Apparently not with this when you're early. I took it seriously when a third degree polynomial fit worked too well and then suddenly didn't.

OK, looking at this, the curve is upwards without inflection. What would you expect to get if you fitted a D3 poly to it? Why would you even try? Serious Q.

First thing you do is try to make sense of the data, if I can model 15 points with 2, 3, 4 parameters and further ones don't add any improvement I'm onto something. I've always done polynomials first, you can see if there's something much simpler than Lagrange interpolation, which in my experience means you have to go straight to the literature about that kind of problem.

(Of course this works as long as you aren't seeing any peaks)

oefrha, for some reason I can't reply to your comment just yet so I'll post it here: Of course. This is just my own criterion when I start with a bunch of data I know nothing about. Is there a complicated law behind them or maybe not? Am I seeing noise or there's a signal? You can fit anything smooth with a low order polynomial, so maybe there's a differentiable function right in front of you. It's just something I do and if you see no reason for it I might even agree with you on that. It never ends up in the model, though. It's just something I find useful at a preliminary stage.

OK, We're not being responsible doing this and I'm not qualified to do it. I just have been fitting the data and maybe I've been lucky and I'm just an idiot. Having said that, this is also my problem, I have right now a hotspot in the vicinity and I'm worried. I just want to have a quantitative idea of what's going on. Now it's your job as experts to explain what's going on to the politicians and make sure they hear and they can do the right thing. I wouldn't be worried if the messages had matched the numbers when this started, they didn't. At some point we need someone to tell us "we're at this point and tomorrow we'll be at that point". I shouldn't feel compelled to find out by myself what all this is about. I feel awful by posting all this, I'm perfectly aware that non-experts in a field spout nonsense, but this is a very nonsensical situation and I'm tired of hearing we've been doing fine.

I mean, any smooth curve (without singularities) is well approximated by simple polynomials locally, which is simply its power series expansion. Doesn’t mean simple polynomials would necessarily hold much predicative power, however well they fit the current data. Higher order terms, if any, will come to dominate.

A logistic curve is indistinguishable from an exponential when you're "early". The earlier you are, the closer they are.

Yes, I found out that later, but while we were in the low hundreds fitting to an exponential didn't seem to work very well in comparison to a polynomial (it was overestimating). It wasn't a quadratic either. There it jumped and I remembered I should try population growth models. I started with Gompertz, which is pretty much indistinguishable from logistic at this stage. Then I found out that logistic was more stable and parameters seemed to converge for a few days, so I learned about SIR/SIS. And then I figured I had some idea about what to expect in the following few days.

I stopped trusting any of my rudimentary models by Sunday+incubation, because conditions changed then. Which data, why I trusted them and the set of assumptions taken to consider them representative for the shape of the time series/distribution, that's something I don't think I should share here at this point. In any case I'm used to extract some information from imperfect data, you approximate and estimate. I mean there was by then 12, then 16, then 30 positives in a nursery home next to my door, and no lockdown measures, now there's 100, an improvised hospital there and I'm not allowed go out except for buying groceries. Two weeks ago I needed some picture which I wasn't getting anywhere, the alternative was freaking out after comparing what the authorities were saying with what I knew about the situation. Now they are making sense and the measures in place too, so I expect it getting much better soon.

I don't want to go into epidemiology and I want to respect and trust blindly the epidemiologists, but in any field you expect the professionals having predictive skills working before your eyes, that's their job. Hearing that we should wait for the post-mortem to know where we are now, I mean, come on... And now I'll just shut up.

Nursing home, obviously.