Combining Beta Distributions

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jdtoellner
Posts: 71
Joined: Mon Aug 01, 2016 9:45 pm

Combining Beta Distributions

Post by jdtoellner »

Thanks so much for version 2.2!

I've developed a network with multiple Beta distributions. I have a sigma and a beta chooser (set up as chance nodes).

I need to combine two beta distributions. Multiplying them doesn't work. I've attached a model where I add the sigmas and the betas.

Can you verify that this is the proper way to combine Beta distributions? (Adding the sigmas and the betas.)

Is there a more straightforward way to combine Beta distributions built into GeNie?

If I'm combining two Normal distributions I'd use the following equations for mean and standard deviation:
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marek [BayesFusion]
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Re: Combining Beta Distributions

Post by marek [BayesFusion] »

I will be glad to help. Do you mean a new variable that is a mixture of two Beta distributions? In your model, you have both a product and a sum of the Beta distributions. If you want to have a mixture, I propose to add a new variable that will define the proportions (I assumed 50/50 but this is not necessary) and then use Choose (or Switch) to mix them. I'm attaching a modification of your model. I have used a discrete Proportion node but you could also use a uniformly distributed Switch node and an If function that defines the proportions inside the Mixture node. I hope I have understood your problem correctly.
Cheers,

Marek
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jdtoellner
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Re: Combining Beta Distributions

Post by jdtoellner »

Thanks so much for this. You understood my problem precisely. This is exactly what I was looking for.

I didn't realize how the Choose function worked. I didn't realize that it's still choosing something even though the states in the chooser node haven't been selected.

Can you send an example of a uniformly distributed Switch node and an If function that defines the proportions inside the Mixture node.

I'm not sure how I'd construct that.
shooltz[BayesFusion]
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Re: Combining Beta Distributions

Post by shooltz[BayesFusion] »

Can you send an example of a uniformly distributed Switch node and an If function that defines the proportions inside the Mixture node.
The example is attached. It uses two beta nodes with fixed parameters and mixes them in the MixedBeta node. This has the same effect as having a separate discrete node in the previous model.
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marek [BayesFusion]
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Re: Combining Beta Distributions

Post by marek [BayesFusion] »

I have extended the model proposed by Tomek to produce a mixture of three Beta distributions. I have also taken the Uniform distribution outside of the mixture node to make it more explicit. It may be handier in debugging your model (in case you need it).
Cheers,

Marek
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jdtoellner
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Re: Combining Beta Distributions

Post by jdtoellner »

Can you explain what this function is doing?

Code: Select all

MixedBeta=If(Uniform(0,1)>0.5,Beta1,Beta2)
When is Uniform(0,1)>0.5 and when is Uniform(0,1)<=0.5?
shooltz[BayesFusion]
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Re: Combining Beta Distributions

Post by shooltz[BayesFusion] »

Uniform(0,1) draws a random, uniformly distributed sample from the interval between zero and one. On average, 50% calls will give you Uniform(0,1) < 0.5.
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