Conditional vs. Joint Probability: The Foundations Matter
Most AI systems today — including all LLMs — rely on conditional probability. They predict the next word or label based on what’s come before. This works well in many cases, but there’s a catch: the structure of the world — how different variables relate to one another — is never made explicit in this type of model; it is only conditional on input. Structure is learned implicitly, absorbed into model weights during training, and only accessible via creative “prompting.”
This architecture choice has consequences. Because the structure is hidden, it has to be re-learned — or re-prompted — every time you query the model. The results can be powerful, but they’re also stochastic, hard to reproduce, and difficult to trace. And because this approach has become so standard, one might forget to ask whether there’s a better way.
At Sturdy Statistics, we build models using joint probability. That means we model the full structure of the data — not just what happens next, but how everything fits together. Joint probability represents a theory about your data, not just an interpolation of it. A joint model doesn’t just predict — it understands relationships.
These kinds of models are the workhorses of the natural and social sciences. They’re used when you have a theory to test, when you care about uncertainty, and when getting the answer right matters. Until now however, joint models were too slow and too complex to apply to large-scale text. Sturdy Statistics has changed that. Our model runs where you need it to — whether your dataset is tiny or massive.
With joint modeling, Sturdy Statistics can tell you:
- How consumer sentiment depends on product category, and why
- Which trends emerged (or went away) in a company’s most recent quarterly report
- How each agent in your contact center handles each type of question, and which are most effective
- What’s present in your data that you didn’t know to ask about
- How uncertainty shifts when data volume changes
- Which words or phrases most influence each and every prediction
This structure is explicit, auditable, and grounded in statistical theory.
Why does this matter? Because joint models reveal the underlying structure of your data — while conditional models can’t tell you what they don’t know, or what you didn’t think to ask for.
Structure Is Power: The Practical Upside
When LLMs succeed, it’s because they’ve absorbed patterns from enormous datasets. But they find structure implicitly, by internalizing statistical regularities without ever exposing them to the user.
This makes LLMs brittle on rare or unusual inputs. It also means you can’t ask them why they gave a particular answer, or how confident they are in it.
By contrast, explicit structure allows our models to generalize more effectively from less data. Because the model represents a theory about the world, it doesn’t learn ab initio; it uses prior knowledge. Neither does our model have to relearn the context, every time you use it. Instead, our models use incoming data efficiently, focusing on what’s new rather than what’s already known.
Our approach has major benefits:
- Higher few-shot accuracy: Because the structure is built in, we don’t need large datasets to perform well on tasks.
- Quantified uncertainty: Every prediction comes with a confidence estimate, not just a guess.
- Interpretability: If a prediction seems wrong, you can inspect the assumptions, the priors, and the data that drove it. If there’s a mistake, you can fix it — directly and deterministically.
This kind of transparency is invaluable in regulated environments, audit settings, or any situation where trust matters.
Zipf’s Law: Why Rare Data Matters
Real-world data has a long tail. A few things happen often, but most things happen rarely. This is formalized in Zipf’s Law, which shows that the most frequent words in a corpus are extremely common—but most words are not. In language, the tail dominates the meaning.
LLMs are inherently biased toward the head of the distribution. They rely on overwhelming amounts of data to learn rare patterns, and even then, performance on long-tail items is inconsistent.
Our models are different. We’re built to expect rarity. We use:
- Zipf-aware priors that model skewed (power-law) frequency distributions
- Robust handling of unseen categories
- Clean extrapolation even when examples are sparse
This makes our system excel where others struggle: identifying rare issues, analyzing niche domains, and delivering insights even when data is incomplete.
Practical Technology: A Probabilistic Engine with a Friendly Interface
You don’t need to know anything about Bayesian statistics to use our system. All you need to do is:
- Upload your documents: reviews, call transcripts, support tickets, or any other unstructured text.
- We process and structure the data into meaningful rows and columns.
- You query the results using ordinary SQL.
Behind the scenes, our engine runs a combination of:
- Hierarchical Bayesian inference
- Zipf-aware modeling
- Transparent, interpretable probabilistic computation of the joint distribution
The result is a structured dataset that’s ready for analysis, reporting, or automation — no black box, no guesswork.
How We’re Different from LLMs
| Feature | Sturdy Statistics | Large Language Models |
|---|---|---|
| Structure | Explicit, statistical, & informed by domain knowledge | Implicit & learned |
| Uncertainty estimates | Built-in and interpretable | Absent or ad hoc |
| Data requirements | Works with any size dataset | Needs massive data |
| Error diagnosis | Transparent and explainable | Opaque and hard to debug; typically solved with unreliable prompt engineering |
| Interface | SQL + structured output | Natural language, prompting |
| Best For | Precision analysis of real-world data | Creative or generative tasks without a defined correct answer |
We’re not trying to compete with LLMs at storytelling or code generation. But when it comes to extracting structure, measuring confidence, and analyzing text you care about, we’re in a different league.
The Future of Trustworthy AI
AI doesn’t have to be a black box.
LLMs will often tell you something plausible. We’ll tell you something probable—and how probable it is.
If your decisions depend on the data, you need that data to be sturdy. That’s what we deliver: dependable models for real-world understanding.