When something is part random and part deterministic, it's called a statistical relationship or probabilistic relationship. Both terms mean the. Interpreting causation as a deterministic relation means that if A causes B, then A must always. Part of understanding variation is understanding the difference between deterministic and probabilistic (stochastic) models. The NZ curriculum.
A probabilistic model includes elements of randomness. Every time you run the model, you are likely to get different results, even with the same initial conditions.
A probabilistic model is one which incorporates some aspect of random variation. Deterministic models and probabilistic models for the same situation can give very different results. Consider a very simple model of a cash machine. Customers arrive to use the machine every two minutes on average.
Customers take 2 minutes to use the machine on average. What is the probability that a customer has to wait 3 minutes or more? A deterministic model of the situation just uses the average gap between customers and the average time of usage, and assumes these have no variation, that is, all gaps are 2 min, and all usage times are 2 min. The model assumes that someone arrives exactly every two minutes and uses the machine for exactly two minutes, so there is never any waiting time.
Probabilistic causation - Wikipedia
The distribution of waiting times is that all waiting times are zero minutes. A simple probabilistic model of the same situation might keep the time of use at the machine as 2 minutes for each person, but include random arrival times.What's the Difference Between Probabilistic and Deterministic
One way to include randomness in the model is to do a simulation. We can simulate 15 random arrival times in a 30 minute period, for example, 2 4 5 5 10 11 12 15 16 19 20 24 29 29 Suppes, by contrast, relies on events defined set-theoretically, and much of his discussion is informed by this terminology.
The correct formulation, according to Pearl, should read: The conditional probability Pr E Cin contrast, represents a probability resulting from a passive observation of C, and rarely coincides with Pr E do C. Indeed, observing the barometer falling increases the probability of a storm coming, but does not "cause" the storm; were the act of manipulating the barometer to change the probability of storms, the falling barometer would qualify as a cause of storms.
In general, formulating the notion of "probability raising" within the calculus of do-operators  resolves the difficulties that probabilistic causation has encountered in the past half-century,    among them the infamous Simpson's paradoxand clarifies precisely what relationships exist between probabilities and causation. The establishing of cause and effect, even with this relaxed reading, is notoriously difficult, expressed by the widely accepted statement " Correlation does not imply causation ".
For instance, the observation that smokers have a dramatically increased lung cancer rate does not establish that smoking must be a cause of that increased cancer rate: Scientists are always seeking the exact mechanisms by which Event A produces Event B.
But scientists also are comfortable making a statement like, "Smoking probably causes cancer," when the statistical correlation between the two, according to probability theory, is far greater than chance. In this dual approach, scientists accept both deterministic and probabilistic causation in their terminology. In statisticsit is generally accepted that observational studies like counting cancer cases among smokers and among non-smokers and then comparing the two can give hints, but can never establish cause and effect.
Often, however, qualitative causal assumptions e. Random assignment plays a crucial role in the inference to causation because, in the long run, it renders the two groups equivalent in terms of all other possible effects on the outcome cancer so that any changes in the outcome will reflect only the manipulation smoking.