There is a literature in this area. You might start here:

https://www.bing.com/search?q=+population+density+interpolation+using+Bayesian+Statistics%3F&qs=n&form=QBRE&sp=-1&pq=population+density+interpolation+using+bayesian+statistics%3F&sc=0-59&sk=&cvid=5A9108078DA94FCE8F7A0389EEC39918

Best wishes, D Booth

@ Antonela Marozzi ,

It is possible to estimate the missing observation.

Some techniques are known to me.

However, that depends upon the type of data available.

I suggest you to show me the data you have.

I will observe the data and think of how to handle the problem.

There are several ways. You can replace the missing values with an average; or use the midpoint between the observations on each side of the gap; or use regression to infer the midpoint. Or use other statistical techniques that allow for missing data, such as mixed models. As others have advised, check the literature for methods and data considerations.

Hi! Thank you for all the answers. @ Dhritikesh Chakrabarty I am sending the data attached here.

Regards!

@ Jerry Miller ,

The ways mentioned by you, as I understand, are rough estimation methods only and they cannot yield accuracy in findings.

@ Antonela Marozzi ,

As I have observed your data, there are 9 observed values of population density corresponding to 9 consecutive years starting from 2008 upto 2017 excluding 2013I can suggest two methods:

1st Method :

Fit a curve of appropriate degree to the data by least squares method or by orthogonal polynomial and then estimate the value of population density corresponding to the year 2013 from the fitted curve.

2nd Method :

Represent the 9 pairs of observations by a polynomial of degree 8 and then evaluate the value of the population density corresponding to the year 2013 from the polynomial obtained.

Thank you for your suggestions, @Dhritikesh Chakrabarty. They were very helpful!

Regards

Antonela