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I have a database filled with different bird species that were seen on different dates (10 years of records).

Each row in the table contains:

Date, Time, Bird Species, Spot where it was seen

So it looks like:

2008-04-07, 14:22:48, Himalayan Snowcock, Spot-4
2008-04-19, 11:44:01, Ring-necked Pheasant, Spot-12
...
2019-05-20, 08:51:14, American Kestrel, Spot-8

It contains thousands of records like this.

Now I need to create a calendar detailing Birds x Months and on each cell it will contain the probability of seeing that bird on that month.

How can I compute the probability based on the records I have?

1. A simple approach would be to create a 2 × 2 contingency table (Bird × Month) and then for each unique combination of bird and month divide the number of years where that species was seen in that month by 10, which would give you a proportion. However, this approach throws away some information




2. If you wanted to incorporate the fact that some birds are much more common than others and that different months are of different lengths you could use the # of sightings / the number of days (accounting for leap years probably). This would capture the rarity of birds as well as make use of the fact that your information is at a finer than month resolution. If data wasn't collected on a daily basis you could instead divide by the number of days were there was an observer.




3. You do much more complex and employ something like a time-series model to account for changes in detectability through time.... that is probably a question in itself and would be much more challenging to carry out, at least for me.

You could potentially use a Poisson regression to model monthly counts of birds of a particular species as a function of explanatory/independent variables that you think affect the monthly rate of observations, such as linear time trends/calendar month/season/year (potentially supplementing this data with external data sources on things like weather).

After estimating the regression, you could then compute probabilities. As Poisson is a discrete probability distribution, you can calculate the probability of X (specify desired count here) of events for specified values of predictors you used in the regression. If you wanted to know the probability of seeing at least one bird, you can compute it as 1 minus the probability of 0 birds seen. Here is another CV Q&A on predicting probabilities with Poisson regression: Poisson Regression : expectation vs probability for each outcome

For this type of regression, you would normally be assuming that counts in consecutive months are not correlated, meaning that you do not have autocorrelation. If that assumption is not valid, which it probably is not, given that you have time series data, you can examine this Q&A for potential approaches: Poisson regression with (auto-correlated) time series

Poisson regression has a couple of well-known relatives: Negative Binomial and Zero-Inflated Poisson (also zero-truncated Poisson, but that one should not apply here, as you should have a non-zero probability of 0 birds observed). Negative Binomial is needed when the variance of data exceeds the mean in a given month. Zero-Inflated Poisson is used when there are "excess" zeros in the data generated by a separate process.