Bed forecasting without data I have recently started working on bed forecasting project. I don't have data and I am asked to figure out a way to forecast the bed occupancy. As per the discussion with my supervisor/boss, I have to use probability to find out how many beds the hospital needs to start. For example: if there are 5 patients admitted (they had stroke), 1 of the admitted patients leave home the same day, of the remaining 4 patients:

*

*1 patient leaves after 2 days

*1 patient leaves after 5 days

*1 patient leaves after 2 weeks

*1 patient goes to rehab

How many beds are needed in this situation? I am not sure if I can correctly identify the overall hospital needs with this information for the patients admitted for stroke. (this forecast is only meant for the patients admitted with stroke.) I would appreciate some opinions on how to get started with this problem without having access to the data. As my supervisor said that it is not about the trend in the data, which is increasing of course, it is about the probability.
I was about fitting probability distribution such as Binomial or Poisson.

First off, I would not put ARIMA at the top of my list. On the one hand, as you write, you need data to fit an ARIMA model. On the other hand, ARIMA allows for non-integer and negative values, which does not make a lot of sense in your situation, but this is usually not a major problem. On the third hand, I see little reason for bed occupancy to exhibit autoregressive or moving average behavior, so an automatic ARIMA model selection algorithm is likely to get hung up on noise.
(Then again, if your hospital is overworked, then people may not get good enough care, so high occupancy today may be associated with high occupancy tomorrow. Or conversely, if your beds are full, your staff may have an incentive to "encourage" patients to be discharged, so high occupancy today may be associated with low occupancy tomorrow. You could take a look once you have data, but I would not expect the signal to be strong. ARIMA is not very good at forecasting, see here and here.)
Instead, I would simply simulate. Ask your domain experts about how many new stroke patients they expect each day, and what variability this figure might have. Also, ask the same question about how long any given new patient might stay. You will probably need to translate your experts' opinions into some sort of probability distributions, like Poissons or Negbins.
You might already have data on at least some of these pieces of information; I find it hard to believe a hospital does not have records about past patients, their indications and their length of stay. If so, you can draw from these empirical distributions.
Then simulate: draw a random number of new patients coming in today, and for each patient, draw how long they will stay. Fill your virtual beds, tracking how long each bed occupant still has to stay. Increment the date, discharge some patients, take new ones in, rinse and repeat. Do this over 100 days, multiple times, plot time courses or calculate summary statistics like averages and quantiles. This should not be hard in any programming environment, like Python or R.
The advantage is that you can immediately perform a sensitivity analysis, e.g., on what happens if the length of stay has more or less variability than your experts expected.
