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:
Combining Beta Distributions
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Combining Beta Distributions
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Re: Combining Beta Distributions
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
Cheers,
Marek
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Re: Combining Beta Distributions
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.
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.
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Re: Combining Beta Distributions
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.Can you send an example of a uniformly distributed Switch node and an If function that defines the proportions inside the Mixture node.
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Re: Combining Beta Distributions
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
Cheers,
Marek
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Re: Combining Beta Distributions
Can you explain what this function is doing?
When is Uniform(0,1)>0.5 and when is Uniform(0,1)<=0.5?
Code: Select all
MixedBeta=If(Uniform(0,1)>0.5,Beta1,Beta2)
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Re: Combining Beta Distributions
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.