<p>@amoeba and I had a lengthy (and hence not particularly productive, if the sheer length is any indication of the proximity to consensus) <a href="https://stats.meta.stackexchange.com/a/3227/5739">discussion</a> of tag synonyms in the main <a href="https://stats.meta.stackexchange.com/q/1200/5739">"Tag synonyms candidates"</a> thread, and I think both of us got lost in this, so let's take it up to a higher level of a separate thread.</p>

<p>Everything weighted includes the following tags:</p>

<ul>
<li><a href="https://stats.stackexchange.com/questions/tagged/weights" class="post-tag" title="show questions tagged &#39;weights&#39;" rel="tag">weights</a></li>
<li><a href="https://stats.stackexchange.com/questions/tagged/weighted-data" class="post-tag" title="show questions tagged &#39;weighted-data&#39;" rel="tag">weighted-data</a></li>
<li><a href="https://stats.stackexchange.com/questions/tagged/weighted-sampling" class="post-tag" title="show questions tagged &#39;weighted-sampling&#39;" rel="tag">weighted-sampling</a></li>
<li><a href="https://stats.stackexchange.com/questions/tagged/weighted-regression" class="post-tag" title="show questions tagged &#39;weighted-regression&#39;" rel="tag">weighted-regression</a></li>
<li><a href="https://stats.stackexchange.com/questions/tagged/weighted-mean" class="post-tag" title="show questions tagged &#39;weighted-mean&#39;" rel="tag">weighted-mean</a></li>
</ul>

<p>At this stage, I quicked-and-dirtied wiki summaries for the first three, and  they are mostly driven by my personal opinion. (I am a survey statistician, so the production and the use of survey weights is my main line of business; I also hold strong opinions on <a href="https://stats.stackexchange.com/a/27693/5739">the proper use of terminology</a>, so my approach is to make everything as clear as possible.) I have put a relatively strong language to avoid some of these confusing / ambiguous tags, and suggested to put something more specific to the problem at hand.</p>

<p>Basically, my take is that in "tidy" rectangular data sets, we can put weights:</p>

<ul>
<li>on observations/rows -- in which case they usually serve as the multipliers to the likelihood contributions / squared residuals in least squares problems. I am used to weights coming from probability sampling from finite populations, so they roughly represent the inverse probability of selection and response. Many other uses of weights, such as precision weights or frequency weights, as discussed in <a href="http://www.ats.ucla.edu/stat/stata/faq/weights.htm" rel="nofollow noreferrer">http://www.ats.ucla.edu/stat/stata/faq/weights.htm</a>, are probably deprecated by now, with the modern software allowing all the analysis in a better shape than what all of these historic tricks been used for. The problem-specific weights also arise in robust procedures, where the weights are used to limit the influence of outlying observations.</li>
<li>on variables/columns -- some literatures refer to regression coefficients as regression weights, for instance. And there are also weights in deep learning networks, and these weights are "learned" rather than "estimated". Also, weights on variables come up in principal component analysis / factor analysis (in which case my preferred language is that of "loadings").</li>
</ul>

<p>There are also data sets auxiliary to the main data, such as those generated by computational Bayesian / Monte Carlo Markov chains. The importance sampling weight is the ratio of the "true" density of interest to the density of a convenient distribution to sample from.</p>

<p>Yet another concept of weights may arise in model averaging, where the weights are attached to models rather than neither observations nor variables. For these, <a href="https://stats.stackexchange.com/questions/tagged/model-averaging" class="post-tag" title="show questions tagged &#39;model-averaging&#39;" rel="tag">model-averaging</a> may be a better home than <a href="https://stats.stackexchange.com/questions/tagged/weighted-mean" class="post-tag" title="show questions tagged &#39;weighted-mean&#39;" rel="tag">weighted-mean</a>.</p>

<p>Yet another use of weights is when the marketing folks try to aggregate ratings of a product from different users. I am not sure what to recommend here.</p>

<p>There is probably more than meets the eye.</p>

<p>As I have been going through these trying to clean up (I started with <a href="https://stats.stackexchange.com/questions/tagged/weighted-sampling" class="post-tag" title="show questions tagged &#39;weighted-sampling&#39;" rel="tag">weighted-sampling</a> retagging to <a href="https://stats.stackexchange.com/questions/tagged/survey-sampling" class="post-tag" title="show questions tagged &#39;survey-sampling&#39;" rel="tag">survey-sampling</a> or <a href="https://stats.stackexchange.com/questions/tagged/importance-sampling" class="post-tag" title="show questions tagged &#39;importance-sampling&#39;" rel="tag">importance-sampling</a> where appropriate), I discovered a wild variety of ways to use the idea of weights... and the topics and problems that people tag with these (often out of confusion). So that one can be clarified. Also, <a href="https://stats.stackexchange.com/questions/tagged/weights" class="post-tag" title="show questions tagged &#39;weights&#39;" rel="tag">weights</a> can probably be cleaned and frozen/killed, as the one having fewest questions.</p>

<p>At this point, we are seeking a community input to:</p>

<ul>
<li>proper definition of weights as a concept;</li>
<li>delineation of what to consider the weights on observations in rectangular data sets, and the best tag name for that;</li>
<li>delineation of what to consider the weights on variables in rectangular data sets, and the best tag name for that;</li>
<li>what the concept of weights may mean for irregular data sets;</li>
<li>other uses of weights in statistics / machine learning / data science, and whether these should go under some general tag, or have their own tags developed.</li>
</ul>

<p>Let me put some tentative ideas for up/down voting, but please feel free to express more on the topic. In particular, post your "case studies" of other uses of weights in statistics, with the specific posts that use weights in that way.</p>

<p><strong>UPDATE</strong>: I am guilty of creating another tag, <a href="https://stats.stackexchange.com/questions/tagged/survey-weights" class="post-tag" title="show questions tagged &#39;survey-weights&#39;" rel="tag">survey-weights</a>. I will send the questions about <em>sampling design</em> to <a href="https://stats.stackexchange.com/questions/tagged/survey-sampling" class="post-tag" title="show questions tagged &#39;survey-sampling&#39;" rel="tag">survey-sampling</a>, while the questions about <em>analysis</em> with survey data and survey weights will go to <a href="https://stats.stackexchange.com/questions/tagged/survey-weights" class="post-tag" title="show questions tagged &#39;survey-weights&#39;" rel="tag">survey-weights</a>.</p>
