Bayes’ Theorem is typically stated as: \[ P(A \mid E) = \frac{P(E \mid A) \, P(A)}{P(E \mid A) \, P(A) + P(E \mid \neg A) \, P(\neg A)} \]This form explicitly shows all the pieces of Bayesian reasoning: The posterior probability of the hypothesis \(A\), given evidence \(E\): \(P(A \mid E)\). The probability prior to the evidence: \(P(A)\). The likelihood observing the evidence if the hypothesis is true: \(P(E \mid A)\). ...
We are two months into a presidential administration that is clearly making a break with past administrations. Many prominent observers like Paul Krugman and Robert Reich are calling this an authoritarian autogolpe, or self-coup. Of course, both of these observers are left of center, so being skeptical of these claims is a natural—and even prudent—reaction. After all, we have experienced 250 years of democratic government. On the other hand, maybe they are correct. Many of the stories coming out of Washington seem alarming and the sheer number of stories is overwhelming. The Department of Government Efficiency (DOGE) shutting down agencies such as USAID. DOGE asking federal workers to justify the work they performed last week in an email or risk termination. Deciding how to think about this moment in light of emotionally charged claims and commentary is difficult. To not be sure what to think is completely understandable. ...