eerge remote-tracking branch 'origin/develop' into ts-property
This commit is contained in:
commit
a5cb34ff7f
7
.github/workflows/codeql-analysis.yml
vendored
7
.github/workflows/codeql-analysis.yml
vendored
|
@ -18,13 +18,6 @@ on:
|
||||||
- production
|
- production
|
||||||
- staging
|
- staging
|
||||||
- develop
|
- develop
|
||||||
pull_request:
|
|
||||||
# The branches below must be a subset of the branches above
|
|
||||||
branches:
|
|
||||||
- master
|
|
||||||
- production
|
|
||||||
- staging
|
|
||||||
- develop
|
|
||||||
schedule:
|
schedule:
|
||||||
- cron: "42 19 * * 0"
|
- cron: "42 19 * * 0"
|
||||||
|
|
||||||
|
|
|
@ -1,6 +0,0 @@
|
||||||
{
|
|
||||||
"extends": "@parcel/config-default",
|
|
||||||
"transformers": {
|
|
||||||
"*.res": ["@parcel/transformer-raw"]
|
|
||||||
}
|
|
||||||
}
|
|
|
@ -2,3 +2,5 @@ dist
|
||||||
lib
|
lib
|
||||||
*.bs.js
|
*.bs.js
|
||||||
*.gen.tsx
|
*.gen.tsx
|
||||||
|
.nyc_output/
|
||||||
|
coverage/
|
||||||
|
|
|
@ -86,7 +86,9 @@ module Exponential = {
|
||||||
|
|
||||||
module Cauchy = {
|
module Cauchy = {
|
||||||
type t = cauchy
|
type t = cauchy
|
||||||
let make = (local, scale): symbolicDist => #Cauchy({local: local, scale: scale})
|
let make = (local, scale): result<symbolicDist, string> => Ok(
|
||||||
|
#Cauchy({local: local, scale: scale}),
|
||||||
|
)
|
||||||
let pdf = (x, t: t) => Jstat.Cauchy.pdf(x, t.local, t.scale)
|
let pdf = (x, t: t) => Jstat.Cauchy.pdf(x, t.local, t.scale)
|
||||||
let cdf = (x, t: t) => Jstat.Cauchy.cdf(x, t.local, t.scale)
|
let cdf = (x, t: t) => Jstat.Cauchy.cdf(x, t.local, t.scale)
|
||||||
let inv = (p, t: t) => Jstat.Cauchy.inv(p, t.local, t.scale)
|
let inv = (p, t: t) => Jstat.Cauchy.inv(p, t.local, t.scale)
|
||||||
|
|
|
@ -44,7 +44,7 @@ let defaultBindings: T.bindings = Belt.Map.String.empty
|
||||||
/*
|
/*
|
||||||
Recursively evaluate/reduce the expression (Lisp AST)
|
Recursively evaluate/reduce the expression (Lisp AST)
|
||||||
*/
|
*/
|
||||||
let rec reduceExpression = (expression: t, bindings: T.bindings): result<expressionValue, 'e> => {
|
let reduceExpression = (expression: t, bindings: T.bindings): result<expressionValue, 'e> => {
|
||||||
/*
|
/*
|
||||||
After reducing each level of expression(Lisp AST), we have a value list to evaluate
|
After reducing each level of expression(Lisp AST), we have a value list to evaluate
|
||||||
*/
|
*/
|
||||||
|
@ -135,6 +135,7 @@ let rec reduceExpression = (expression: t, bindings: T.bindings): result<express
|
||||||
)
|
)
|
||||||
racc->Result.flatMap(acc => acc->doMacroCall(bindings))
|
racc->Result.flatMap(acc => acc->doMacroCall(bindings))
|
||||||
}
|
}
|
||||||
|
| T.EBindings(bindings) => T.EBindings(bindings)->Ok
|
||||||
}
|
}
|
||||||
|
|
||||||
let rec reduceExpandedExpression = (expression: t): result<expressionValue, 'e> =>
|
let rec reduceExpandedExpression = (expression: t): result<expressionValue, 'e> =>
|
||||||
|
@ -155,6 +156,7 @@ let rec reduceExpression = (expression: t, bindings: T.bindings): result<express
|
||||||
)
|
)
|
||||||
racc->Result.flatMap(acc => acc->reduceValueList)
