Sense & Reference

Another take on information literacy, Bayesian inference, and a possible research agenda


by mattbuck, CC-BY-SA 3.0

So, I’ve been trying to come up with a research agenda. I mean, I can’t be the “Framework is stupid” guy forever;1 I don’t want to get pigeonholed.

Anyway, it’s Sunday night and I’m thinking that if I’m going to turn my back on whatever the ACRL comes up with, I’ve still got to have a working concept of “information literacy” (or something to that effect.) Well, I’ve had this idea rattling around for over a year and the other day I finally thought I’d pursue it. So I fired up the LISTA database and started searching for something I figured some librarians somewhere had already researched thoroughly: Bayesian interpretations of information literacy.

Nothing. Not a single article. I checked a few of the major journals. Nada. Google Scholar? Just one 2002 article by Carol Gordon (formerly of Rutgers and clearly on to something). I headed over to Twitter and asked where the rest of the research was? Crickets. From what I can tell, no librarians are applying Bayesian theory to information literacy. Shoot, the impression I’m getting is that most information literacy librarians have never even heard of Bayesian inference. So that’s going to be it. My research agenda will be to introduce a Bayesian approach to information literacy.

But what does that even mean? Here’s a brief overview:


That formula at the top of this post is the simple form of Bayes’ Theorem. It’s been around for a few hundred years and even though you’ve probably never seen it in library studies, it is absolutely everywhere in information science, cognitive science, legal studies, communication, epistemology, logic, and other assorted fields where people talk about concepts like reliability, credibility, the trustworthiness of information sources, how to evaluate online news, and other things that sound a hell of a lot like “information literacy.” When applied to information literacy, the basic idea behind a Bayesian approach is that your confidence level in the truth of some claim that you’ve read (or watched, heard, etc) is proportional to your confidence level in that claim being true before you read (or watched, or heard, etc) about it times the likelihood that it is actually true. Let’s look at a fairly standard example of Bayes’ Theorem in action.

Suppose there’s a 12% chance that a woman will develop breast cancer (which is scary true). Now, let’s say that contemporary mammograms have an 85% success rate at discovering breast cancer (about right). However, they also have around a 55% false positive rate, meaning they falsely show cancer when there really isn’t any (again, about the right number). Now, if a woman gets her mammogram results back and they come up positive for breast cancer, how worried should she be? This is where Bayes comes in. We’ll start with a slightly extended version of the theory:

where in our example, the values are like this:

Pr(A|B) = probability of breast cancer given that the mammogram results are positive

Pr(B|A) = probability of positive mammogram results when cancer is actually present. A.K.A., the reliability of the mammogram = 85%

Pr(A) = likelihood of a woman developing breast cancer = 12%

Pr(B|¬A) = probability the mammogram is reporting a false positive = 55%

Pr(¬A) = likelihood a woman does not develop breast cancer = 88% (100% – 12%)

Plugging in the values and you get:

Which means that when a typical mammogram returns a positive diagnosis, there’s only a 17% chance that cancer is actually present.

With me still? Wondering what this has to do with information literacy? Instead of thinking about “does vs. does not have cancer,” how about thinking of “is or is not a fact.” And instead of thinking “how reliable and accurate is this medical test” how about thinking “how reliable and accurate is this information source.” See where I’m going?

