Discrete Bayesian update: given competing hypotheses each with a prior and the likelihood of the observed evidence, return normalised posteriors. Priors are renormalised to sum to 1.
| Name | Required | Description | Default |
|---|---|---|---|
| hypotheses | Yes |
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Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description must disclose behavioral detail. It usefully states that priors are renormalised to sum to 1 and that posteriors are normalised. However, it leaves out edge-case behavior, constraints on prior/likelihood values, and the exact return structure.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
Two focused sentences with no filler. The primary action is front-loaded, and the renormalisation detail follows naturally. Every sentence earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
The description is sufficient for understanding the basic calculation but lacks the output format, handling of degenerate inputs, and any restrictions on prior/likelihood values. Given no output schema and no annotations, these gaps make it incomplete for fully reliable invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description carries the burden. It explains that 'hypotheses' is a collection of competing hypotheses, each with a prior and likelihood, directly mapping to the required schema fields. It doesn't discuss the optional 'name' field, but the core semantics are clear and add value beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description names a specific operation ('Discrete Bayesian update'), the resource (competing hypotheses with priors and likelihoods), and the output (normalised posteriors). This clearly differentiates it from the frequentist statistical siblings like confidence_interval and hypothesis_test.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description gives clear context for when the tool applies: when updating discrete hypotheses given priors and evidence likelihoods. It does not spell out exclusions or alternatives, but the framing is specific enough for an agent to make the right selection among the listed siblings.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
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Each tool targets a distinct statistical operation: descriptive summaries, distribution calculations, hypothesis tests, confidence intervals, Bayesian updating, and linear regression. The only mild adjacency is between confidence intervals and hypothesis tests, but their descriptions clearly separate estimation from significance testing.
All six tool names follow the same lowercase snake_case pattern and are straightforward noun phrases describing the statistical concept. There is no mixing of conventions or inconsistent verb styles across the set.
Six tools is well within the ideal range and each one covers a broad, meaningful area of statistics. The count feels appropriately scoped without redundancy or bloat.
The set covers core statistical workflows: description, distributions, estimation, tests, Bayesian updates, and regression. Some common additions like ANOVA or nonparametric tests are absent, but they are not necessary for most basic statistics tasks.