|
racc->Result.flatMap(acc => acc->reduceValueList)
|
||||||
}
|
}
|
||||||
|
| T.EBindings(bindings) => RETodo("Cannot return bindings")->Error
|
||||||
}
|
}
|
||||||
|
|
||||||
let rExpandedExpression: result<t, 'e> = expression->seekMacros(bindings)
|
let rExpandedExpression: result<t, 'e> = expression->seekMacros(bindings)
|
||||||
|
|
|
@ -149,6 +149,7 @@ module SymbolicConstructors = {
|
||||||
| "uniform" => Ok(SymbolicDist.Uniform.make)
|
| "uniform" => Ok(SymbolicDist.Uniform.make)
|
||||||
| "beta" => Ok(SymbolicDist.Beta.make)
|
| "beta" => Ok(SymbolicDist.Beta.make)
|
||||||
| "lognormal" => Ok(SymbolicDist.Lognormal.make)
|
| "lognormal" => Ok(SymbolicDist.Lognormal.make)
|
||||||
|
| "cauchy" => Ok(SymbolicDist.Cauchy.make)
|
||||||
| "to" => Ok(SymbolicDist.From90thPercentile.make)
|
| "to" => Ok(SymbolicDist.From90thPercentile.make)
|
||||||
| _ => Error("Unreachable state")
|
| _ => Error("Unreachable state")
|
||||||
}
|
}
|
||||||
|
@ -182,7 +183,7 @@ let dispatchToGenericOutput = (call: ExpressionValue.functionCall): option<
|
||||||
->E.R.bind(r => r(f1))
|
->E.R.bind(r => r(f1))
|
||||||
->SymbolicConstructors.symbolicResultToOutput
|
->SymbolicConstructors.symbolicResultToOutput
|
||||||
| (
|
| (
|
||||||
("normal" | "uniform" | "beta" | "lognormal" | "to") as fnName,
|
("normal" | "uniform" | "beta" | "lognormal" | "cauchy" | "to") as fnName,
|
||||||
[EvNumber(f1), EvNumber(f2)],
|
[EvNumber(f1), EvNumber(f2)],
|
||||||
) =>
|
) =>
|
||||||
SymbolicConstructors.twoFloat(fnName)
|
SymbolicConstructors.twoFloat(fnName)
|
||||||
|
|
2
packages/website/.prettierignore
Normal file
2
packages/website/.prettierignore
Normal file
|
@ -0,0 +1,2 @@
|
||||||
|
.docusaurus
|
||||||
|
build
|
|
@ -1,12 +1,15 @@
|
||||||
---
|
---
|
||||||
|
title: "Functions Reference"
|
||||||
sidebar_position: 7
|
sidebar_position: 7
|
||||||
---
|
---
|
||||||
|
|
||||||
import { SquiggleEditor } from "../../src/components/SquiggleEditor";
|
import { SquiggleEditor } from "../../src/components/SquiggleEditor";
|
||||||
|
|
||||||
# Squiggle Functions Reference
|
_The source of truth for this document is [this file of code](https://github.com/quantified-uncertainty/squiggle/blob/develop/packages/squiggle-lang/src/rescript/ReducerInterface/ReducerInterface_GenericDistribution.res)_
|
||||||
|
|
||||||
## Distributions
|
## Inventory distributions
|
||||||
|
|
||||||
|
We provide starter distributions, computed symbolically.
|
||||||
|
|
||||||
### Normal distribution
|
### Normal distribution
|
||||||
|
|
||||||
|
@ -15,6 +18,10 @@ and standard deviation.
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="normal(5, 1)" />
|
<SquiggleEditor initialSquiggleString="normal(5, 1)" />
|
||||||
|
|
||||||
|
#### Validity
|
||||||
|
|
||||||
|
- `sd > 0`
|
||||||
|
|
||||||
### Uniform distribution
|
### Uniform distribution
|
||||||
|
|
||||||
The `uniform(low, high)` function creates a uniform distribution between the
|
The `uniform(low, high)` function creates a uniform distribution between the
|
||||||
|
@ -22,86 +29,281 @@ two given numbers.
