Categories → Causal Inference , Statistics
Initial distribution of a variable before inclusion of new data.
In statistics and inference, a prior is a probability distribution that represents an initial state for the unknown parameters of a model, before observing new data.
The prior distribution is combined with the observed data to obtain a posterior distribution, which represents the updated belief about the unknown parameters. This process is known as Bayesian inference, and it allows researchers to update their beliefs as new data becomes available.
For example, if a researcher believes that a treatment has a strong positive effect, they might use a prior that assigns higher probabilities to large positive effects. Alternatively, if the researcher believes that the treatment has no effect, they might use a prior that assigns higher probabilities to small or zero effects.
A prior may be derived from, or incorporate, a researcher's beliefs or knowledge about the system or model in question. In Causal Wizard, the domain knowledge provided by you - in the form of a Causal Diagram and the form of the question and hypothesis - is a form of prior.
In causal inference, priors play an important role in estimating causal effects. When estimating the effect of a treatment or intervention on an outcome, researchers often use a prior to represent their beliefs about the potential causal effects before observing any data - these beliefs can be in the form of a Causal Diagram, where the presence and absence of edges constrains the resulting causal models.
Omitting an edge is a very strong prior that there is no causal effect between a pair of variables.
The choice of prior can have a significant impact on the estimated causal effect. Poorly chosen priors can lead to biased or unreliable estimates of the causal effect. Therefore, it is important for researchers to carefully consider their priors and to conduct sensitivity analyses to assess the robustness of their results to different prior specifications.