feat(Probability/Posterior): Posterior PMFs and Various Lemmas

[SamuelSchlesinger]

Upstreaming the probability lemmas needed in leanprover/cslib#464.

[github-actions]

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[github-actions]

PR summary c27c098f0d

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Probability.ProbabilityMassFunction.Posterior (new file)	1517

---

Declarations diff

+ joint
+ joint_apply
+ mem_support_joint_iff
+ mem_support_posterior_iff
+ posterior
+ posterior_apply
+ posterior_hasSum
+ support_joint
+ support_posterior
+ tsum_joint_fst
+ tsum_joint_snd

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[SamuelSchlesinger]

Accidentally closed. I believe the previous CI fail wasn't related to this PR, but I've rebased on master so we'll see :)

[EtienneC30]

There is ongoing work to deprecate PMF (see https://leanprover.zulipchat.com/#narrow/channel/113489-new-members/topic/generic.20shannon.20entropy.20formalization.20mathlib4/near/584361371), so this can't be added. Also are you aware of ProbabilityTheory.posterior? You should use this definition and provide your results for measures that are sums of Dirac masses.

[SamuelSchlesinger]

This is very helpful context! I will go back to the drawing board for the cslib work we just merged using it.

Thank you.

[SamuelSchlesinger]

There's a lot of discussion going on in the Zulip, planning to leave this open while we discuss: #CSLib > PMF monad and discrete probability. Let me know if I should just close it.