Moinak Bhaduri develops change-detection algorithms for point processes through trend permutations and is an assistant professor with the Department of Mathematical Sciences, Bentley University. He heads the editorial board of the NextGen column of the New England Journal of Statistics in Data Science. Moinak’s research has found applications in computer science, finance, reliability and repairable systems, geoscience, and oceanography.
Episode Description
It's been 70 years since Edmund Hillary and Tenzing Norgay summited Mount Everest. Since then hundreds of people attempt to climb the mountain each year. Many of those climbers are injured during their attempts. And during the 2023 climbing season 17 people died. Preparing for Everest takes years of training. Though there's disagreement among mountaineers about how to best prepare for the climb, statistics might be able to help and that's the focus of this episode of Stats and Stories with guest Moinak Bhaduri.
+Full Transcript
Rosemary Pennington
It's been 70 years since Edmund Hillary and Tenzing Norgay summited Mount Everest. Since then hundreds of people attempt to climb the mountain each year. Many of those climbers are injured during their attempts. And during the 2023 climbing season, 17 people died. Preparing for Everest takes years of training. Though there's disagreement among mountaineers about how to best prepare for the climb, statistics might be able to help and that's the focus of this episode of Stats and Stories, where we explore the statistics behind the stories and the stories behind the statistics. I'm Rosemary Pennington. Stats and Stories is a production of Miami University's departments of statistics and media, journalism and film, as well as the American Statistical Association. Joining me is regular panelist John Bailer, emeritus professor of statistics at Miami University. Our guest today is Moinak Bhaduri, an assistant professor of Mathematical Sciences at Bentley University. His primary interest includes developing change detection algorithms for point processes, but during his research has found applications and computer science, finance, reliability and repairable systems, Geoscience and oceanography. He also leads the editorial board of the next gen column for the New England Journal in data science. Bhaduri recently authored an article for Significance about how stats might help mountain climbers prepare for Everest. Welcome, thank you so much for joining us today.
Moinak Bhaduri
Thanks for having me.
Rosemary Pennington
Well, what got you interested in this, this issue of climbing Everest?
Moinak Bhaduri
Right. So I have always been fascinated by mountains. I have always been intrigued by mountains and those that climb mountains, especially the long peaks, the big mountains. So I would say it's a combination of personal interest and the kind of nuanced the kinds of subtleties we have here for this project for this problem. Because there are many factors, there are many sessions you have to juggle while you climb a peak like Everest. So there are some that you can control like whether or not you can use oxygen, whether you want to use oxygen, or you want to be like Reynold Messner, who says that mountain climbing should be just very pure, you should be a purist way or you should not use bottled oxygen at all. So those are things you can control. But there are others that you cannot, like the number of other teams you have on the mountain, on Everest that season. So it's a combination of things that you can control and the ones that you cannot control. So there are many subtleties to consider. That's another reason why the complexity of the problem attracted me. There are others that you can answer with these predictive models, such as, there are many open questions and mountaineering folklore for instance, there are many mysteries, such as we all know that Ed Hillary and Tenzing Norgay the first climb the peak, but many believe that around 30 years, three decades earlier, like Mallory Irvine and Sandy Irvine, they could reach the top, it could have reached the top. But there's no conclusive evidence for that. So there are things that you can answer with these predictive models, we can shed some light on those mysteries. Those are the two main reasons for my main interest in mountains and the subtleties and nuances. And also one sub interesting thing was teaching, so I teach these courses in class, these models in class, so if I can have a topic that is very attractive for them to direct the students, then that would be good. Yeah, combination of those three, yeah.
John Bailer
And as long as it's interesting to you, they're just gonna have to suck it up.
Moinak Bhaduri
That's true, too. Yeah, it always worked for me.
John Bailer
Can you talk a little bit about the types of features or the typing symbols you'd use for prediction?
Moinak Bhaduri
You're right, there was, I think in all, there were 15 variables; there were 15 predictor variables. So some were categoricals. Like whether or not you wanted to use oxygen. The others would be pretty much quantitative like the amount of days you take to climb. There's a slight distinction which is the total one quantitative was, which turned out eventually to be very crucial. One quantitative was the total amount of days you spend on the expedition. And which is a thing called the total number of days on the paper, and the other would be summit days. So those would be how much time do you spend beyond the Basecamp to climb the mountain? So those who are quantitative, and then how much fixed rope do you use? How many sherpas do you have in your team? What other kinds of nationalities do you have? What are the kinds? So those were quantitative. So I think it's a healthy mix of categorical and quantitative.
