# Problem with hyperbolic discount model

**URL:** <https://discourse.pymc.io/t/problem-with-hyperbolic-discount-model/8367>\
**Category:** Questions\
**Created:** [November 26, 2021, 2:47pm UTC](https://discourse.pymc.io/t/problem-with-hyperbolic-discount-model/8367 "2021-11-26T14:47:23Z")\
**Posts on this page:** 7\
**Page:** 1

<div class="post-metadata">

**Author:** ![aetius](https://avatars.discourse-cdn.com/v4/letter/a/c2a13f/32.png) [@aetius](https://discourse.pymc.io/u/aetius)\
**Post date:** [November 26, 2021, 2:47pm UTC](https://discourse.pymc.io/t/problem-with-hyperbolic-discount-model/8367/1 "2021-11-26T14:47:23Z")

</div>

Dear Pymc experts,

As a beginner of pymc3, I am learning how to use pymc3 to fit simple quantitative psychology/cognitive science models . Firstly, I want to try a simple hyperbolic discount model for intertemporal choice tas, I followed the procedure in this great post:  
[Fitting a simple Reinforcement Learning model to behavioral data with PyMC3 (Jupyter NB)](https://discourse.pymc.io/t/fitting-a-simple-reinforcement-learning-model-to-behavioral-data-with-pymc3-jupyter-nb/4651).  
However, there always is an error, as a layman, I don’t understand what is going wrong, can somebody help me fix this stupid and naive problem? Thanks.  
Here is my code:

```auto
import numpy as np
import pandas as pd
import pymc3 as pm
import seaborn as sns
import theano
from theano import tensor as t
# generate some fake data
def hyperbolic_rng(k,beta,ll_a,ll_t,ss_a,ss_t):
    dsv = ll_a / (1+k*ll_t) - ss_a / (1+k*ss_t)
    p = 1/(1+np.exp(-beta*dsv))
    size = p.size
    choice = np.random.binomial(1,p,size)
    return choice
ss_amount = np.random.normal(20,4,60)
ll_amount = ss_amount + 10
ss_time = np.random.binomial(1,0.5,60)*4
ll_time = np.concatenate([ss_time[0:30] +4,ss_time[30:] + 8]) 
fake_data = hyperbolic_rng(0.1,0.9,ll_amount,ll_time,ss_amount,ss_time)
def sv_diff(k,ll_amount,ll_delay,ss_amount,ss_delay):
    k = pm.math.exp(k)
    return ll_amount/(1+k*ll_delay)-ss_amount/(1+k*ss_delay)
def hyperbolic_llf(k,beta,ll_a,ll_t,ss_a,ss_t):
    #theano log likelihood function
    ll_amount_ = theano.shared(ll_amount)
    ss_amount_ = theano.shared(ss_amount)
    ll_delay_ = theano.shared(ll_time)
    ss_delay_ = theano.shared(ss_time)
    k = t.scalar('k')
    beta = t.scalar('beta')
    sv = sv_diff(k,ll_amount_,ll_delay_,ss_amount_,ss_delay_)
    sv_ = -sv * beta
    llf = pm.math.log(1/(1+pm.math.exp(sv_))) 
    neg_llf = -t.sum(llf)
    return neg_llf
with pm.Model() as m:
    k = pm.Normal('k', 0, 4)
    beta = pm.HalfNormal('beta', 10)
    like = pm.Potential('like', hyperbolic_llf(k, beta, ll_amount,ll_time,ss_amount,ss_time))
    tr = pm.sample()