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="uniform(3, 7)" />
|
<SquiggleEditor initialSquiggleString="uniform(3, 7)" />
|
||||||
|
|
||||||
|
#### Validity
|
||||||
|
|
||||||
|
- `low < high`
|
||||||
|
|
||||||
### Lognormal distribution
|
### Lognormal distribution
|
||||||
|
|
||||||
The `lognormal(mu, sigma)` returns the log of a normal distribution with parameters
|
The `lognormal(mu, sigma)` returns the log of a normal distribution with parameters
|
||||||
mu and sigma. The log of lognormal(mu, sigma) is a normal distribution with parameters
|
`mu` and `sigma`. The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu` and standard deviation `sigma`.
|
||||||
mean mu and standard deviation sigma.
|
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="lognormal(0, 0.7)" />
|
<SquiggleEditor initialSquiggleString="lognormal(0, 0.7)" />
|
||||||
|
|
||||||
An alternative format is also available. The "to" notation creates a lognormal
|
An alternative format is also available. The `to` notation creates a lognormal
|
||||||
distribution with a 90% confidence interval between the two numbers. We add
|
distribution with a 90% confidence interval between the two numbers. We add
|
||||||
this convinience as lognormal distributions are commonly used in practice.
|
this convenience as lognormal distributions are commonly used in practice.
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="2 to 10" />
|
<SquiggleEditor initialSquiggleString="2 to 10" />
|
||||||
|
|
||||||
|
#### Future feature:
|
||||||
|
|
||||||
Furthermore, it's also possible to create a lognormal from it's actual mean
|
Furthermore, it's also possible to create a lognormal from it's actual mean
|
||||||
and standard deviation, using `lognormalFromMeanAndStdDev`.
|
and standard deviation, using `lognormalFromMeanAndStdDev`.
|
||||||
|
|
||||||
|
TODO: interpreter/parser doesn't provide this in current `develop` branch
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="lognormalFromMeanAndStdDev(20, 10)" />
|
<SquiggleEditor initialSquiggleString="lognormalFromMeanAndStdDev(20, 10)" />
|
||||||
|
|
||||||
|
#### Validity
|
||||||
|
|
||||||
|
- `sigma > 0`
|
||||||
|
- In `x to y` notation, `x < y`
|
||||||
|
|
||||||
### Beta distribution
|
### Beta distribution
|
||||||
|
|
||||||
The `beta(a, b)` function creates a beta distribution with parameters a and b:
|
The `beta(a, b)` function creates a beta distribution with parameters `a` and `b`:
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="beta(20, 20)" />
|
<SquiggleEditor initialSquiggleString="beta(10, 20)" />
|
||||||
|
|
||||||
|
#### Validity
|
||||||
|
|
||||||
|
- `a > 0`
|
||||||
|
- `b > 0`
|
||||||
|
- Empirically, we have noticed that numerical instability arises when `a < 1` or `b < 1`
|
||||||
|
|
||||||
### Exponential distribution
|
### Exponential distribution
|
||||||
|
|
||||||
The `exponential(mean)` function creates an exponential distribution with the given
|
The `exponential(rate)` function creates an exponential distribution with the given
|
||||||
mean.
|
rate.
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="exponential(1)" />
|
<SquiggleEditor initialSquiggleString="exponential(1.11)" />
|
||||||
|
|
||||||
### The Triangular distribution
|
#### Validity
|
||||||
|
|
||||||
|
- `rate > 0`
|
||||||
|
|
||||||
|
### Triangular distribution
|
||||||
|
|
||||||
The `triangular(a,b,c)` function creates a triangular distribution with lower
|
The `triangular(a,b,c)` function creates a triangular distribution with lower
|
||||||
bound a, mode b and upper bound c.
|
bound `a`, mode `b` and upper bound `c`.
|
||||||
|
|
||||||
|
#### Validity
|
||||||
|
|
||||||
|
- `a < b < c`
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="triangular(1, 2, 4)" />
|
<SquiggleEditor initialSquiggleString="triangular(1, 2, 4)" />
|
||||||
|
|
||||||
### Multimodal distriutions
|
### Scalar (constant dist)
|
||||||
|
|
||||||
The multimodal function combines 2 or more other distributions to create a weighted
|
Squiggle, when the context is right, automatically casts a float to a constant distribution.