John Bailer
So, there are two variables that as I was looking at this, I thought, gee, I wonder if this was even available at that time? Like, what was the weather? I mean, season, which is right, think of it as a surprise. That is, yes, yes. It was the experience of the team. Obviously, you know, early on, there was no one who had experience. But I'm curious if those other variables might be something that would be valuable in the future.
Moinak Bhaduri
You're very right. So those are variables, we didn't have inside of this dashboard, inside of this resource, they have the U ml, in machinery database, maintained by Liz Holly. So they didn't have this information. But there are proxies. So if you have like, as you mentioned, season is a good proxy for the kind of weather they may face. But still, if you have precise weather information, precise weather data for that specific day when they're trying to climb the peak, or others, such as a mountain years, like tenacity or experience, as you mentioned, and so those would be good things to have, those would be good things to look at. But if you think closely, it's a I mean, you may have other predictors that are good proxies for those. Yeah. Like, like, if you look at some of the expeditions that are happening, like nowadays, the guided expeditions on Everest, so they charge quite a lot. So like $50,000 to $75,000, at least. So if you're willing to pay that much money, then you're probably very motivated. So there are proxies, although you do not have data on it. And it would be good to have concrete data. But as long as you can approximate, that's quite good, too. Yeah.
Rosemary Pennington
When in your first response, you were talking a bit about sort of this conversation around oxygen like should you not use it? And the state of like, you have, like, you know, separated like, oh, to climb? Yeah. Yeah. So can you talk about sort of how you thought about and looked at oxygen and its use or not use in relation, sort of the success of an Everest climb?
Moinak Bhaduri
Right. So that would be in two ways, basically, one is what you would normally expect, if you talk to any climber, if you have no special goal to achieve, like nowadays, many mountaineers, they just do not want to climb, they want to climb without using oxygen. Or they want to climb two peaks at the same time in the same expedition to get sponsorships and things like this. So unless you have any specific goal in mind like that, then you would argue that it's of course better to use oxygen. So your body gets acclimatized, and things like this. So you have more red blood cells flowing to your brain. So that's one reason to help your body adapt. That's the intuitive understanding and even the model is still the same. So the tree based models of VR are used basically, they rely on some factors, like what questions should you ask at the very beginning to help you decide whether you should? Whether you could climb or not? What's the most crucial factor? So from the perspective of model two, we had the same result. But oxygen is quite crucial indeed. Yes.
John Bailer
So before we dive into the models, and a little more, you talked about the features of these predictor variables. Can you talk about what were the responses that you were that you were modeling?
Moinak Bhaduri
So that is a very good question. Because if you look into the database, and there is a possibility, there is a way there's a chance you can tweak your response a little bit. So for this project, the response was success or failure, and success was defined this way, if even one member inside of your expedition, even if one member inside of your team could reach the top, that counts as success, but you may be more demanding. You may want to say, No, I'm not good with their definition. I want all of my members or a substantial number of my members to reach the top. There is a chance to tweak that definition to see your modeling or whether or not please one and any team got to the top? Yes. That's the response.
John Bailer
So, I know that if people are listening, they're probably practicing this, the basic question is, well, you know, how hard is it? I mean, what's the crude proportion of times that aren't successful?
Moinak Bhaduri
So, strangely enough, it's 62%. If you look at the full history 62%, almost 62%, are successful. And how is that? Yes, over time, right? Yes, you'd expect if you look into the literature, you would expect that time is a very crucial factor. Because as time goes on, you get more and more knowledge about the mountain, and your climbing gear improves. So we did use the time variable as a predictor, but it turns out to be the fourth crucial, the fourth most the fifth most crucial. Oh, yeah. It's still, I mean, no matter what, when would you want to climb the mountain in the recent past or in the primitive history, whatever it is, oxygen, and the route taken, whether or not you're spending quite a long time on the road, they are becoming more crucial. Time is still very relevant, it's very crucial, which could be a proxy for the quality of gear that's evolving, or the amount of knowledge you have about the mountain. But it's, I think it's the fourth and the fifth most crucial factor. Yes.
