Added `Joint_Handmade` and `MarginalDistribution` in stats #14989

akash9712 · 2018-07-29T09:12:04Z

References to other Issues or PRs

Brief description of what is fixed or changed

Added JointRV, which allows the user to create a joint random variable
with each of its component varying over the real line. Also added
JointDistributionHandmade for this purpose.
Added MarginalDistribution to allow random variables with components marginalized out. This also adds the ability to handle compound random variables by marginalizing over latent distributions, with or without a given condition.

Other comments

Same code as #14951 is added, which has to be closed due to some extra commits showing up.

Release Notes

stats
- Add JointRV to allow user to create Joint random variables
- Add MarginalDistribution, CompoundDistribution
- Ability to handle compound distributions

Added `JointRV`, which allows the user to create a joint random variable with each of its component varying over the real line. Added `JointDistributionHandmade` for this purpose. Also made minor modification in core/function.py to allow `Lambda` to accept indexed symbols. Added tests.

Fix in `JointRV` to order indexed symbols extracted by their index, instead of using the set as it is. Also replaced symbols by indexed symbols in `marginal_distribution`. `Indexed` are not used directly and instead replace `Symbol` towards the end of the function because `integrate` raised error in some cases when the variable of integration was of type `Indexed`.

Added class `MarginalDistribution` and the ability to handle compound distributions using this.

Modified some tests, and added `evaluate` flag for marginal distributions.

Fixed some of the previously failing tests in stats module, by constructing marginal distribution with existing distributions instead of PDFs.

Fixed `domain` for JointPSpace and made some corrections to `pdf` in `MarginalDistribution`.

Removed trailing whitespaces, corrected import statements in stats.

sympy-bot · 2018-07-29T09:12:13Z

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#### References to other Issues or PRs
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#### Brief description of what is fixed or changed
Added `JointRV`, which allows the user to create a joint random variable
with each of its component varying over the real line. Also added
`JointDistributionHandmade` for this purpose. 
Added `MarginalDistribution` to allow random variables with components marginalized out. This also adds the ability to handle compound random variables by marginalizing over latent distributions, with or without a given condition.
#### Other comments
Same code as #14951 is added, which has to be closed due to some extra commits showing up.
#### Release Notes
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<!-- BEGIN RELEASE NOTES -->
* stats
    * Add `JointRV` to allow user to create Joint random variables
    * Add `MarginalDistribution`, `CompoundDistribution`
    * Ability to handle compound distributions 
<!-- END RELEASE NOTES -->

Your release notes are in good order.

Here is what the release notes will look like:

stats
- Add JointRV to allow user to create Joint random variables (#14989 by @akash9712)
- Add MarginalDistribution, CompoundDistribution (#14989 by @akash9712)
- Ability to handle compound distributions (#14989 by @akash9712)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.2.1.

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Update

The release notes on the wiki have been updated.

Upabjojr · 2018-07-29T10:13:38Z

When I look at

In [11]:     x = Symbol('x')
    ...:     l = Symbol('l', positive=True)
    ...:     rate = Beta(l, 2, 3)
    ...:     X = Poisson(x, rate)
In [12]: X
Out[12]: x
In [13]: X.pspace
Out[13]: JointPSpace(x, MarginalDistribution(PoissonDistribution(l), (x,)))

I mean, PoissonDistribution(l) where l is a random symbol is a bit weird, because the distribution is not a single continuous distribution as the class structure would lead to think:

In [23]: pd
Out[23]: PoissonDistribution(l)
In [24]: type(pd)
Out[24]: sympy.stats.drv_types.PoissonDistribution
In [25]: type(pd).__mro__
Out[25]: 
(sympy.stats.drv_types.PoissonDistribution,
 sympy.stats.drv.SingleDiscreteDistribution,
 sympy.core.basic.Basic,
 sympy.stats.rv.NamedArgsMixin,
 object)

Upabjojr · 2018-07-29T10:15:09Z

Can we represent the joint distribution of a compound random variable?

akash9712 · 2018-07-29T10:25:25Z

Can we represent the joint distribution of a compound random variable?

Such distributions would need to go into either JointDistributionHandmade(represented using a PDF), or another JointDistribution(usually represented using the arguments and the methods defined in the subclass). To represent it using a Joint distribution, I think it would need to have either a subclass like CompoundDistribution, or a class independent of JointDistribution, because different constructor might be needed.

Upabjojr · 2018-07-29T10:28:47Z

The problem remains that PoissonDistribution(rate) is technically a joint distribution, but it is handled as a single variate distribution right now.

