Introduction Regarding the proof presented in Hoff (2009) and Hoff et al. (2022), Section 10.4.2 “Why does the Metropolis-Hastings algorithm work?”, I encountered a point of confusion, so I decided to write about it to organize my thoughts. Hoff’s Proof Flow In Hoff (2009) and Hoff et al. (2022), the proof explaining why the Markov chain generated by the M-H algorithm can approximate the target distribution \(p_0\) proceeds as follows: ...

Whassup, peeps! It’s been a minute since my last post (shoutout to the one person probably reading this, you the real MVP!). My Master’s thesis, with some fresh updates, just dropped on arXiv. Check it: Paper: Babasaki, K., Sugasawa, S., McAlinn, K. and Takanashi, K. (2024). Ensemble doubly robust Bayesian inference via regression synthesis. (arXiv:2409.06288) So, this paper, it’s all about takin’ this ensemble method called Bayesian Predictive Synthesis (BPS) that Professor McAlinn cooked up, and flexing it into the world of causal inference, specifically for estimatin’ Average Treatment Effects (ATE). We’re callin’ our new method “doubly robust Bayesian regression synthesis”. If you wanna get into the nitty-gritty, peep the paper, ya dig? ...

Question a Make up a nonmathematical function that is one to one but not onto. b Make up a mathematical function that is one to one but not onto. Answer a “The student number of” from Keio University students to integers. b \(f(x) = 2^x\)

Question Explain Why one of these statements is true and the other is false: \begin{align*} (\forall \text{ man } M)(\exists \text{ woman } W) \mid W \text{ is the mother of } M \\ (\exists \text{ woman } W)(\forall \text{ man } M) \mid W \text{ is the mother of } M \end{align*} Answer The first statement is true, and the second is false because every man has a mother but there doesn’t exist a woman who is the mother of all men. ...