Example 2

Example 2a: Fully Observed Particle

• For this example, we use a simple network consisting of the Parent Node $\mathit{Sex}$ and the Child Node $\mathit{Treatment}$, which have a probabilistic relationship.

• For Parameter Updating, we will add a fully observed particle, i.e., a particle that contains a value for both $\mathit{Sex}$ and $\mathit{Treatment}$.

• For a compact presentation, we show both nodes in Monitor Style, which means that, in Validation Mode, the distribution of the states is directly shown on the node.

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• To start Parameter Updating, select Main Menu > Inference > Parameter Updating.

• Next, we need to specify the Prior Weight. For our purposes, we select a value of 100.

  

• Choosing an overall Prior Weight of 100 specifies a Prior Weight of 100 for $\mathit{Sex}$, and spreads this weight to $\mathit{Treatment}$, i.e., the Prior Weights are allocated based on the joint probability of each condition.

• We can review the Prior Weights of each node by opening the Node Editor.

  

• In the Node Editor, Prior Weights can also be edited.

• Alternatively, you can assign Prior Weights by selecting Node Context Menu > Properties > Prior Weights. In that case, the Prior Weight is distributed uniformly across all conditions.

• In the Node Editor, you can also edit Discounts.

• You can also assign Discounts for a node by selecting Node Context Menu > Properties > Discounts. In this context, the same Discounts are applied to all conditions.

Adding Particles

• We now take this network and perform Parameter Updating by adding particles one-by-one.
• The following screenshots focus on the relevant parts of the control panel in the Toolbar and the Monitor Panel.

Particle #1

• For the first particle, we set the evidence $\mathit{Sex}=\mathit{Male}$ and $\mathit{Treatment}=\mathit{False}$.

  

• Upon validating the evidence we just set, we open the corresponding Node Editors to see the new probabilities and the new Prior Weight.

  

• Note that for the $\mathit{Treatment}$ node, only the $\mathit{Male}$ condition was updated. The probabilities and the Prior Weight for $\mathit{Female}$ remain unchanged.

• Below is the result of the update after mixing our virtual particles with a particle corresponding to a male that did not take the treatment.

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Example 2b: Partially-Observed Particle

• In the following variation of the above example, we return to the original set of probabilities and a Prior Weight of 100.

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• Now, however, we only apply a particle containing an observation for $\mathit{Treatment}$ but not for $\mathit{Sex}$.

  

• Upon validating this incomplete particle, we can review the probability tables in the Node Editor:

  

• As we can see, even though we do not know the state of the node $\mathit{Sex}$, knowing $\mathit{Treatment}=\mathit{True}$ changed the distribution of $\mathit{Sex}$.

• The new particle is split according to the posterior probability of $\mathit{Sex}$.

• Note that the distribution of the node $\mathit{Sex}$ has been updated as well:

  

Example 2c: Partially-Observed Particle with Soft Evidence

• In a further variation of this example, we apply a partial observation with Soft Evidence.
• More specifically,

For example, we just see a pill box next to the person, which increases our belief that he/she has taken the treatment, say 75%.

This changes the posterior distribution of $\mathit{Sex}$. The new particle will thus be split to take into account the uncertainty on both $\mathit{Sex}$ and $\mathit{Treatment}$.

Below is the result of the update after mixing our virtual particles with this particle. The entire table of $\mathit{Treatment}$ has been updated.

Setting the Prior Weight to 0 allows indicating that you do not want to update the corresponding node.

Obviously, you need to have at least one node that has a Prior Weight greater than 0 for being able to use the Parameter Updating feature.