|
||||||
|
|
||||||
|
## Operating on distributions
|
||||||
|
|
||||||
|
Here are the ways we combine distributions.
|
||||||
|
|
||||||
|
### Mixture of distributions
|
||||||
|
|
||||||
|
The `mixture` function combines 2 or more other distributions to create a weighted
|
||||||
combination of the two. The first positional arguments represent the distributions
|
combination of the two. The first positional arguments represent the distributions
|
||||||
to be combined, and the last argument is how much to weigh every distribution in the
|
to be combined, and the last argument is how much to weigh every distribution in the
|
||||||
combination.
|
combination.
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="mx(uniform(0,1), normal(1,1), [0.5, 0.5])" />
|
<SquiggleEditor initialSquiggleString="mixture(uniform(0,1), normal(1,1), [0.5, 0.5])" />
|
||||||
|
|
||||||
It's possible to create discrete distributions using this method.
|
It's possible to create discrete distributions using this method.
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="mx(0, 1, [0.2,0.8])" />
|
<SquiggleEditor initialSquiggleString="mixture(0, 1, [0.2,0.8])" />
|
||||||
|
|
||||||
As well as mixed distributions:
|
As well as mixed distributions:
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="mx(3, 8, 1 to 10, [0.2, 0.3, 0.5])" />
|
<SquiggleEditor initialSquiggleString="mixture(3, 8, 1 to 10, [0.2, 0.3, 0.5])" />
|
||||||
|
|
||||||
## Other Functions
|
An alias of `mixture` is `mx`
|
||||||
|
|
||||||
### PDF of a distribution
|
#### Validity
|
||||||
|
|
||||||
The `pdf(distribution, x)` function returns the density of a distribution at the
|
Using javascript's variable arguments notation, consider `mx(...dists, weights)`:
|
||||||
|
|
||||||
|
- `dists.length == weights.length`
|
||||||
|
|
||||||
|
### Addition
|
||||||
|
|
||||||
|
A horizontal right shift
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dist1 + dist2`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
### Subtraction
|
||||||
|
|
||||||
|
A horizontal left shift
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dist1 - dist2`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
### Multiplication
|
||||||
|
|
||||||
|
TODO: provide intuition pump for the semantics
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dist1 * dist2`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
We also provide concatenation of two distributions as a syntax sugar for `*`
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="(0.1 to 1) triangular(1,2,3)" />
|
||||||
|
|
||||||
|
### Division
|
||||||
|
|
||||||
|
TODO: provide intuition pump for the semantics
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dist1 / dist2`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
### Exponentiation
|
||||||
|
|
||||||
|
TODO: provide intuition pump for the semantics
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString={`(0.1 to 1) ^ beta(2, 3)`} />
|
||||||
|
|
||||||
|
### Taking the base `e` exponential
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist = triangular(1,2,3)
|
||||||
|
exp(dist)`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
### Taking logarithms
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist = triangular(1,2,3)
|
||||||
|
log(dist)`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist = beta(1,2)
|
||||||
|
log10(dist)`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
Base `x`
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`x = 2
|
||||||
|
dist = beta(2,3)
|
||||||
|
log(dist, x)`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
#### Validity
|
||||||
|
|
||||||
|
- `x` must be a scalar
|
||||||
|
- See [the current discourse](https://github.com/quantified-uncertainty/squiggle/issues/304)
|
||||||
|
|
||||||
|
### Pointwise addition
|
||||||
|
|
||||||
|
**Pointwise operations are done with `PointSetDist` internals rather than `SampleSetDist` internals**.
|
||||||
|
|
||||||
|
TODO: this isn't in the new interpreter/parser yet.
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dist1 .+ dist2`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
### Pointwise subtraction
|
||||||
|
|
||||||
|
TODO: this isn't in the new interpreter/parser yet.
