# Parametric vs. Nonparametric

I did perform a search for this question (I thought it was bound to be asked), but I haven't found one; hopefully this won't be a duplicate.

I'm trying to decide if I should take a course in stats that is more parametric or one that is nonparametric.

From a maths perspective, what would be the advantages of learning one over the other? Would one be more advantageous over the other as far as working in industry?

• Parametric does NOT mean "Bayesian based". Feb 16, 2013 at 21:20
• "Bayesian or frequentist" techniques is not related to "parametric or non-parametric". It would be simpler to answer the question if you focused on just one of the issues - probably by dropping all references to Bayesianism. Feb 16, 2013 at 21:28
• Non-parametric Bayesian is just a way more complicated model. You need to learn a lot of parametric Bayesian to start tapping the non-parametric Bayesian issues. Frequentist non-parametric (as in, rank statistics) requires only probability on finite discrete spaces, and its set of assumptions is so much more general -- something like a continuous cdf, that's all. It's too bad that the classic non-parametric stuff from the 1940-50-s has all but died off; this has been a valuable set of techniques. These days, psychologists understand Kruskal-Wallis better than newly minted statisticians do. Feb 16, 2013 at 21:52
• There are many flavors of non-parametric statistics. One, as I mentioned in the previous comment, is rank-based robust statistics (as I said, that's 1950s hot material). Another is kernel-based estimation (that's probably 1980s hot material). These days, you would hear a lot about machine learning as non-parametric techniques; and you would also hear about non-parametric Bayesian. These directions are nearly mutually exclusive, so I am somewhat at a loss as to which of these four (and there may be more meaning of "non-parametric" that I have no knowledge of) you are thinking of pursuing. Feb 16, 2013 at 21:56

Parametric does NOT mean "Bayesian based".

Here is one definition of "parametric statistics"

Parametric statistics is a branch of statistics that assumes data come from a type of probability distribution and makes inferences about the parameters of the distribution

(From Wikipedia).

As Wikipedia goes on to note, most of the common, elementary statistics are parametric. For example, ordinary least squares regression is parametric. Loess regression is nonparametric.

Parametric statistics are usually easier to interpret and may be more powerful (in a statistical sense) but they are based on more assumptions than nonparametric statistics. They vary in their degree of robustness, but are usually less robust than nonparametric statistics.

For example, the equation derived from ordinary least squares regression is (in most cases, anyway) quite easy to understand. That from a regression involving splines is often much less clear and may require graphical representation to be understood well.

Bayesian statistics is something altogether different, having to do with using prior information.

• Wikipedia was the first source I referred to, but I started reading about Bayesian statistics and it just went over my head. Thanks for clarifying.
– user20914
Feb 16, 2013 at 21:36
• Your final sentence is misleading - Bayesian statistics is about thinking of the parameter as having a probability distribution (e.g. the conditional distribution of the parameter conditioned on the data), reflecting degrees of believe about the parameter - it has nothing to do with using prior information. You can use prior information in a frequentist model in the form of a penalty (LASSO or ridge regression are familiar examples). In fact, the mode of the posterior distribution agrees exactly with the penalized maximum likelihood estimate if you choose the prior/penalty the same way. Feb 18, 2013 at 13:42
• The Wikipedia quotation is an invalid "definition" because it is vague and circular ("parametric" is explained in terms of "parameters"). Some of the examples in this post may be misunderstood, too: for instance, many formulations of OLS are nonparametric. As another instance, the use of splines may be parametric or nonparametric, depending on how the spline knots are determined.
– whuber
Jan 27, 2021 at 23:59