```

And the error is:

```auto
TestValueError Traceback (most recent call last)
~\anaconda3\lib\site-packages\theano\graph\op.py in compute_test_value(node)
     80 try:
---> 81 storage_map[ins] = [ins.get_test_value()]
     82 compute_map[ins] = [True]

~\anaconda3\lib\site-packages\theano\graph\basic.py in get_test_value(self)
    421 detailed_err_msg = get_variable_trace_string(self)
--> 422 raise TestValueError(f"{self} has no test value {detailed_err_msg}")
    423 

TestValueError: k has no test value  
Backtrace when that variable is created:

  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 2877, in run_cell
    result = self._run_cell(
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 2923, in _run_cell
    return runner(coro)
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\async_helpers.py", line 68, in _pseudo_sync_runner
    coro.send(None)
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3146, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3338, in run_ast_nodes
    if (await self.run_code(code, result, async_=asy)):
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3418, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "<ipython-input-6-0bf33b6fde4a>", line 5, in <module>
    like = pm.Potential('like', hyperbolic_llf(k, beta, ll_amount,ll_time,ss_amount,ss_time))
  File "<ipython-input-5-c3ad5e2e4ef5>", line 7, in hyperbolic_llf
    k = t.scalar('k')

During handling of the above exception, another exception occurred:

ValueError Traceback (most recent call last)
<ipython-input-6-0bf33b6fde4a> in <module>
      3 beta = pm.HalfNormal('beta', 10)
      4 
----> 5 like = pm.Potential('like', hyperbolic_llf(k, beta, ll_amount,ll_time,ss_amount,ss_time))
      6 tr = pm.sample()

<ipython-input-5-c3ad5e2e4ef5> in hyperbolic_llf(k, beta, ll_a, ll_t, ss_a, ss_t)
      7 k = t.scalar('k')
      8 beta = t.scalar('beta')
----> 9 sv = sv_diff(k,ll_amount_,ll_delay_,ss_amount_,ss_delay_)
     10 sv_ = -sv * beta
     11 llf = pm.math.log(1/(1+pm.math.exp(sv_)))

<ipython-input-4-55b4b528b9e8> in sv_diff(k, ll_amount, ll_delay, ss_amount, ss_delay)
      1 def sv_diff(k,ll_amount,ll_delay,ss_amount,ss_delay):
----> 2 k = pm.math.exp(k)
      3 return ll_amount/(1+k*ll_delay)-ss_amount/(1+k*ss_delay)

~\anaconda3\lib\site-packages\theano\graph\op.py in __call__ (self, *inputs, **kwargs)
    251 
    252 if config.compute_test_value != "off":
--> 253 compute_test_value(node)
    254 
    255 if self.default_output is not None:

~\anaconda3\lib\site-packages\theano\graph\op.py in compute_test_value(node)
     92 detailed_err_msg = get_variable_trace_string(ins)
     93 
---> 94 raise ValueError(
     95 f"Cannot compute test value: input {i} ({ins}) of Op {node} missing default value. {detailed_err_msg}"
     96 )

ValueError: Cannot compute test value: input 0 (k) of Op Elemwise{exp,no_inplace}(k) missing default value.  
Backtrace when that variable is created:

  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 2877, in run_cell
    result = self._run_cell(
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 2923, in _run_cell
    return runner(coro)
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\async_helpers.py", line 68, in _pseudo_sync_runner
    coro.send(None)
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3146, in run_cell_async
    has_raised = await self.run_ast_nodes(code_ast.body, cell_name,
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3338, in run_ast_nodes
    if (await self.run_code(code, result, async_=asy)):
  File "C:\Users\KLIPS\anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3418, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "<ipython-input-6-0bf33b6fde4a>", line 5, in <module>
    like = pm.Potential('like', hyperbolic_llf(k, beta, ll_amount,ll_time,ss_amount,ss_time))
  File "<ipython-input-5-c3ad5e2e4ef5>", line 7, in hyperbolic_llf
    k = t.scalar('k')

```

Thanks a lot.

---

<div class="post-metadata">

**Author:** ![ricardoV94](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ricardov94/32/5775_2.png) [@ricardoV94](https://discourse.pymc.io/u/ricardoV94)\
**Post date:** [November 26, 2021, 3:06pm UTC](https://discourse.pymc.io/t/problem-with-hyperbolic-discount-model/8367/2 "2021-11-26T15:06:59Z")

</div>

You are overwriting k and beta inside the likelihood function.

---

<div class="post-metadata">

**Author:** ![aetius](https://avatars.discourse-cdn.com/v4/letter/a/c2a13f/32.png) [@aetius](https://discourse.pymc.io/u/aetius)\
**Post date:** [November 26, 2021, 10:12pm UTC](https://discourse.pymc.io/t/problem-with-hyperbolic-discount-model/8367/3 "2021-11-26T22:12:34Z")

</div>

Sorry, what is overwriting k and beta? How should I correct it  
? Thanks.

---

<div class="post-metadata">

**Author:** ![cluhmann](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cluhmann/32/3083_2.png) [@cluhmann](https://discourse.pymc.io/u/cluhmann)\
**Post date:** [November 27, 2021, 2:41am UTC](https://discourse.pymc.io/t/problem-with-hyperbolic-discount-model/8367/4 "2021-11-27T02:41:09Z")

</div>

I believe these lines:

```python
k = t.scalar('k')
beta = t.scalar('beta')

```

(re-)initialize the arguments `k` and `beta`, overwriting what is being passed into `hyperbolic_llf()`.

---

<div class="post-metadata">

**Author:** ![drbenvincent](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/drbenvincent/32/4313_2.png) [@drbenvincent](https://discourse.pymc.io/u/drbenvincent)\
**Post date:** [December 7, 2021, 10:13am UTC](https://discourse.pymc.io/t/problem-with-hyperbolic-discount-model/8367/5 "2021-12-07T10:13:42Z")

</div>

This approach is perhaps more complex than it needs to be. See this thread for another example which has implemented discounting models [Replacing nested for loops from JAGS code for cognitive model of temporal discounting - #6 by drbenvincent](https://discourse.pymc.io/t/replacing-nested-for-loops-from-jags-code-for-cognitive-model-of-temporal-discounting/6763/6)

---

<div class="post-metadata">

**Author:** ![aetius](https://avatars.discourse-cdn.com/v4/letter/a/c2a13f/32.png) [@aetius](https://discourse.pymc.io/u/aetius)\
**Post date:** [December 7, 2021, 8:52pm UTC](https://discourse.pymc.io/t/problem-with-hyperbolic-discount-model/8367/6 "2021-12-07T20:52:25Z")

</div>

Yeah, thank you. Also, I am reading your last year published paper’s code(I forgot the name, that JEP:General paper) to learn pymc3. I think they are well organized, and thank you for making this paper’s code online!

---

<div class="post-metadata">

**Author:** ![drbenvincent](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/drbenvincent/32/4313_2.png) [@drbenvincent](https://discourse.pymc.io/u/drbenvincent)\
**Post date:** [December 8, 2021, 10:43am UTC](https://discourse.pymc.io/t/problem-with-hyperbolic-discount-model/8367/7 "2021-12-08T10:43:51Z")

</div>

If I get some time over the break, I should really put it all together as a pymc-example.