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dist1 .- dist2`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
### Pointwise multiplication
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dist1 .* dist2`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
### Pointwise division
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dist1 ./ dist2`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
### Pointwise exponentiation
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dist1 .^ dist2`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
### Pointwise logarithm
|
||||||
|
|
||||||
|
TODO: write about the semantics and the case handling re scalar vs. dist and log base.
|
||||||
|
|
||||||
|
<SquiggleEditor
|
||||||
|
initialSquiggleString={`dist1 = 1 to 10
|
||||||
|
dist2 = triangular(1,2,3)
|
||||||
|
dotLog(dist1, dist2)`}
|
||||||
|
/>
|
||||||
|
|
||||||
|
## Standard functions on distributions
|
||||||
|
|
||||||
|
### Probability density function
|
||||||
|
|
||||||
|
The `pdf(dist, x)` function returns the density of a distribution at the
|
||||||
given point x.
|
given point x.
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="pdf(normal(0,1),0)" />
|
<SquiggleEditor initialSquiggleString="pdf(normal(0,1),0)" />
|
||||||
|
|
||||||
### Inverse of a distribution
|
#### Validity
|
||||||
|
|
||||||
The `inv(distribution, prob)` gives the value x or which the probability for all values
|
- `x` must be a scalar
|
||||||
lower than x is equal to prob. It is the inverse of `cdf`.
|
- `dist` must be a distribution
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="inv(normal(0,1),0.5)" />
|
### Cumulative density function
|
||||||
|
|
||||||
### CDF of a distribution
|
The `cdf(dist, x)` gives the cumulative probability of the distribution
|
||||||
|
|
||||||
The `cdf(distribution,x)` gives the cumulative probability of the distribution
|
|
||||||
or all values lower than x. It is the inverse of `inv`.
|
or all values lower than x. It is the inverse of `inv`.
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="cdf(normal(0,1),0)" />
|
<SquiggleEditor initialSquiggleString="cdf(normal(0,1),0)" />
|
||||||
|
|
||||||
### Mean of a distribution
|
#### Validity
|
||||||
|
|
||||||
|
- `x` must be a scalar
|
||||||
|
- `dist` must be a distribution
|
||||||
|
|
||||||
|
### Inverse CDF
|
||||||
|
|
||||||
|
The `inv(dist, prob)` gives the value x or which the probability for all values
|
||||||
|
lower than x is equal to prob. It is the inverse of `cdf`.
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="inv(normal(0,1),0.5)" />
|
||||||
|
|
||||||
|
#### Validity
|
||||||
|
|
||||||
|
- `prob` must be a scalar (please only put it in `(0,1)`)
|
||||||
|
- `dist` must be a distribution
|
||||||
|
|
||||||
|
### Mean
|
||||||
|
|
||||||
The `mean(distribution)` function gives the mean (expected value) of a distribution.
|
The `mean(distribution)` function gives the mean (expected value) of a distribution.
|
||||||
|
|
||||||
|
@ -112,3 +314,55 @@ The `mean(distribution)` function gives the mean (expected value) of a distribut
|
||||||
The `sample(distribution)` samples a given distribution.
|
The `sample(distribution)` samples a given distribution.
|
||||||
|
|
||||||
<SquiggleEditor initialSquiggleString="sample(normal(0, 10))" />
|
<SquiggleEditor initialSquiggleString="sample(normal(0, 10))" />
|
||||||
|
|
||||||
|
## Normalization
|
||||||
|
|
||||||
|
Some distribution operations (like horizontal shift) return an unnormalized distriibution.
|
||||||
|
|
||||||
|
We provide a `normalize` function
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="normalize((0.1 to 1) + triangular(0.1, 1, 10))" />
|
||||||
|
|
||||||
|
#### Validity - Input to `normalize` must be a dist
|
||||||
|
|
||||||
|
We provide a predicate `isNormalized`, for when we have simple control flow
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="isNormalized((0.1 to 1) * triangular(0.1, 1, 10))" />
|
||||||
|
|
||||||
|
#### Validity
|
||||||
|
|
||||||
|
- Input to `isNormalized` must be a dist
|
||||||
|
|
||||||
|
## Convert any distribution to a sample set distribution
|
||||||
|
|
||||||
|
`toSampleSet` has two signatures
|
||||||
|
|
||||||
|
It is unary when you use an internal hardcoded number of samples
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="toSampleSet(0.1 to 1)" />
|
||||||
|
|
||||||
|
And binary when you provide a number of samples (floored)
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="toSampleSet(0.1 to 1, 100)" />
|
||||||
|
|
||||||
|
## `inspect`
|
||||||
|
|
||||||
|
You may like to debug by right clicking your browser and using the _inspect_ functionality on the webpage, and viewing the _console_ tab. Then, wrap your squiggle output with `inspect` to log an internal representation.
