Conditional Distributions

[harriet-mason]

Hi, me again.

What is your stance on implementing conditional distributions in distributional? I assume you have had this conversation before, but I did search the GitHub issues for the word "conditional" before posting this, and nothing came up.

Specifically, I have been thinking about this example from the ggdibbler vignette:

library(ggdibbler)
library(ggplot2)
library(fable)
#> Loading required package: fabletools
#> Registered S3 method overwritten by 'tsibble':
#>   method               from 
#>   as_tibble.grouped_df dplyr
forecast <- as_tsibble(sunspot.year) |> 
  model(ARIMA(value)) |> 
  forecast(h = "10 years") 

ggplot(forecast) +
  geom_line_sample(aes(x = index, y = value),
                       times=100, alpha=0.5)

^{Created on 2026-01-01 with reprex v2.1.1}

Since ggdibbler just assumes independence between distributions and joins them up with a line, the time series looks more erratic than it probably should. I have considered assuming a conditional distribution if the plot type (e.g. line plot) implies inexchangeability, but I actually don't even know how I would implement that. Conditional sampling would require some heavy-handed assumptions about the model and data that are not always justified.

Since the inexchangeability is a feature of the data itself (in this case, time series), I wonder if this would be better implemented in distributional?

[mitchelloharawild]

Conditional distributions are probably out of scope for distributional. I think this steps from probability distributions (in-scope) toward modelling (out-of-scope), since being able to sub-sample/condition a distribution introduces a lot of domain specific structure and data.

For example, in {fable} the model encodes how the forecast distribution is conditional on the past, e.g. $p(y_{T+h} | y_{t}, y_{t-1}, …)$ or concisely $p(y_{T+h|T})$. Changing the condition to get an updated distribution (e.g. to incorporate a new observation) is very model specific, and would require both the structure of the model and the data (e.g. AR(3) and all past/present/future observations in time).

If you also want to condition on the previous predictions, e.g. $p(y_{T+h|T+h-1} | \hat{y}_{T+h-1|T+h-2}, \hat{y}_{T+h-2|T+h-3}, ...)$ (where $\hat{y}_{T+h-1|T+h-2} = \mathbb{E}(y_{T+h-1|T+h-2})$), then this requires passing the predictions through the model's structure in sequence. This can be done in {fable} with generate() or forecast(simulate = TRUE), but I think it is out of scope for {distributional} since it is closer to modelling than sampling probability distributions.

library(ggplot2)
library(fable)
#> Loading required package: fabletools
#> Registered S3 method overwritten by 'tsibble':
#>   method               from 
#>   as_tibble.grouped_df dplyr
forecast <- as_tsibble(sunspot.year) |> 
  model(ARIMA(value)) |> 
  generate(h = "10 years", generate = TRUE, times = 100) 

ggplot(forecast) +
  geom_line(aes(x = index, y = .sim, group = .rep), alpha=0.5)

^{Created on 2026-01-01 with reprex v2.1.1}

[mitchelloharawild]

I'll also disambiguate, that all forecasts from {fable} are conditional distributions. The standard forecast() output distributions are conditional on the all past observations, $p(y_{T+h} | y_{t}, y_{t-1}, …)$ or concisely $p(y_{T+h|T})$. These conditional distributions works perfectly fine with {distributional} since the model predicts $y_{T+h\mid T} {\sim} \mathcal{N}(\mu, \sigma^2)$.

---

The closest to what will fix your problem within {distributional} is an indexed dist_sample() - which is required to accurately represent a series of sequential draws from a distribution. A use-case for this is rvars (#27 (comment)), and of course the forecasting above.

Essentially dist_sample(indexed = TRUE) (or similar) would sample an index to be used for all distributions in the vector (rather than sampling different indices for each sample distribution in the vector). Although this approach introduces more challenges when different sets of co-indexed sample distributions exist in the same vector.

[harriet-mason]

Wait, I am confused. Are you saying that the distributions output by the {fable} model are technically conditional distributions even though that information is not explicitly coded in the distributional object?

I understand your issues, so I will see if I can get something working with the indexed sample thing you suggested and maybe just insist on some kind of model decomposition from the user. Thanks for the suggestions. I will report back if it doesn't work and just prolongs my suffering.

As a side note, I am not sure I have the same implicit connection between conditional distributions and modelling that you do. Like, while models basically always use conditional distributions, I don't think the reverse is true (i.e. that all uses of conditional distributions imply a model). To me, conditional distributions are just a subset of the probability space, so it feels natural to include them if you already have joint distributions and marginal distributions, especially since they are usually covered alongside the joint and marginal distributions in probability courses.

I also don't understand why the conditional distribution needs to be able to change the conditions to incorporate observation. That feels like a big leap from just being able to represent conditional distributions and is certainly firmly in the modelling category. I don't think that is required to just generate them in sequence, though, is it? Since you can have $y_t = N(y_{t-1}, t)$ or something, which doesn't require the data, just the previously generated value. I figured you could do something with thelag function, but I'm not a time guy, so I haven't thought that much about it.

While it is nice that this functionality exists in forecast (I actually originally tried to make the conditional sampling function based on forecasts generate function), it isn't particularly helpful for all the other versions of this issue lol. This problem does seem to generalise beyond just time series data, and problems with autocorrelation has been the most consistent complaint I get about using ggdibbler and distributional. I can pull three examples just off the top of my head.

• One of the participants in the wombat conference workshop wanted to represent the predictions of a spatially autocorrelated model
• Michael wanted to plot random variables in each cell of the contact tracing heatmap (like the ones in contmap ), but the estimates have autocorrelation
• I have a friend from the physics department who wanted help visualising estimated observations from her experiment, where the experimental observations had autocorrelation, while the theoretical ones didn't (don't ask me about the specifics of what she was doing, I didn't understand the details, and I gave up trying to).

I told all three of these people that they could just break the function down into the deterministic model component and independent random error, and then plot that, so that the random component is independent between observations, and they all kind of looked at me like I was demented and said something like "nah, I'm good".

But either way, all g if it can't be implemented in distributional. I will just try and do something on my end.