by londonmatt on Flickr, CC BY 2.0

Bayesian Information Literacy

Consider the “fake news” problem everyone is talking about. Let’s say your Facebook friend hears that Bernie Sanders can still win the presidential election thanks to “this one weird trick.” You know the kind of story I’m talking about. Now, let’s say that before reading anything but a headline, your friend is already 90% sure that’s not really true, but decides to read anyway. The first article she reads is from U.S. Uncut and she already thinks that U.S. Uncut is a pretty dodgy news source, so she only gives the website around 40% reliability. That is, it’s more unreliable than reliable. Applying Bayesian probability, we can say that her belief changes from 90% to 93% sure it’s not true. As in, if an unlikely piece of news is reported by a source you deem unreliable, you are slightly more inclined to reject the news than accept it. But, let’s say she then reads a CNN article that says the same thing and she thinks CNN is moderately reliable. Maybe CNN reports are more like 75% true. Bayesian approaches allow us to combine her prior confidence from after reading U.S. Uncut with the information from CNN and give your friend room to doubt. Now she’s only 82% sure the story is a fake. She reads more about Bernie’s chances on Occupy Democrats (55% reliable), NPR (90% reliable), and ABC News (80% reliable) and ends up being 91% sure that Bernie still has “one weird trick.” Neat, huh?

Sure, those percentages are just made-up, but the exact numbers aren’t important. And, it’s important to note that this example only addresses her subjective attitudes towards how reliable various sources are. It’s also worth noting that the formula for combining these multiple, sequential prior probabilities is a bit more complicated than the one I put up earlier. Yet, still, broader insights fall out when we think about information literacy in Bayesian terms:

  1. For any given claim we encounter, we always have a prior credence in that claim being true. Maybe it’s low, maybe it’s neutral, maybe it’s high. Maybe we’ve never heard anything like it before and we’re 50-50. The exact numbers don’t matter. What matters is that what we are inclined to believe after encountering information is proportional to our prior belief times the reliability/credibility we assign to the information source.
  2. Values like credibility, reliability, or trustworthiness are not binary; they exist on a continuum between 0 and 100%. We need to stop asking “is this source reliable?” and start asking “how reliable is this source given what it is reporting?”
  3. We are more inclined to believe something if we think it comes from a reliable source.
  4. We are more inclined to think a source is reliable if we believe what it’s telling us.
  5. How plausible we deem something is connected to how reliable we think the source reporting it is and vice-versa.
  6. A single highly reliable source can outweigh several weakly reliable sources.
  7. But, consistent reporting across multiple weakly reliable sources can yield high levels of belief.

It’s Bayesian inference that explains why your racist uncle believes everything on Breitbart and InfoWars and refuses to accept the New York Times as a legitimate news source. It’s Bayesian inference that explains why a flood of spurious news stories from barely reliable sources can add up to convince otherwise rational people that…yeah, maybe Hillary Clinton did intentionally let Benghazi happen or, yeah, maybe Barack Obama wasn’t born in the United States. It’s not a question of true or false. It’s a question of levels of confidence, and if a news source shared on Facebook says 99 true things and 1 false thing, you’re more likely to believe the false thing at least a little bit. It’s why sites like Breitbart are so successful: the (slight) majority of the things reported on Breitbart are factual, but selectively reported or couched in false claims. Like, right now, the cover story on Breitbart is that Trump hasn’t selected a Secretary of State yet. I think Breitbart is a garbage source for news, but I believe that particular story is most likely factual. Same for the stories about Trump selecting (the asshat voucher-lover) Betsy DeVos as Education Secretary or about some right-wing immigration group arguing that the SPLC should lose tax exempt status. These are plausible, factual stories. They’re selectively reported, to be sure, but they are largely factual. But there’s an article right in the middle defending a alt-right Nazi rally, and this is where we need to think critically about how people engage with information sources, because modern members of the alt-right Nazis aren’t created by late night Mein Kampf study marathons. They don’t get their start on fringe alt-right Nazi websites. They’re wooed by hateful, racist garbage “news” sources that receive a veneer of plausibility by being couched in factually reported information. You tell a student that Breitbart is biased and point to the article defending the alt-right Nazi rally; the student says it’s not and points to the dozen other more-or-less factually correct articles. How do you respond to that? We naturally evaluate information on Bayesian lines, to one degree or another and when we get too subjective with how we assign credibility to sources or too dogmatic/uninformed/etc. about what we want to be true, we stumble into confirmation bias, selective reading, echo chambers, filter bubbles, and so on.Bayes explains it. Check out this NPR story from Friday about a dude who’s built a fake news publishing empire in the San Francisco suburbs. He never explicitly says Bayes, but he absolutely describes how he uses Bayes to manipulate his (mostly right-wing) audience. If peddlers of misinformation and disinformation are using Bayesian concepts to manipulate, shouldn’t we pay attention so we can set things straight?