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="inspect(toSampleSet(0.1 to 1, 100))" />
|
||||||
|
|
||||||
|
Save for a logging side effect, `inspect` does nothing to input and returns it.
|
||||||
|
|
||||||
|
## Truncate
|
||||||
|
|
||||||
|
You can cut off from the left
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="truncateLeft(0.1 to 1, 0.5)" />
|
||||||
|
|
||||||
|
You can cut off from the right
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="truncateRight(0.1 to 1, 10)" />
|
||||||
|
|
||||||
|
You can cut off from both sides
|
||||||
|
|
||||||
|
<SquiggleEditor initialSquiggleString="truncate(0.1 to 1, 0.5, 1.5)" />
|
||||||
|
|
|
@ -1,5 +1,5 @@
|
||||||
---
|
---
|
||||||
title: Statistical properties of algebraic combinations of distributions for property testing.
|
title: Invariants of Probability Distributions
|
||||||
urlcolor: blue
|
urlcolor: blue
|
||||||
author:
|
author:
|
||||||
- Nuño Sempere
|
- Nuño Sempere
|
||||||
|
@ -7,13 +7,17 @@ author:
|
||||||
abstract: This document outlines some properties about algebraic combinations of distributions. It is meant to facilitate property tests for [Squiggle](https://squiggle-language.com/), an estimation language for forecasters. So far, we are focusing on the means, the standard deviation and the shape of the pdfs.
|
abstract: This document outlines some properties about algebraic combinations of distributions. It is meant to facilitate property tests for [Squiggle](https://squiggle-language.com/), an estimation language for forecasters. So far, we are focusing on the means, the standard deviation and the shape of the pdfs.
|
||||||
---
|
---
|
||||||
|
|
||||||
|
Invariants to check with property tests.
|
||||||
|
|
||||||
_This document right now is normative and aspirational, not a description of the testing that's currently done_.
|
_This document right now is normative and aspirational, not a description of the testing that's currently done_.
|
||||||
|
|
||||||
|
## Algebraic combinations
|
||||||
|
|
||||||
The academic keyword to search for in relation to this document is "[algebra of random variables](https://wikiless.org/wiki/Algebra_of_random_variables?lang=en)". Squiggle doesn't yet support getting the standard deviation, denoted by $\sigma$, but such support could yet be added.
|
The academic keyword to search for in relation to this document is "[algebra of random variables](https://wikiless.org/wiki/Algebra_of_random_variables?lang=en)". Squiggle doesn't yet support getting the standard deviation, denoted by $\sigma$, but such support could yet be added.
