T15:01:50Z")

</div>

Okay so i defined the errors as a shared variable

```
from theano import shared
yerrs = shared(yerr)

```

Now the problem seems to be that i multiply the shared variable with the scalar

```
TypeError Traceback (most recent call last)
<ipython-input-25-474ba5c7f8de> in <module>
 40 k = pm.Uniform('k', lower=1.0, upper=2.0)#pm.HalfNormal("σ", sigma=np.sqrt(np.pi/(np.pi-2)))#pm.HalfCauchy("σ", beta=0.5)
 41 
---> 42 y_ = pm.Normal("y", mu=f, sd=k*yerrs, observed=y)
 43 
 44 trace = pm.sample(2000) #The NUTS sampling

TypeError: unsupported operand type(s) for *: 'TransformedRV' and 'SharedVariable'

```

But again if i do sd=yerrs\*k instead i get a different error

```
AsTensorError Traceback (most recent call last)
<ipython-input-26-fc78c0bbd20b> in <module>
 40 k = pm.Uniform('k', lower=1.0, upper=2.0)#pm.HalfNormal("σ", sigma=np.sqrt(np.pi/(np.pi-2)))#pm.HalfCauchy("σ", beta=0.5)
 41 
---> 42 y_ = pm.Normal("y", mu=f, sd=yerrs*k, observed=y)
 43 
 44 trace = pm.sample(2000) #The NUTS sampling

~\Anaconda3\lib\site-packages\theano\tensor\var.py in __rmul__ (self, other)
231 
232 def __rmul__ (self, other):
--> 233 return theano.tensor.basic.mul(other, self)
234 
235 def __rdiv__ (self, other):

~\Anaconda3\lib\site-packages\theano\gof\op.py in __call__ (self, *inputs, **kwargs)
613 """
614 return_list = kwargs.pop('return_list', False)
--> 615 node = self.make_node(*inputs, **kwargs)
616 
617 if config.compute_test_value != 'off':

~\Anaconda3\lib\site-packages\theano\tensor\elemwise.py in make_node(self, *inputs)
478 using DimShuffle.
479 """
--> 480 inputs = list(map(as_tensor_variable, inputs))
481 out_dtypes, out_broadcastables, inputs = self.get_output_info(
482 DimShuffle, *inputs)

~\Anaconda3\lib\site-packages\theano\tensor\basic.py in as_tensor_variable(x, name, ndim)
156 if not isinstance(x.type, TensorType):
157 raise AsTensorError(
--> 158 "Variable type field must be a TensorType.", x, x.type)
159 
160 if ndim is None:

AsTensorError: ('Variable type field must be a TensorType.', <Generic>, <theano.gof.type.Generic object at 0x00000202C62B76A0>)
```

---

<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [November 1, 2019, 4:19pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/9 "2019-11-01T16:19:52Z")

</div>

Would you be able to share the notebook and data with me? I can take a closer look.

---

<div class="post-metadata">

**Author:** ![Bobrepoman](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bobrepoman/32/2255_2.png) [@Bobrepoman](https://discourse.pymc.io/u/Bobrepoman)\
**Post date:** [November 1, 2019, 4:42pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/10 "2019-11-01T16:42:21Z")

</div>

Gladly let me just make an example notebook

---

<div class="post-metadata">

**Author:** ![Bobrepoman](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bobrepoman/32/2255_2.png) [@Bobrepoman](https://discourse.pymc.io/u/Bobrepoman)\
**Post date:** [November 1, 2019, 5:07pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/11 "2019-11-01T17:07:36Z")

</div>

Okay so i found the error while creating the example notebook. The yerr array had “dtype=float32” and i had to convert it to “dtype=float” to work. I think it was the extra infomation about the dtype that was messing with the model since it looked like

```
array([0.00485131, 0.00487679, 0.01067159, 0.00494462, 0.00560853,
   0.00562166, 0.00541271, 0.0053869 , 0.00802224, 0.00387515,
   0.00430117, 0.00468504, 0.00432127, 0.00454601, 0.00390065,
   0.00520721, 0.00578553, 0.00405268, 0.00448521, 0.00422477,
   0.00439943, 0.00501591, 0.00491921, 0.00525864, 0.0170183 ,
   0.0238815 , 0.00497915, 0.0048724 , 0.00481433, 0.00570282,
   0.02026841, 0.00499057, 0.00472333, 0.00661963, 0.00475204,
   0.00480907, 0.00482606, 0.00537344, 0.00541538, 0.00564796,
   0.00554904, 0.00553942, 0.01326797, 0.00609176, 0.00613547,
   0.00639062, 0.00638895, 0.00599033, 0.00716414], dtype=float32)