Rosemary Pennington
You mentioned the route. Are there particular routes up Everest that are more prone to sort of? Yeah, and others?
Moinak Bhaduri
Yeah. So if you look into it I think there is a bigger inside of a bigger tree, where each dot that you see on the top left represents a route. So the most popular would be the south called southeast Ridge, which is what Hillary and Tenzing took for the first climb. But the other expedition I was mentioning Mallory and Irvine, they took the North col and the Northeast route. So yeah, there are some routes, which would elevate your chances if you take that route, that could impact your chances on its own. I figured three, I think the top, the top left region and the proven route seemed like a combination. Yeah, also, the other recommendation that we will offer is get your expedition over very quickly. Because if you take a long time, I'm talking about the other graph, and read just right below it says, if you look at the yellow portion, that's the region where you are a log of the odds it maximizes, meaning your chances for climbing the top for climbing the mountain would be maximized. And that yellow is a combination of two things. The first is the number of Summit days would be more or less similar to the average. And the total number of days would be below the average. Which means basically, you would spend a long time at the base camp if you want to get yourself properly acclimatized. But the total expedition is like the total, maybe if you're starting from Kathmandu, so then the total expedition should be done very quickly. Because otherwise probably the reason what's happening here is people get bored, and their motivation drops and things like this could go wrong.
Rosemary Pennington
You're listening to Stats and Stories. And today we're talking with Bentley University's Moinak Bhaduri about statistics and Mount Everest.
John Bailer
Okay, so now you've got the 62%. You know, that sort of thing that's going to flip success probability just without thinking about anything else. So your investigation here then dove into different models or strategies for there are three candidates that are competitors in this game, why don't we step through each of those in turn? So the first method that you picked was one of the favorites for medical science? Yes. for predicting probabilities of success logistic. Yeah. Could you give us just a quick summary of what that method does? And then what variables did you use in it?
Moinak Bhaduri
Right, so the logistic is, as you mentioned, quite a big favorite. It tries to model log of the odds. So if you're looking at any binary response, like a success or a failure, which we have, in this case, the odds are defined. The trouble is if you want to play a linear regression, standard linear regression on these probability values just won't work because probabilities are bounded by zeros and ones. So we need to have some kind of a transformation, some kind of a conversion so we can apply our linear regression understanding on it. And one common transformation we use is log of the odds. The odds is basically the probability that you will succeed to the property that you will not. And if you take the log of this fraction, it turns out to be some variable, which is just like your salary can be over any given range. So that can be modeled as a straight line function, which is probably what you are more familiar with. So, the basic idea behind logistic is you take the log of the odds, just like some kind of a transformation, some kind of a transformed variable, and you pretend you apply your linear regression understanding on it. So, once you have this transformed variable to look at, not the original properties, not the binaries, but as a transformed variable, then your entire linear regression understanding carries over to, to this to this level. So, then you can use all the all the all the variables that you have in here, all the 15 variables to basically get some kind of a prediction of what your probability would be the probability of climbing, and hence, the property of not climbing to the top would be. So if that property turns out to be, let's say, 70%, or 80%, based on that equation based on that formula, then you would have overwhelming evidence, you'll have a big deal of confidence that you will get to the top. So, that's how logistics are mainly used. But there's one caveat, there's one thing we have to keep in mind, no matter what model we build, we have to ensure that it's substantially better than what you could have done if you've just gone with a random flip, which was the 62%.
John Bailer
Yeah, so that's right. I know I'm gonna get speed right? 62% of the time, right?
Moinak Bhaduri
Yes, yes, that is where the P values we notice carefully inside of table two, or think there are a few p values going on, which is exactly what you're mentioning. Shown, it's basically evidence that you have done substantially better. So let's say you play logistics and your success probability, your guess that you'll get to the top turns out to be about 70%. And since it's like, pretty close to one, more or less, it's more than 30%. The other hand, you would claim that you are likely to reach the top, let's say that this is your best guess. And when you really had this experiment, you really had the climb, you could not get to the top, and then your accuracy, your overall accuracy goes down a little bit. Whereas if you could get to the top, then your accuracy goes up a little bit. So if you keep a long record, if you keep a track record of all these mistakes you have been making, then ideally, if your model is any good if it's substantially better than random guessing you would expect this grand accuracy to be bigger than that 62%. Because otherwise, if you had said every expedition will be successful, you would have been right 62% of the time, which is the least the most basic, you could have been the least you could have done. So that P value basically says whether the accuracy that you have from logistic or for any model for that matter is substantially more than 62. So like if it's 63, then it's a little subjective. Yeah, 63 is a little better than 62. But some others may argue that it would have been 72 for the sake of 82. So the test is the formal statistical test, it compares the number you found at some benchmark with that with that basic benchmark, and says whether it's substantially more, so the smaller the p value, the better it is.
John Bailer
All right. So you know, as you get here, that looking at your results, it sounds like so you go up; you get about a 7% lift here.
Moinak Bhaduri
Yeah, yeah. Yeah, that's true.
John Bailer
So you do a bit. So using information means that you're, you're better at predicting this. So that's a positive sign. I mean, hey, that's job security for people.
Moinak Bhaduri
And that's very true. Yes, yes. And it keeps on going up. Like if you leave the logistics to the cat and to the bags. Yeah, it just keeps on increasing.
John Bailer
And so you know, I've got a nearest neighbor right now, it's 30. Yeah. So yeah, come on. Yeah. So what does it mean to say go to the next model that you've talked about, which is the nearest neighbor and nearest neighbor idea, so help paint that picture? Because, you know, while logistics are really popular, yeah. Medical science, Epidemiology, these nearest neighbor models, I mean, this might be something that recommender systems are using when we're, that's very true. You are the next you to watch.
Moinak Bhaduri
So, why did we go there? Right. So, I mean, the main reason logistics is it's quite a popular choice, but every model they come with strings attached. So if you look at logistics, it's not free lunch. I mean, there are assumptions. So one of the most common assumptions behind logistic is something called separability, which is, if all the successful climbs, they line up with specific values for the predictor. Like if all the successful climbs correspond to us single oxygen, to those that used oxygen and all the unsuccessful climbs all the failed crimes, they line up with expeditions that did not use oxygen. And so if it's very, very automatic, if saying one is automatically implying the other, then there is this problem called separability, which basically means the slopes that you find the constants that you find inside of the logistic equation, those constants will be very unreliable, but be very unstable. So if you have a different expedition, if you have a different climate in mind, if you for now have 72 as one of the constants, it can totally change to something entirely different to 97, or something like that. So that's one reason why we need to move on to the nearest neighbor approach. And that in turn also has drawbacks that have the assumption of low dimension. So you have to ideally have a small number of features one number of details to predict your response with because if you don't, if you have a high number of details, a large number of columns, a large number of predictors to predict your response out of, then there is something called a curse of dimensionality, which says that your KNN would find no friends to take help from. in higher dimensions, you're very prone to be different from somebody, you are less likely to be similar to somebody.
John Bailer
So you're doing this with this nearest neighbor thing. You're looking at 2200 climbs, right? And you're saying, hey, what do you find distances between them? Yes. On some measure of distance between correct. And then you're saying, okay, my claim is going to look like this? Yes, yes. 200? Or with sort of maybe seven or so of those 20? Yeah, most?
Moinak Bhaduri
Yes, you find expeditions that are very similar to the one that you are planning. And you find out the, the the result that was most common to all those seven, so maybe a five out of those seven climbs the seven other expeditions that are very similar to you, if five of them were successful, then you would go with the majority vote, you would say that you would you'd be good to, you'd be good to go to. Whereas if maybe six out of those seven are failed attempts, then you would fail so you'd go with the majority. Yes.
John Bailer
This puts us, so now we've gone from 62 to 69. With logistic regression. Yes, yes. Three with K nearest neighbors. Maybe we're just cooking with oil. Yeah. So you know, you then embraced another set, another family of alternatives. Talk a little bit about what was this final family of alternatives that you considered.
