How to incorporate evidence into parameters of a Bayesian network?

[sarikan]

Greetings,
Maybe I'm getting a little bit confused, but I'm looking for resources which explain how to update parameters of a Bayesian network as a result of observations.

There are various inference methods, but unless I'm missing something here, these methods produce a posterior distribution based on evidence (a set of observations of some nodes).

This posterior distribution is specific to the evidence, but there must be a way of incorporating this into the network, so that the prior distribution of the following observations are modified.

Can I simply use the posterior distribution after observation of evidence E as the prior for the next? This should correspond to a Bayesian update of the network, but I fear that they me be a catch here. Would this be the right way of continuously updating the parameters of the network as evidence is observed?

Regards

 

[SW VandeCarr]

Greetings,


Can I simply use the posterior distribution after observation of evidence E as the prior for the next? This should correspond to a Bayesian update of the network, but I fear that they me be a catch here. Would this be the right way of continuously updating the parameters of the network as evidence is observed?
Regards

This paper may be helpful. You generally need to create conjugate priors as you update. If you are starting with an uninformative prior or hyperparameters (of prior distributions) the process is more complicated.

http://cran.r-project.org/web/packages/LaplacesDemon/vignettes/BayesianInference.pdf

 

[sarikan]

Thanks. A good overall paper it appears. I'll read it in detail. Conjugacy is useful, though I approach it with some hesitation, since my work may end up with arbitrary distributions, where conjugacy may not be possible.
I think I've found the right term for what I'm looking for by the way: adaptive inference in Bayesian networks. For anyone else who may look for something similar in the future...

Regards

 

[SW VandeCarr]

Thanks. A good overall paper it appears. I'll read it in detail. Conjugacy is useful, though I approach it with some hesitation, since my work may end up with arbitrary distributions, where conjugacy may not be possible.
I think I've found the right term for what I'm looking for by the way: adaptive inference in Bayesian networks. For anyone else who may look for something similar in the future...

Regards

Here's a paper on adaptive Bayesian inference based on tree structured networks. It describes the sum-product updating algorithm for re-evaluating marginal distributions and other quantities and proposes a faster alternative. I can't say I have any experience in this particular area of Bayesian applications, but it looks interesting.

http://people.cs.uchicago.edu/~osumer/nips07.pdf

 

[blue_raver22]

,

I can provide some insights on how to incorporate evidence into parameters of a Bayesian network. First, it is important to understand that Bayesian networks are probabilistic graphical models that represent relationships between variables and their probabilities. These probabilities, also known as parameters, can be updated based on new evidence using Bayesian inference methods.

One approach to incorporating evidence into parameters of a Bayesian network is by using the Bayesian updating formula. This formula takes into account the prior distribution (based on previous knowledge) and the likelihood of the evidence to calculate the posterior distribution (updated probabilities). This posterior distribution can then be used as the prior for the next set of observations, allowing for continuous updating of the network's parameters.

Another approach is to use Markov Chain Monte Carlo (MCMC) methods, which involve simulating a large number of possible networks and selecting the one that best fits the observed data. This method can be useful when dealing with complex networks with many variables.

Incorporating evidence into parameters of a Bayesian network requires careful consideration of the type and strength of the evidence, as well as the structure of the network. It is important to properly model the relationships between variables and to use appropriate inference methods to update the parameters.

In conclusion, incorporating evidence into parameters of a Bayesian network involves using Bayesian inference methods such as the Bayesian updating formula or MCMC. It is crucial to carefully consider the evidence and the structure of the network to ensure accurate and meaningful updates of the parameters.