andrew_gelman_stats andrew_gelman_stats-2014 andrew_gelman_stats-2014-2161 knowledge-graph by maker-knowledge-mining
Source: html
Introduction: OK, so this sort of thing happens sometimes. I was working on a new idea (still working on it; if it ultimately works out—or if it doesn’t—I’ll let you know) and as part of it I was fitting little models in Stan, in a loop. I thought it would make sense to start with linear regression with normal priors and known data variance, because then the exact solution is Gaussian and I can also work with the problem analytically. So I programmed up the algorithm and, no surprise, it didn’t work. I went through my R code, put in print statements here and there, and cleared out bug after bug until at least it stopped crashing. But the algorithm still wasn’t doing what it was supposed to do. So I decided to do something simpler, and just check that the Stan linear regression gave the same answer as the analytic posterior distribution: I ran Stan for tons of iterations, then computed the sample mean and variance of the simulations. It was an example with two coefficients—I’d originally cho
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1 I was working on a new idea (still working on it; if it ultimately works out—or if it doesn’t—I’ll let you know) and as part of it I was fitting little models in Stan, in a loop. [sent-2, score-0.066]
2 I thought it would make sense to start with linear regression with normal priors and known data variance, because then the exact solution is Gaussian and I can also work with the problem analytically. [sent-3, score-0.522]
3 So I programmed up the algorithm and, no surprise, it didn’t work. [sent-4, score-0.15]
4 I went through my R code, put in print statements here and there, and cleared out bug after bug until at least it stopped crashing. [sent-5, score-0.681]
5 But the algorithm still wasn’t doing what it was supposed to do. [sent-6, score-0.161]
6 So I decided to do something simpler, and just check that the Stan linear regression gave the same answer as the analytic posterior distribution: I ran Stan for tons of iterations, then computed the sample mean and variance of the simulations. [sent-7, score-0.646]
7 The means looked fine but the covariance matrix from the Stan simulations was off. [sent-9, score-0.297]
8 The correlations were wrong—not by a lot, but by a nonzero amount, I think the value from the formula was 0. [sent-10, score-0.222]
9 Which I did, actually, but fixing the formula didn’t solve the problem. [sent-15, score-0.224]
10 I also tried direct simulation, and that gave the right answer too. [sent-16, score-0.248]
11 So I just fed Stan the posterior distribution directly. [sent-18, score-0.13]
12 I simplified further, forget regression entirely, just give independent normal priors: parameters { real b1; real b2; } model { b1 ~ normal (0, 1); b2 ~ normal (0, 1); } You can’t get much more stripped down than that. [sent-20, score-1.014]
13 Still had the problem: > library ("rstan") > gaussian2 <- stan (file="gaussian2. [sent-21, score-0.425]
14 stan", iter=20000, chains=4) > sims <- extract(gaussian2)$b1 > print (mean (sims)) [1] -0. [sent-22, score-0.677]
15 I then tried to go even simpler, to one dimension: parameters { real b1; } model { b1 ~ normal (0, 1); } This time it gave the right answer: > gaussian1 <- stan (file="gaussian1. [sent-27, score-0.919]
16 stan", iter=20000, chains=4) > sims <- extract(gaussian1)$b1 > print (mean (sims)) [1] 0. [sent-28, score-0.677]
17 I have two adjacent examples, one where Stan works and one where it doesn’t. [sent-31, score-0.147]
18 Just to be clear: the above is not meant to represent exemplary practice. [sent-35, score-0.073]
19 It seems to be a general rule of programming, and of research, that no matter how simple we start, we should start even simpler, to get that solid rock of computational certainty on which we can stand while building our complex structures. [sent-37, score-0.081]
20 The indents just don’t show up when I use the “code” tag in html. [sent-42, score-0.15]
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