Likelihood Function

Instance of: joint probability

AKA: Likelihood

Distinct from:

English: The joint probability of the data, conditional on the parameters parameters. How likely are we to observe these data, given this paramater is the True one.

(Etz 2017)

  • Likelihood is not probability, but is proportional to a probability.

  • Likelihoods are relative, scaled by an arbitrary constant, and need not sum to one.

  • Under likelihood the data are fixed, and the hypothesis vary.


\[ \mathcal{L}(\theta|X) \]

Where \(\theta\) are the parameters, and \(X\) is the evidence.

Also written in terms of a probability of observing X given the a parameter value \[ \mathcal{L}(\theta) = K \times P(X|\theta) \]

Where \(\theta\) are the parameters, and \(X\) is the evidence, and \(K\) is an arbitrary scaling constant.

Cites: Wikipedia ; Wikidata ; Wolfram




# Create an ephemeral in-memory RSQLite database
#con <- dbConnect(RSQLite::SQLite(), dbname = ":memory:")
#dbWriteTable(con, "mtcars", mtcars)

#Configuration failed because libpq was not found. Try installing:
#* deb: libpq-dev libssl-dev (Debian, Ubuntu, etc)
#Took forever because my file permissions were broken
Loading required package: RPostgres
# Connect to the default postgres database
#I had to follow these instructions and create both a username and database that matched my ubuntu name
con <- dbConnect(RPostgres::Postgres())
import torch


Etz, Alexander. 2017. “Introduction to the Concept of Likelihood and Its Applications.” PsyArXiv.