Moinak Bhaduri
The final family is basically a nonlinear family. So if you look at, say, a logistic, for instance, then yes, you model log of the odds, but still, it's a straight line function. And so the main logic behind the last family would be this way of adding variables, it's just not right, no matter how long you make that equation last. So also the separability issue goes away the curse of dimensionality problem, in a way goes away if you have the tree based models. So the last family molds, they, they, they basically ask irrelevant questions to the top. So like, we have one example here in the paper, which is about squirrels and humans. So it says like, if you have to classify whether you're human or a squirrel, then one question you can ask to have a very good classification, you have a very good separation between the squirrels and the humans would be, or do you have a tailor or not? So initially, if you had 100 objects, 100 individuals, and he had to classify them, you were totally lost if it's 50/50. But if you ask a very relevant question, which is like, Do you have a tailor now than all the squirrels would go onto one side, very similar to separability, which is not good for logistics at all, but very good for trees, then all the squirrels would go to one side, and all those that said, we do not have tail to go on to the other side doesn't be humans. So your entropy or your uncertainty will reduce drastically. So this is how trees work by asking relevant questions. But in practice, of course, it won't be the sort of a problem where it's very simple. But here, too, for the main problem, you ask questions that are relevant, like whether or not you used oxygen, that will go to the very top of the tree, because that's the most crucial decision. And those questions, those details that are not that relevant, they go to the bottom of the tree, they go down, and down and down and down. So you can always look at one single tree, and when you have a fresh expedition, you follow the right twists and turns, and you reach the last node terminal nodes. And again, you do something very similar to what you did on the can and you say that your result would be the one that's most common in that note So that's when you do one single tree for which we have an accuracy of something. But the trouble with that approach is to make your, your classifications perfect, those trees may become very, very deep, which is why the new average, that's the reason why you average a bunch of trees, which is like you put your expedition through not just one tree, but many trees, and then you take the majority vote. Last last category of models.
Rosemary Pennington
So we have so far talked about how oxygen, yes, oxygen is important. Using a popular route is important. Correct. Your trip is short? Yes, yes. What have we left out as far as what we need to be successful to climb Everest?
Moinak Bhaduri
Um, as far as the data is concerned, those are the key factors. Those are the key things that we need to think about. There is something else we cannot really control. All the things that you mentioned rosemary, they are within our control whether or not we wanted to use oxygen, the amount of time you spend on the road. But the other is the number of teams you have on the mountain that season. Yeah, so that is beyond our control. And there are mountaineers who believe that it's, it's that the crowding is to blame quite a lot. So if you look at the Hillary step, which is right above, I mean, very near the top, it is pretty crowded. If it's a good day, it's a good day, if it's a good day to climb, then many people, many, many climbers, they throng that slope. So it's, you had to wait, there are quite a lot, and you may get frozen to death. So yeah, so the number of teams on the mountain that season, it's a crucial decider to it's probably the third, the second or third most crucial decider, but that's beyond your control. So maybe one of the one of the one of the results you're trying to get across is that if you convert this to the real scale, from the scaled framework to the real scale, it's probably around 46. Teams. That's the sweet spot because beyond it, the log of the out, your chances would go down. That's what the data says. So if you are probably giving permits, or giving licenses to climb that season, could cap at 46 or run about that mark, because beyond it CEU credits Yeah.
John Bailer
So I'm curious as you've done this, what was the most surprising thing? Time?
Moinak Bhaduri
I would say time? Yeah, the time is, yeah, it's not the most crucial decider, it's still oxygen, it's still the route taken. It's still the number of teams you have on the mountain, it's still the number of days you spend on the road. I would have expected time to be a very crucial decider because it's correlated with the climbing gear experiences getting better or you don't have better climbing gear. It's still relevant, but it's not at the very top. It's the fourth or the fifth most crucial decider. Yes.
Rosemary Pennington
Well, that's all we have for this episode of Stats and Stories. It was really interesting talking to you as a childhood dream I once thought I would not have thought I once dreamed of climbing Everest, and then realized I did not have that kind of dedication in me to do that. So it was really interesting to read this article.
Moinak Bhaduri
Thank you. You could still do the Everest base camp, though you don't have to be an athlete. Basecamp is still doable.
Rosemary Pennington
Now put that back in my bucket list. Thank you so much for being here today, Moinak.
Moinak Bhaduri
Thanks for having me. Nice catching up.
Rosemary Pennington
Stats and Stories is a partnership between Miami University's Department of Statistics and media, journalism and film as well as the American Statistical Association. You can follow us on Twitter @StatsandStories, Apple podcasts or other places you find podcasts. If you'd like to share your thoughts on the programs and your email to statsandstories@miami.oh.edu or check us out at statsandstories.net, and be sure to listen for future editions of Stats and Stories, where we discuss the statistics behind the stories and the stories behind the statistics.