```

while for the new one i have

```
yerr = np.array(magerr_ref1[mask], dtype=float)
yerr
array([0.00485131, 0.00487679, 0.01067159, 0.00494462, 0.00560853,
   0.00562166, 0.00541271, 0.0053869 , 0.00802224, 0.00387515,
   0.00430117, 0.00468504, 0.00432127, 0.00454601, 0.00390065,
   0.00520721, 0.00578553, 0.00405268, 0.00448521, 0.00422477,
   0.00439943, 0.00501591, 0.00491921, 0.00525864, 0.0170183 ,
   0.0238815 , 0.00497915, 0.0048724 , 0.00481433, 0.00570282,
   0.02026841, 0.00499057, 0.00472333, 0.00661963, 0.00475204,
   0.00480907, 0.00482606, 0.00537344, 0.00541538, 0.00564796,
   0.00554904, 0.00553942, 0.01326797, 0.00609176, 0.00613547,
   0.00639062, 0.00638895, 0.00599033, 0.00716414])

```

For those interested here is the full model:

```
import numpy as np
import pymc3 as pm

X=[[57690.156444],
   [57702.042152],
   [57714.09288],
   [57727.058406],
   [57785.33735],
   [57799.337204],
   [57835.345248],
   [57847.218598],
   [57870.38101],
   [57872.34736],
   [57887.334724],
   [57901.294798],
   [57913.261906],
   [57925.123674],
   [57937.187432],
   [57949.16307],
   [57962.127284],
   [57974.094412],
   [57987.048386],
   [58000.303966],
   [58018.23316],
   [58047.208566],
   [58072.050364],
   [58084.055702],
   [58127.353694],
   [58151.287814],
   [58166.326436],
   [58183.323268],
   [58222.31519],
   [58236.377956],
   [58237.3749525],
   [58250.340886],
   [58263.305154],
   [58276.365486],
   [58289.241552],
   [58307.182884],
   [58320.122346],
   [58332.115664],
   [58344.081428],
   [58356.048366],
   [58368.331064],
   [58380.28918],
   [58433.114668],
   [58445.050324],
   [58458.058774],
   [58517.347406],
   [58529.33535],
   [58541.3453],
   [58569.380416]]
X=np.reshape(X,(len(X),1))
y=[-0.04021454, -0.04408264, 0.00086784, -0.03276062, -0.09445763,
   -0.11571121, -0.0334301 , -0.08233452, -0.09807587, -0.02315331,
   -0.02507591, 0.00783348, -0.05967522, -0.03184891, -0.05742645,
    0.00561142, -0.02413559, -0.02518654, 0.01398849, 0. ,
    0.07386398, 0.09370232, 0.09769058, 0.05272102, 0.04765701,
    0.16421509, 0.0471611 , 0.00388718, -0.02775383, -0.0708313 ,
   -0.12369347, -0.07772446, -0.09989738, -0.11494827, -0.09436607,
   -0.0891819 , -0.01688957, 0.04362106, 0.03388023, 0.06066322,
    0.11610603, 0.12976837, 0.23965454, 0.04725456, 0.04477501,
    0.0041008 , 0.08264542, 0.02942657, 0.13908195]
yerr=[0.00485131, 0.00487679, 0.01067159, 0.00494462, 0.00560853,
   0.00562166, 0.00541271, 0.0053869 , 0.00802224, 0.00387515,
   0.00430117, 0.00468504, 0.00432127, 0.00454601, 0.00390065,
   0.00520721, 0.00578553, 0.00405268, 0.00448521, 0.00422477,
   0.00439943, 0.00501591, 0.00491921, 0.00525864, 0.0170183 ,
   0.0238815 , 0.00497915, 0.0048724 , 0.00481433, 0.00570282,
   0.02026841, 0.00499057, 0.00472333, 0.00661963, 0.00475204,
   0.00480907, 0.00482606, 0.00537344, 0.00541538, 0.00564796,
   0.00554904, 0.00553942, 0.01326797, 0.00609176, 0.00613547,
   0.00639062, 0.00638895, 0.00599033, 0.00716414]

with pm.Model() as model:
ℓ = pm.Uniform('ℓ', lower=np.sqrt(5.0), upper=50.0*np.sqrt(2.0))
η = pm.Uniform('η', lower=0.0, upper=1.0)

cov = η**2 * pm.gp.cov.Exponential(1, ℓ)
gp = pm.gp.Latent(cov_func=cov)

f = gp.prior("f", X=X)

k = pm.Uniform('k', lower=1.0, upper=2.0)

y_ = pm.Normal("y", mu=f, sd=k*yerr, observed=y)

trace = pm.sample(2000)
```

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<div class="post-metadata">

**Author:** ![Bobrepoman](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bobrepoman/32/2255_2.png) [@Bobrepoman](https://discourse.pymc.io/u/Bobrepoman)\
**Post date:** [November 1, 2019, 5:10pm UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/12 "2019-11-01T17:10:40Z")

</div>

Again thanks a bunch for the help =) I am going to work at trying to optimize the sampling time now, since i want to do a bunch of these of models.

---

<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [November 2, 2019, 7:43am UTC](https://discourse.pymc.io/t/marginal-likelihood-implementation-and-measurement-uncertainty/4029/13 "2019-11-02T07:43:19Z")

</div>

You are welcome! I guess you have some specific reason for the uniform prior, but otherwise, you really should use informative prior that will makes sampling much faster and your inference more robust in general.