Progress Blog Post 2

Few weeks passed from our last blog post and until now we wanted to try to investigate mathematical models as many as we could. To remind our readers once again, our goal is to find a way how to reconstruct population fluctuation of Venice over time.

For solving this problem, first we proposed whole set of different methods how to approach and how to try finish successful population reconstruction. Last week we were trying to implement any kind of proposed laws and approaches, but for every single case we got quite unrealistic representation of population. From natural growth model we didn’t expect to have anything that would have looked like nice population representation. As well, we knew that our other models were not really reliable, so we were not that confused when we saw models auch as adapted Nicholson-Baily’s model, Nurgaliev’s law and Couttsian model were far from our expectations.

At the end of day, we conclude for mentioned models that they are only appliable for doing future predictions and optimistically based on growth population. After realizing that, we came up with two ideas how to try to do a reconstruction of population without integrating any existing model.

Our first idea was to try to get function of population by doing regression of data that we have collected and then to try to fit regression model as better as we could towards to real data. We had an opinion that regression model would be nice blind prediction how population were changing over time. We expected that we would get a polynomial function of 3rd or 4th order. In that case, we thought that polynomial function would follow real data nicely and our next step would be put the weights on the specific segments of it based on the historic events. Since, we got a polynomial function of 9th order that was the closest fit to real data we had to drop our idea and to try something new.

Finally, we decided to divide the real data into period segments and to weight curves only at specific years . We would like to explain through the example. If you give a look to our real data and imagine that one period segment is part between 1300 and 1450, we were looking to events for years in between which had any kind of influence on population. Depends on our interpretation of influence we were giving respectively positive and negative scores that we used to weight curves.

After this monotonic representation how to give scores, we will explain how to implement them.
First, we take difference between beginning and ending years, ydiff. Then we create an array with population at specific years from extracted from real data. In that array we will weight specific years by multiplying assigned score with ydiff and adding to value from real data, so our formula would look like this:

ynew=[yp1300    yp1348/2    yp1350+(-0.5)*ypdiff    yp1363+(-0.25)*ypdiff    yp1368+1*ypdiff yp1378+(-0.5)*ypdiff    yp1388+1*ypdiff    yp1409+1*ypdiff    yp1425+(-0.5)*ypdiff    yp1450],

where yp1300 presents “population in 1300” and so on.

We have done this procedure for periods: 1300-1450, 1450-1509, 1509-1540, 1642-1696 and 1696-1760. Why only for these periods? Give a look at the next figure and you will see for 1540-1568, there is a huge population increment in short period of time and other thing is that nothing historically important happened in that period, so there is no reason to make any predictions. The same case is for rashly decrements in 1563-1581 and in 1624-1633. Other periods were full of non-influencing historic events.

Our goals until next stop are to improve score assignment, since we are aware that is not that precise this time, as well to try to find more population-influencing events and to incorporate them into the model and at the end to match together all reconstructed periods. Also, our task for next time is also to see what to do with population prediction between 1797 and 1871, since there are no many information about population in that period, since Venice became a property of Austria.

At the end we present other reconstructed periods: