Remake X: DiscreteDistribution should have pmv not pmf

[sbenthall]

Clarifying the scope of this ticket: It involves two changes to the DiscreteDistribution class:

• replacing 'pmf' with 'pmv'
• replacing 'X' with 'values'

https://github.com/econ-ark/HARK/blob/master/HARK/distribution.py#L816-L829

The class needs to be refactored with this change. Then, downstream code using DiscreteDistribution needs to be updated to reflect this change.

---

# CDC 20210621: We should not use pmf for the point masses of the realizations, because it
# is not a probability mass 'function.' Scipy.discrete_rv, sympy, and Mathematica all
# return pmf (or pdf) as a function. They have different syntaxes for retrieving the
# vector of point masses; here it is called the pmv (probability mass vector)


class DiscreteDistribution(DiscreteDistributionOld):
    __doc__ = DiscreteDistributionOld.__doc__
    __doc__ += """
        XYZ : np.array
            Restructure the dimensions of the np.array so that successive
            columns in XYZ correspond to the vectors of values of each
            discrete random variables across the broadcasted combinations.
            Thus, [instance].XYZ[0] will return the vector of discrete
            realizations of the first variable, [instance].XYZ[-1] will
            get the last RV, etc.
        pmv : The vector of point masses of the broadcasted collection
            of random variables
"""

    def __init__(self, pmf, X, seed=0):  # Get the old definition
        super().__init__(pmf, X, seed)  # execute the old def
        XYZ = np.column_stack(X)  # stack actually unstacks them
        if self.dim() == 1:  # numpy 1 dimensional arrays want to be
            XYZ = XYZ.T  # the wrong shape
        self.XYZ = XYZ  # [ N dimensional matrix ]
        # The pmf should be a function, not a vector (as now)
        # TODO: Replace invocations of pmf with pmv
        self.pmv = pmf

 

[sbenthall]

Also, "X" should not be "X", but a more descriptive and lowercase term, like "values"

[sbenthall]

See discussion here:
https://github.com/econ-ark/HARK/pull/1146/files#r883016319

Because of the ambiguity about the semantics of "X" -- a dimension of X can mean either a dimension of the state values of of random variable, or the 'nature's choice' dimension -- it would be better if X/values were a different kind of data structure that makes these differences more explicit.

For example, if X were a Pandas dataframe, the index could be nature's choice, and the columns would be dimensions of the RV value. However, that might not work for matrix-valued (as opposed to vector-valued) RVs.

[sbenthall]

It might be possible to take inspiration, or an implementation, from another distribution library.

https://github.com/econ-ark/HARK/wiki/Distribution-Libraries

[alanlujan91]

xarray.DataArray has attributes values and data by default. The DiscreteDistributionXRA could easily make this change without significant work.

@llorracc how about data and prob?

[llorracc]

Don't like ".data" because usually it will NOT be from empirical measurement but rather from numerical approximations to theoretical objects. A general purpose option would be "atoms" and "probs" -- encompassing the abstract possibility that the distribution being described is, say, the probability of a particular word occurring in a text (and the atoms are the words).

…

On Wed, Aug 3, 2022 at 9:17 AM alanlujan91 ***@***.***> wrote: xarray.DataArray has attributes values and data by default. The DiscreteDistributionXRA could easily make this change without significant work. @llorracc <https://github.com/llorracc> how about data and prob? — Reply to this email directly, view it on GitHub <#1051 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAKCK76WHX3ZA62LJV7CHSLVXJWPPANCNFSM5BPSM7ZA> . You are receiving this because you were mentioned.Message ID: ***@***.***>

-- - Chris Carroll

[sbenthall]

scipy.stats.rv_discrete uses values() to access both the atoms and the probabilities:
https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.html#scipy.stats.rv_discrete

[alanlujan91]

At the last meeting I think we had consensus on .pmv and .atoms. I'll work on that.