Sequence prediction problem

zartan2k@comcast.net · science forum beginner Joined: 23 Jun 2006 Posts: 3

I would like some advice on how to solve the following problem. I
observe a system that typically sends a series of data to me as
follows.

1,2,3,4,5,6,1,2,3,4,5,6,1,2, ...

Only the values 1,2,3,4,5 and 6 can show up in the series. And in the
absence of any disturbances the numbers are always sequential. However
on occasion one or more of these numbers can drop out of the series.
For example:

1,2,3,5,6,1,2,3, ... (the 4 was dropped)

Another form of disturbance that can occur is that a random number
(with values from 1 to 6) can also be interjected into the series. For
example:

1,2,3,4,1,5,6,1,2,3, ... (a 1 was randomly inserted)

Note that both forms of disturbance can occur at the same time:

1,2,3,4,1,6,1,2,3, ... (a 5 was dropped and a 1 was randomly inserted)

What I would like to do is label each data point in a series with an
approximate probability that the given number was randomly inserted
into the data stream. Note that the length of these sequences will grow
over time and that the probabilities can be updated as new numbers are
observed. The starting point of a sequence doesn't have to be 1. There
is no additional information available about the system (e.g.
probablilities of drop outs or insertions).

Thanks,
zartan2k

dave@autobox.com · science forum beginner Joined: 16 Feb 2006 Posts: 12

zartan2k@comcast.net wrote:

Google