For anyone interested in “information literacy,” understanding how people actually evaluate sources is vitally important. It also helps as we try to determine how people should evaluate information. Again, these all may sound like obvious observations, but that’s only because Bayesian inference underlies most of our common-sense understanding of how people reason from information sources and I think it’s time library studies took notice. I hope to write more as I learn more, but I can already see several research questions that are unanswerable within the current literature on information literacy, but that might be addressed with Bayesian concepts:

I could keep coming up with questions. And if, after this post, I get the impression that this is an area of information literacy that people might be interested in, then I’ll keep asking questions. But, keep in mind that this is a hastily written sketch of Bayesian inference. I can point to a few mathematical errors and omissions I left in for the sake of explaining the general theory better. There’s also a lot of work out there on assigning reliability, assigning confidence levels, estimating prior probabilities, and so on. There’s also a lot of related work that needs to be covered on things like the epistemology of testimony. So this post only barely scratches a scratch on the surface. Here’s the Stanford Encyclopedia of Philosophy entry on Bayesian Epistemology if you’re interested in a longer introduction. You can also just Google it and find hundreds and hundreds of articles and essays delving into Bayesian source evaluation.

So, I don’t know why this has escaped the notice of librarians for so long (Carol excluded!), but it’s where I’d like to take information literacy. And, I’m not just interested in bringing the theories of cognitive science, psychology, information science, economics, philosophy, law, decision theory, and so on into library studies; I’m also interested in asking how librarians can bring their expertise to bear on the problems being investigated in those other, related fields.

What do you think? Does this make any sense at all? I’d love to hear in the comments.

EDIT 11/30/2016: Just to be clear, I’m not saying we should teach students about Bayesian inference. I’m saying that Bayesian theory can help improve our understanding of how people use information. A Bayesian approach can help highlight important concepts that we need to address. How we choose to address those concepts is quite separate.

This was on Flickr, captioned “Do Bayesian networks dream of training data?” Not sure what that means. by plchenttes, CC BY-NC-ND 2.0

ADDENDUMY THING: I was just about to hit post, I stepped away to grab a beer, and I had another thought I want to put down. One of the interesting areas of inquiry with Bayesian inference is how the coherence of our beliefs affects are receptivity to new information. Let’s say there’s a hypothetical person, Jan, who only has three beliefs: (1) Trump won the electoral college, (2) the presidential election was rigged to favor Hillary Clinton, and (3) Trump won the popular vote. Clearly, these aren’t all true, but it’s plausible that Jan believes them. And, importantly, they form a coherent set of beliefs. Now, let’s say we introduce a new piece of information: (4) Hillary Clinton won the popular vote. Bayes tells us that Jan’s willingness to accept (4) is very small given that it does not cohere with (1)-(3). So, the subjective confidence Jan places in an information source reporting (4) is going to have to be incredibly high for Jan to be willing to reassess (1)-(3). That, or an incredibly large number of highly reliable (according to Jan) sources are going to have to consistently report (4) in order to overcome the coherent set of beliefs (1)-(3). Now, think back on your Thanksgiving meal and ask yourself if any of your relatives sound like Jan. Are you a sufficiently reliable source to overcome Jan’s coherent web of beliefs? Interesting, right? (see BonJour’s The Structure of Empirical Knowledge (1985) for an intro to coherentism.   I’m not a coherentist per se, but I do think coherence is a huge factor in belief acquisition. Addendumy thing over.


[1] No, but seriously, the Framework is pretty stupid.