|
||||||
|
|
||||||
## Means and standard deviations
|
### Means and standard deviations
|
||||||
|
|
||||||
### Sums
|
#### Sums
|
||||||
|
|
||||||
$$
|
$$
|
||||||
mean(f+g) = mean(f) + mean(g)
|
mean(f+g) = mean(f) + mean(g)
|
||||||
|
@ -29,7 +33,7 @@ $$
|
||||||
mean(normal(a,b) + normal(c,d)) = mean(normal(a+c, \sqrt{b^2 + d^2}))
|
mean(normal(a,b) + normal(c,d)) = mean(normal(a+c, \sqrt{b^2 + d^2}))
|
||||||
$$
|
$$
|
||||||
|
|
||||||
### Subtractions
|
#### Subtractions
|
||||||
|
|
||||||
$$
|
$$
|
||||||
mean(f-g) = mean(f) - mean(g)
|
mean(f-g) = mean(f) - mean(g)
|
||||||
|
@ -39,7 +43,7 @@ $$
|
||||||
\sigma(f-g) = \sqrt{\sigma(f)^2 + \sigma(g)^2}
|
\sigma(f-g) = \sqrt{\sigma(f)^2 + \sigma(g)^2}
|
||||||
$$
|
$$
|
||||||
|
|
||||||
### Multiplications
|
#### Multiplications
|
||||||
|
|
||||||
$$
|
$$
|
||||||
mean(f \cdot g) = mean(f) \cdot mean(g)
|
mean(f \cdot g) = mean(f) \cdot mean(g)
|
||||||
|
@ -49,15 +53,15 @@ $$
|
||||||
\sigma(f \cdot g) = \sqrt{ (\sigma(f)^2 + mean(f)) \cdot (\sigma(g)^2 + mean(g)) - (mean(f) \cdot mean(g))^2}
|
\sigma(f \cdot g) = \sqrt{ (\sigma(f)^2 + mean(f)) \cdot (\sigma(g)^2 + mean(g)) - (mean(f) \cdot mean(g))^2}
|
||||||
$$
|
$$
|
||||||
|
|
||||||
### Divisions
|
#### Divisions
|
||||||
|
|
||||||
Divisions are tricky, and in general we don't have good expressions to characterize properties of ratios. In particular, the ratio of two normals is a Cauchy distribution, which doesn't have to have a mean.
|
Divisions are tricky, and in general we don't have good expressions to characterize properties of ratios. In particular, the ratio of two normals is a Cauchy distribution, which doesn't have to have a mean.
|
||||||
|
|
||||||
## Probability density functions (pdfs)
|
### Probability density functions (pdfs)
|
||||||
|
|
||||||
Specifying the pdf of the sum/multiplication/... of distributions as a function of the pdfs of the individual arguments can still be done. But it requires integration. My sense is that this is still doable, and I (Nuño) provide some _pseudocode_ to do this.
|
Specifying the pdf of the sum/multiplication/... of distributions as a function of the pdfs of the individual arguments can still be done. But it requires integration. My sense is that this is still doable, and I (Nuño) provide some _pseudocode_ to do this.
|
||||||
|
|
||||||
### Sums
|
#### Sums
|
||||||
|
|
||||||
Let $f, g$ be two independently distributed functions. Then, the pdf of their sum, evaluated at a point $z$, expressed as $(f + g)(z)$, is given by:
|
Let $f, g$ be two independently distributed functions. Then, the pdf of their sum, evaluated at a point $z$, expressed as $(f + g)(z)$, is given by:
|
||||||
|
|
||||||
|
@ -110,15 +114,31 @@ let pdfOfSum = (pdf1, pdf2, cdf1, cdf2, z) => {
|
||||||
};
|
};
|
||||||
```
|
```
|
||||||
|
|
||||||
## Cumulative density functions
|
### Cumulative density functions
|
||||||
|
|
||||||
TODO
|
TODO
|
||||||
|
|
||||||
## Inverse cumulative density functions
|
### Inverse cumulative density functions
|
||||||
|
|
||||||
TODO
|
TODO
|
||||||
|
|
||||||
# To do:
|
## `pdf`, `cdf`, and `inv`
|
||||||
|
|
||||||
|
With $\forall dist, pdf := x \mapsto \texttt{pdf}(dist, x) \land cdf := x \mapsto \texttt{cdf}(dist, x) \land inv := p \mapsto \texttt{inv}(dist, p)$,
|
||||||
|
|
||||||
|
### `cdf` and `inv` are inverses
|
||||||
|
|
||||||
|
$$
|
||||||
|
\forall x \in (0,1), cdf(inv(x)) = x \land \forall x \in \texttt{dom}(cdf), x = inv(cdf(x))
|
||||||
|
$$
|
||||||
|
|
||||||
|
### The codomain of `cdf` equals the open interval `(0,1)` equals the codomain of `pdf`
|
||||||
|
|
||||||
|
$$
|
||||||
|
\texttt{cod}(cdf) = (0,1) = \texttt{cod}(pdf)
|
||||||
|
$$
|
||||||
|
|
||||||
|
## To do:
|
||||||
|
|
||||||
- Provide sources or derivations, useful as this document becomes more complicated
|
- Provide sources or derivations, useful as this document becomes more complicated
|
||||||
- Provide definitions for the probability density function, exponential, inverse, log, etc.
