Sturdy Statistics builds interpretable AI models that understand structure, quantify uncertainty, and work at any scale.
Conditional vs. Joint Probability: The Foundations Matter
Conditional probability is the foundation of nearly all AI systems today — including every large language model. They predict the next word or label based on what’s come before. In other words, they predict outputs conditionally upon the inputs. 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 is only accessible via creative “prompting.”
This architecture choice has consequences. Because the structure is hidden, the model has to rediscover it every time you make a query. 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 start from a different foundation: 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. It doesn’t just fill in missing words; it models how words, topics, and contexts interact. A joint model understands relationships in a way that’s accessible to the model’s author.
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 things like:
- how consumer sentiment depends on product category—and why;
- which trends emerged (or disappeared) in a company’s most recent quarterly report;
- how each agent in your contact center handles each question type—and which are most effective;
- what’s present in your data that you didn’t know to ask about;
- how uncertainty shifts as data volume changes; and
- which words or phrases most influence each 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 when they don’t know something, or anything you didn’t think to ask for.
Structure Is Power: The Practical Upside
LLMs succeed because they’ve absorbed patterns from enormous datasets — but they do so conditionally, not structurally. 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 re-learn its 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: Built-in structure means strong performance even with limited data.
- Quantified uncertainty: Every prediction includes an interpretable confidence estimate.
- Interpretability: You can inspect the assumptions, priors, and data behind every result. 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 have:
- 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 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. Or, if you’d prefer to have us curate the data, use one of our integrations.
- We process and structure the data into meaningful rows and columns.
- You query the results using ordinary SQL, or using one of our prebuilt no-code dashboards.
Under the hood, our engine combines:
- Hierarchical Bayesian inference
- Zipf-aware modeling
- Transparent, interpretable computation of the joint probability 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 | Performs well across dataset sizes | Needs massive data to train; inference most cost-effective with smaller datasets. |
| 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 |
Large language models are extraordinary tools for open-ended creativity — from writing and brainstorming to coding and summarization. Our focus is different. When the goal is to extract structure, quantify uncertainty, or analyze text with precision, Sturdy Statistics offers a more rigorous and interpretable approach.
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 what’s probable — and how probable.
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.