I will think a bit about this problem.

Upabjojr · 2018-07-29T10:59:57Z

I guess the best way to represent a compound distribution is by having a CompoundDistribution object.

Added class `CompoundDistribution`, which requires a distribution with a random parameter for construction.

In case the user creates a compound random variable, the distribution is of the type `CompoundDistribution`. Added and modified some tests.

ArifAhmed1995 · 2018-07-30T04:15:31Z

sympy/stats/joint_rv.py

@@ -46,26 +57,49 @@ def value(self):

    @property
    def component_count(self):
-        return len(self.distribution.set.args)
+        _set = self.distribution.set
+        if isinstance(_set, ProductSet):


You could use ternary operator here.
return len(_set.args) if isinstance(_set, ProductSet) else 1
Doubt would affect execution time though.

ArifAhmed1995 · 2018-07-30T04:21:37Z

sympy/stats/joint_rv.py

+    distributed according to some given distribution.
+    """
+    def __new__(cls, dist):
+        assert isinstance(dist, (ContinuousDistribution, DiscreteDistribution))


Might be beneficial for end-user to get a a better explicit error message if instantiation is attempted to be done from an illegal distribution.
Such as:

if not isinstance(dist, (ContinuousDistribution, DiscreteDistribution)): raise ValueError('CompoundDistribution can only be initialized from ContinuousDistribution or DiscreteDistribution')

or something similar.

ArifAhmed1995 · 2018-07-30T04:23:11Z

sympy/stats/joint_rv.py

+class MarginalDistribution(Basic):
+
+    def __new__(cls,dist, rvs):
+        assert all([isinstance(rv, (Indexed, RandomSymbol))] for rv in rvs)


Same as discussed earlier. Better for end-user to get a proper error message.

ArifAhmed1995 · 2018-07-30T04:28:42Z

sympy/stats/tests/test_joint_rv.py

+    x1, x2 = (Indexed('x', i) for i in (1, 2))
+    pdf = exp(-x1**2/2 + x1 - x2**2/2 - S(1)/2)/(2*pi)
+    X = JointRV('x', pdf)
+    density(X)(1, 2) == exp(-1)/(2*pi)


Did you miss an assert here ?

Thanks, that was an incorrect test. Fixed it now.

Added error messages and fixed one incorrect test in test_joint_rv.py

Upabjojr · 2018-07-30T09:53:02Z

sympy/stats/tests/test_mix.py

+
+def test_compound_distribution():
+    Y = Poisson('Y', 1)
+    Z = Poisson('Z', Y)


I tried Z.pspace.distribution.pdf(x) but I get an exception.

akash9712 added 8 commits July 29, 2018 14:31

[WIP]Added MarginalDistribution

b052ff7

Added class `MarginalDistribution` and the ability to handle compound distributions using this.

Modifications in tests in stats

521df2d

Modified some tests, and added `evaluate` flag for marginal distributions.

Added test for density of compound distribution

7da1ad2

Partially fixed failing tests in stats.

405edb1

Fixed some of the previously failing tests in stats module, by constructing marginal distribution with existing distributions instead of PDFs.

Fixed domain for JointPSpace

fbb659c

Fixed `domain` for JointPSpace and made some corrections to `pdf` in `MarginalDistribution`.

Minor fixes

97b9fd1

Removed trailing whitespaces, corrected import statements in stats.

akash9712 changed the title ~~Joint handmade~~ Added Joint_Handmade and MarginalDistribution in stats Jul 29, 2018

akash9712 added 2 commits July 30, 2018 02:12

Added CompoundDistribution

bb50fe8

Added class `CompoundDistribution`, which requires a distribution with a random parameter for construction.

Modifications for compound random variables

cdcaea6

In case the user creates a compound random variable, the distribution is of the type `CompoundDistribution`. Added and modified some tests.

ArifAhmed1995 reviewed Jul 30, 2018

View reviewed changes

Added error messages in stats/joint_rv.py

a69cf87

Added error messages and fixed one incorrect test in test_joint_rv.py

Upabjojr reviewed Jul 30, 2018

View reviewed changes

Upabjojr merged commit db67393 into sympy:master Jul 30, 2018

This was referenced Jul 30, 2018

Modification in MarginalDistribution.pdf #14995

Merged

[WIP] Add checks for particular compound distributions #14888

Closed

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Added `Joint_Handmade` and `MarginalDistribution` in stats #14989

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