u/Able-Fennel-1228

Hi.

I’ve been told all the time since intro stat that all models are wrong but some are useful, but never about how what happens to interpretability when the model is wrong. (I trust the mathematical statisticians 100% with the mathematical details of what I’m about to ask, Im concerned more so about the practicalities. Forgive any errors in understanding for I am a noob).

Specifically, with likelihood based methods, suppose the distributional assumptions are wrong (I presume they always are because the world is too damn complicated for me to be able to specify them correctly), then (correct me if I’m wrong), the parameters in the model still converge to “something” under certain assumptions about the likelihood. This pseudo true parameter is the parameter that minimizes the KL-divergence between the true distribution and our assumed distribution. Also, under certain assumptions, it will be asymptotically normally distributed and it’s recommended to use the sandwich estimator of its variance.

For the sake of not fooling myself every-time I use a model, I will presume it is always the case that I am estimating a pseudo true parameter (diagnostics only go so far). How am I supposed to interpret this pseudo parameter? My estimators? regression betas and odds ratios? What do they mean now?

I understand that to deal with these problems there are other techniques like estimating equations and the like (I don’t understand that part of the theory yet). How to they help with this issue?

What are some practical alternatives ?

Thanks.

I had a look at some of his books. Quite rigorous. I don’t see it as being accessible for most high school kids although I’m sympathetic to teachers learning it at that level.

Jake Gyllenhaal comes to mind as someone that plays psychopathic and/or broken people a bit **too** well. There is something very viscerally unsettling about his performance as Louis Bloom (Nightcrawler) and Mysterio (Spiderman). It’s the callousness, rage and complete lack of humanity right underneath that charming facade. Even when he’s just playing sympathetic broken characters, he plays the “unhinged” part too well.

Gary Oldman is very similar but I find him more impressive because of the range of roles he’s played (good, bad, grey characters).

Tony Starr’s homelander is another one that stands out. He’s just an empty void on the inside that can never be satisfied. He craves nothing but admiration and his only strategy is to force it, but that never satisfies him because it was forced. He cannot love.

Javier Bardem’s Anton Chigurh is almost supernatural; a force of nature. Same with Anthony Hopkins’s Lecter.

Daniel Day Lewis in there will be blood is cold. Just cold.

Who are some other actors that you think portray the dark side of human nature too well? Do you think you actually have to have that level of darkness in you to play it well, or can you just mimic it without connecting with it at a deep level?