I’m relatively new to pyMC, and I’m trying to implement a state space model whose transition matrix depends on time. So far, I’ve been following the example in this notebook . It does almost everything I need, except for the time-dependence. Is there an easy way to modify it to add a time-varying tra…

I think I get it now. Thanks for clarifying the setup! The index ["transition", 0, 0] is a single element in a matrix, yeah. When you registered d_rand, you said it has shape (None, 2). From your equations, it looks like d_rand should just be a scalar, so the shape should be (None, 1) or (None,), d…

Thanks for the link. Unfortunately, I’m not fluent enough with pyMC to figure out how to modify that example for my purposes. I’ve put together a toy version of what I want to do. It’s a difference equation where one of the rate parameters fluctuates as a function of time, with some mean and varian…

The model you are writing has to be in the form: \begin{align} x_t & = T_t x_{t-1} + c_t + R_t \varepsilon_t, & \varepsilon_t \sim MVN(0, Q_t) \\ y_t &= Z_t x_t + d_t + \eta_t, & \eta_t \sim MVN(0, H_t) \end{align} I don’t know your model, and the 3 lines of comments I see aren’t very clear. I th…

In this example, c = \begin{bmatrix} \Delta t \\ 0 \end{bmatrix}, Z = \begin{bmatrix} 0 &1 \end{bmatrix}, and T=\begin{bmatrix} -d_{rand}\cdot\Delta t & 0 \\ d_{rand}\cdot\Delta t & -1 \end{bmatrix}. All other matrices are zero. (Aside: In the past, I’ve gotten an error message whenever I try to…

Thanks! That’s exactly what I was looking for. Unfortunately, now I’m getting a new, different error message (progress!), which I assume is caused by me incorrectly assigning a shape somewhere. But just in case it’s an actual bug, and not just me doing things wrong, here’s the error. idata = pm.s…

Does pm.sample_prior_predictive() work? Also check what model.debug() says. My guess is that it’s something to do with broadcasting. Can you share the model code? Edit: Looking at the code in the post above, your model still have several problems: You need to define P0, the initial covariance ma…

[image] jessegrabowski: This model will fit, but doing so is hopeless unless you impose some structure on the sequence of d_rand. Otherwise each parameter is informed by only 1 observation. Oh, wait… is d_rand, as currently coded, a vector of several independent random variables, each of whic…

[image] JSR: Oh, wait… is d_rand, as currently coded, a vector of several independent random variables, each of which has a prior that can update independently? I want them all to share the same distribution. What would it mean for them to “share the same distribution”? If you want them to ch…

[image] jessegrabowski: What would it mean for them to “share the same distribution”? Like rolling the same die multiple times. That would give you a sequence of numbers that change from one roll to the next, but they’re all drawn from the same probability distribution. That’s exactly what …

I think you’re confusing two things. Your model is not as simple as rolling a dice, so I need to expand the example a bit to get at what is going on. You have a dice, which you do not observe, and two coins, one which is biased towards heads, and one which is biased towards tails. You roll the dice.…

Does the state_space model support time-dependent transition matrices?

Questions v5

jessegrabowski January 20, 2025, 2:14am 2

Yes, all matrices except x0 and P0 are allowed to be time varying. This discussion goes through some of the implementation details.

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Does the state_space model support time-dependent transition matrices?

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