TransformedRV object is not Callable Error - Non-Linear Regression

Questions
1

G’day Team
I am 3wks old in Python. Trying to implement bayes with pymc3, but i run into error and would appreciate any help i can get…

Prior

$$p(\sigma_{ci}) = \frac{1}{(\sigma_{ci ; upper} - \sigma_{ci ;lower})}$$

$$p(m_i) = \frac{1}{(m_{i ; upper} - m_{i ; lower})}$$

$$p(\sigma) = \frac{1}{100stdev(\sigma_{1 ; data}) - 0.01stdev(\sigma_{1; data})}$$

$$p(\nu) = \frac{1}{29}e^{-\frac{1}{29}(\nu-1)}$$

$$p(\sigma_{ci},m_i,\sigma,\nu) = p(\sigma_{ci})p(m_i)p(\sigma)p(\nu)$$

Likelihood

$$ If >\sigma_{3;data};>0:\
\sigma_{1;model};=;\sigma_{3;data} + \sigma_{ci}\left(m_i\frac{\sigma_{3;data}}{\sigma_{ci}} + 1\right)^{0.5 }$$

$$ error = \sigma_{1 ; data} - \sigma_{1 ; model}$$

$$ If >\sigma_{3;data};<0:\
\sigma_{3;model};=;\frac{\sigma_{ci}}{2}\left(m_i - \sqrt{{m_i}^2 + 4}\right)$$

$$ error = \sigma_{3 ; data} - \sigma_{3 ; model}$$

$$p(data|\sigma_{ci},m_i,\sigma,\nu) = \prod_{j=1}^{n} \frac{\Gamma(\frac{\nu + 1}{2})}{\Gamma(\frac{\nu}{2})\sqrt{\pi\nu\sigma}} \left[1+\frac{1}{\nu}\left(\frac{error_j}{\sigma}\right)^2 \right]^{-\frac{\nu+1}{2}}$$

my code implementation…

with Model() as HB_model:
    
    # Priors
    σ_ci = Uniform('σ_ci', 0.2,120)
    m_i = Uniform('m_i', 1,50)
    σ = Uniform('σ', 0.22, 2200)
    ν = Exponential('ν_minus_one', 1/29.) + 1
    
    #Likelihood
    
    for σ1_data in σ1:
        for σ3_data in σ3:
            if σ3_data > 0:
                σ1_model = σ3_data + σ_ci(m_i(σ3_data/σ_ci)+1)**0.5
                error = σ1_data - σ1_model
            elif σ3_data < 0:
                σ3_model = (σ_ci/2)(m_i-(m_i**2+4)**0.5)
                error = σ3_data - σ3_model
    
    HB_like = StudentT('HB_like', nu=ν, sd=σ, mu=error, observed = 'esatxl')
    trace_HB = sample(5000, random_seed=RANDOM_SEED)

i get the below error below: Can you please help?

TypeError                                 Traceback (most recent call last)
<ipython-input-34-0d41d0e912f5> in <module>()
     12         for σ3_data in σ3:
     13             if σ3_data > 0:
---> 14                 σ1_model = σ3_data + σ_ci(m_i(σ3_data/σ_ci)+1)**0.5
     15                 error = σ1_data - σ1_model
     16             elif σ3_data < 0:

TypeError: 'TransformedRV' object is not callable
2

As the error message read, RVs are not callable. From the description of your model, it seems it should be a multiplication? If that’s the case, you should do something like m_i*(σ3_data/σ_ci) instead of m_i(σ3_data/σ_ci)

3

Thanks. I don’t think it is the multiplication - same error occurs. I am not sure if it has to do with passing two columns sig1 and sig3 to the likelihood in the form of the ‘error’?

4

Also, you can not pass string as observed :slight_smile:

5

Emcee_to_PyMC3.py (17.7 KB)

Hi Junpeng

continuing with our previous discussion, please find attached a file containing my struggle to implement an emcee code in pymc3. You have already assisted me on the pymc3 coding part…but i don’t seem to be able to replicate the results.

Any assistance with this will be greatly appreciated
Liwi

6

You really should not be using emcee. NUTS is your friend and if you dong have gradient, try SMC

If you insist to try emcee, here is some previous effort: https://github.com/pymc-devs/pymc3/pull/2253

7

agreed, if you check the code, now trying to replicate in pymc3. at your convenience please have a look, at the moment not getting similar results