I am trying to estimate a copula model where some of the variables are distributed as zero-one-inflated beta. My goal is to use the Chib and Greenberg approach (as with blavaan ) where discrete values are modeled as continuous values within the bounds implied by the other model parameters. In this ca…

[image] simonbrauer: The conclusion I draw from this is that the specifying the bounded parameters is proportionally equivalent to the corresponding Bernoulli log-likelihood. Yes, that is true for theta. When P0 and P1 are parameters there’s an additional adjustment for the change of variable…

[edit: sorry for the initial fragment] [image] simonbrauer: My goal is to use the Chib and Greenberg approach I’m not familiar with their approach. Why use continuous values rather than modeling discrete variables as discrete? Anyway, let’s not worry about that and just try to answer your …

Thanks for the comments, Bob. I appreciate you taking the time to clean things up (and I apologize in advance for throwing together an updated model for illustration that doesn’t yet take those things into account). The Chib and Greenberg part is core to the issue, so I apologize for not elaboratin…

I’m clearly making at least one other error because the “unbiased” distribution of theta that I’m plotting is still not correct, as it doesn’t align with a Dirichlet([1,1,1]) distribution. I appreciate any other insight others have, but I’ll do some more digging in the meanwhile.

Do you have a definition of the cdfs for the distributions that you’re interested in using? You can use these to estimate the copula model fairly easily, Here’s an example of this with gamma and exponential distributions: Copulas

Hey Andrew. First, thank you for doing all the work of putting together the guide you linked. It, along with @spinkney 's documentation , has been immensely helpful as I’ve been working on this project. The PDF is zoib(x) \begin{cases} \theta_1 & \text{if } x=0 \\ \theta_2 \times beta(x | \alpha, \…

[image] simonbrauer: First, the biased model. This is just a data and parameter definition. You can run it, but what you’re calling “biased” and “unbiased” will give the same posteriors for P0 and P1. So I’m not sure what you mean by “bias” here. Note on terminology: A Bayesian model, by …

[image] Bob_Carpenter: What are the three facets on the plots The densities are the posterior draws of theta from what I had called the unbiased and biased models. The three facets align with each value of theta, which correspond to the ranges X=0, 0<X<1, and X=1 of the original data. As you …

[image] simonbrauer: The densities are the posterior draws of theta from what I had called the unbiased and biased models. I was talking about your post that had two models, what you called “biased” and “unbiased” and they had empty model blocks in the post. I had assumed that’s what you wer…

There’s clearly some things I’m not understanding about the sampler. I’ll try and simplify things and make it clearer what I’m showing. On bias, I made things more confusing than they needed to be. Let’s pretend I didn’t use that word. More concretely I mean “not what I intended/expected.” In the m…

@spinkney gave the authoritative math answer. I just want to chime in and connect this to some intuition. Let’s consider a simpler model, with only 2 parameters: parameters { real<lower=0, upper=1> theta1; real<lower=0, upper=theta1> theta2; } @simonbrauer 's initial expectation was that thi…

Jacobian adjustment for parameter with parameter-based upper+lower bounds

Modeling

spinkney February 24, 2025, 11:43pm 14

Happy to help! And I think the thread you’re looking for is Parameter bounds that depend on other parameters.

Topic		Replies	Views
Jacobian adjustment needed? Modeling fitting-issues , specification	4	959	February 14, 2022
Observing non-linear function of latent variables Modeling	20	429	September 23, 2024
Are Jacobian adjustments necessary when the target parameter is a difference between two parameters? Modeling specification , jacobian-adjustment	6	1526	June 17, 2020
Absent prior draws? Modeling	5	941	January 16, 2018
Jacobian on fandamental examples Modeling	6	598	July 23, 2020

Jacobian adjustment for parameter with parameter-based upper+lower bounds

Related topics