Dubious

Dubious is a Python library for propagating uncertainty through numerical computations. Instead of collapsing uncertain values into single numbers early, Dubious lets you represent values as probability distributions, combine them with normal arithmetic operations, and only evaluate the resulting uncertainty when you ask for it.

from dubious import Normal, Beta, Uncertain, Context

normal = Normal(5, 4)
normal2 = Normal(10,2)

x = Uncertain(normal) + Uncertain(normal2)

print(f"variance: {x.var()} mean: {x.mean()} q(0.05): {x.quantile(0.05)}")

Rounded output: variance: 19.9, mean: 15, q(0.05): 7.7

The core idea behind Dubious is lazy uncertainty propagation. We build a graph of operations applied to uncertain values, and traverse it upon sampling. You can construct complex expressions from uncertain inputs in a simple and readable manner, and evaluate the result using Monte Carlo simulations.

By default, distributions are assumed to be independent. We can correlate two uncertain objects using a.corr(b,rho), implemented via Gaussian copula (see notes for details).

After applying any numerical operations to Uncertain objects, sampling and evaluation only occur when calling a function like mean(), quantile() or sample() is called.

Full documentation can be found at: https://dubious.readthedocs.io/en/latest/api/modules.html

Installation

With python v3.9+ pip install dubious

Caveats

  • If several instances of the same Uncertain object are involved in an operation these are assumed to represent the same variable so the samples used to calculate these values for each will be identical.

  • Correlation between Uncertain objects is currently implemented using Gaussian Copula. This rank based correlation and the rho value used to correlate different objects is NOT the same as the pearson coefficient. Copula based correlation is accurate across most of the distribution, but in the 99th and 1st percentiles we underestimate by about 3%. This under-estimation continues to grow further into the tails.

  • RNG can be controlled via Sampler() objects, these can be constructed using either a seed, or a substratum.Generator() object and passed into any function that uses MC sampling methods. Alternitvely, you can call freeze on a context object to ensure the same samples are used for subsequent methods.

Classes

Distribution(): Currently supporting Normal, LogNormal, Beta and Uniform distributions. Distribution objects also support using other distribution objects for their parameters, although this may lead to unexpected behaviour in cases where parameters can become negative. These cases currently throw a warning and are clamped to 1e-06, but the onus is on the user to ensure that input distributions will provide statistically correct results.

For each you distribution can get mean(), var(), quantile, cdf() and sample().

Uncertain(): Uncertain objects are the wrapper for distributions that allow them to be used like numeric values. Alongside being able to perform numeric operations on these uncertain objects, they support the same properties as standard distributions (mean, variance, sampling and quantile). You can apply the exact same operations on these objects you might apply to real data, and easily calculate the propagated uncertainty that comes from using several unreliable input values.

To ensure the same output after repeated calls, Uncertain objects support freeze() and unfreeze(), although this only freezes a single Uncertain object. It is recommended to instead freeze the entire context for truly deterministic results.

Get a summary of metrics via summary() or check input sensitivity via sensitivity(). local_sensitivity() allows you to pass a dict of uncertain objects and corresponding values, returning the sensitivity at that specific neighbourhood within the sample space.

Context(): Context objects own the graph through which we track computations. You can add uncertain objects from different contexts, but be aware that this creates a new context in the process. To avoid this, create all new uncertain objects with ctx = Your context object. You can also easily get a reference to a newly created Context via ctx = my_uncertain_object.ctx.

Context objects also support freeze() and unfreeze(), freezing results through context objects is recommended for most cases.

Some examples:

from dubious.distributions import Normal
from dubious import Uncertain, Context

ctx = Context()

length_dist = Normal(10, 1)
length = Uncertain(length_dist, ctx=ctx)

width_dist = Normal(5, 0.5)
width = Uncertain(width_dist, ctx=ctx)

#Compute area uncertainty using normal arithmetic
area = length * width

print("Mean area:", area.mean())
print("Variance:", area.var())
print("Some samples:", area.sample(5))

We can also use distribution and uncertain objects as parameters.

from dubious.distributions import Normal, Beta
from dubious import Uncertain, Context

ctx = Context()

#We can define distribution parameters with other distributions.
normal = Normal(10, 1)
beta = Beta(3,normal)

x = Uncertain(normal, ctx=ctx)
y = Uncertain(beta, ctx=ctx)

x = x*y

print(x.sample(5))

#We can also use uncertain objects to define parameters.
normal3 = Normal(y+2, 3)
print(normal3.mean())

An example of correlation:

#two non-Gaussian marginals correlated using copula
from dubious.distributions import Beta, LogNormal
from dubious import Uncertain, Context

ctx = Context()

conv = Uncertain(Beta(20,80), ctx=ctx)
traffic = Uncertain(LogNormal(8.0,0.4), ctx=ctx)

conv.corr(traffic, 0.7)

sales = conv * traffic

print(f"Mean: {sales.mean()}")
print(f"p10, p90: {sales.quantile(0.1)}, {sales.quantile(0.9)}")

Mean: 685.30,

p10, p90: 282.88, 1185.69

Correlated uncertainty propagation currently matches a Gaussian-copula reference to within ~0.25% relative error on tail quantiles. See benchmarks/cor_benchmark.py

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