|
- Provide definitions for the probability density function, exponential, inverse, log, etc.
|
||||||
|
|
|
@ -49,7 +49,7 @@ const config = {
|
||||||
sidebarPath: require.resolve("./sidebars.js"),
|
sidebarPath: require.resolve("./sidebars.js"),
|
||||||
// Please change this to your repo.
|
// Please change this to your repo.
|
||||||
editUrl:
|
editUrl:
|
||||||
"https://github.com/quantified-uncertainty/squiggle/tree/master/packages/website/",
|
"https://github.com/quantified-uncertainty/squiggle/tree/develop/packages/website/",
|
||||||
remarkPlugins: [math],
|
remarkPlugins: [math],
|
||||||
rehypePlugins: [katex],
|
rehypePlugins: [katex],
|
||||||
},
|
},
|
||||||
|
@ -57,7 +57,7 @@ const config = {
|
||||||
showReadingTime: true,
|
showReadingTime: true,
|
||||||
// Please change this to your repo.
|
// Please change this to your repo.
|
||||||
editUrl:
|
editUrl:
|
||||||
"https://github.com/quantified-uncertainty/squiggle/tree/master/packages/website/",
|
"https://github.com/quantified-uncertainty/squiggle/tree/develop/packages/website/",
|
||||||
},
|
},
|
||||||
theme: {
|
theme: {
|
||||||
customCss: require.resolve("./src/css/custom.css"),
|
customCss: require.resolve("./src/css/custom.css"),
|
||||||
|
@ -73,7 +73,7 @@ const config = {
|
||||||
title: "Squiggle",
|
title: "Squiggle",
|
||||||
logo: {
|
logo: {
|
||||||
alt: "Squiggle Logo",
|
alt: "Squiggle Logo",
|
||||||
src: "img/logo.svg",
|
src: "img/quri-logo.png",
|
||||||
},
|
},
|
||||||
items: [
|
items: [
|
||||||
{
|
{
|
||||||
|
@ -85,7 +85,7 @@ const config = {
|
||||||
{ to: "/blog", label: "Blog", position: "left" },
|
{ to: "/blog", label: "Blog", position: "left" },
|
||||||
{ to: "/playground", label: "Playground", position: "left" },
|
{ to: "/playground", label: "Playground", position: "left" },
|
||||||
{
|
{
|
||||||
href: "https://github.com/QURIresearch/squiggle",
|
href: "https://github.com/quantified-uncertainty/squiggle",
|
||||||
label: "GitHub",
|
label: "GitHub",
|
||||||
position: "right",
|
position: "right",
|
||||||
},
|
},
|
||||||
|
@ -103,7 +103,7 @@ const config = {
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
label: "GitHub",
|
label: "GitHub",
|
||||||
href: "https://github.com/QURIresearch/squiggle",
|
href: "https://github.com/quantified-uncertainty/squiggle",
|
||||||
},
|
},
|
||||||
],
|
],
|
||||||
},
|
},
|
||||||
|
|
|
@ -22,10 +22,7 @@ function HomepageHeader() {
|
||||||
export default function Home() {
|
export default function Home() {
|
||||||
const { siteConfig } = useDocusaurusContext();
|
const { siteConfig } = useDocusaurusContext();
|
||||||
return (
|
return (
|
||||||
<Layout
|
<Layout title={`${siteConfig.title}`} description="An estimation language">
|
||||||
title={`Hello from ${siteConfig.title}`}
|
|
||||||
description="Description will go into a meta tag in <head />"
|
|
||||||
>
|
|
||||||
<HomepageHeader />
|
<HomepageHeader />
|
||||||
<main>
|
<main>
|
||||||
<HomepageFeatures />
|
<HomepageFeatures />
|
||||||
|
|
Binary file not shown.
Before Width: | Height: | Size: 3.5 KiB After Width: | Height: | Size: 6.5 KiB |
BIN
packages/website/static/img/quri-logo.png
Normal file
BIN
packages/website/static/img/quri-logo.png
Normal file
Binary file not shown.
After Width: | Height: | Size: 20 KiB |
Loading…
Reference in New Issue
Block a user