Weighted Distributions in Predictive Model

Question

I'm not a statistician but do work with large datasets and have a problem I'd like to use a predictive model for.

I have two datasets that I'd like to use together to build predictions. The first set is of a list of categories:

A, B, B, A, C, D, A, B, D , etc.

I have turned this into a table of histograms. Essentially, I have created categorical probabilities for each of the labels above. Let's call this distribution X.

The second set is a table with counts by source and category, here is a very simple example, though there are many more for each source:

source   cat   count
one      A     19
one      B      0
one      C      10
one      D      1
two      A      0
two      B     20
two      C      1
two      D      0
three    A     100
three    B      30
three    C      57
three    D      3

I've also created a distribution for each source, call this distribution Y. What I'd like to do is given cat A or cat B as a possible next entry, calculate which is more likely and with what margin of error. To do this I will use both the X and Y with a weight for each source:

Predicted_prob(cat A) = w * X(cat A) + (1 - w) * Y(cat A)

Here are some questions about this approach:

1. Is this an ok general approach? I don't need anything super fancy, just something that can work with the data I have and give a way of measuring the confidence of the prediction.
2. I am currently using a uniform distribution for w where w = (1 / n) and n is the number of samples of each source. Is there a better distribution that may work to make sure if n is too small, the effects are not felt as much?

I am working out the research in R but will ultimately need to implement with Python (can use RPy). I'm open to any theoretical or implementation input, as long as it's attainable!

Answer 1

I've kept the weighted distribution using a uniform weight, until further evidence is given.

For further info on how I was using the data, see: How to test a difference in proportions for significance when the underlying distributions are not normal?