Fivethirtyeight has just published their first prediction for the next US presidential election, stating that Clinton has around 80% chance of winning to Trumps' 20%. This has been also reported in the general media (for example here).
I think the tone of the Guardian's article is kind of interesting $-$ basically if first praises Nate Silver's ability but also points out a series of "high-profile misses that could lead some observers to discount their predictions this year". Author Tom McCarthy goes on to report on very wrong predictions for example on Trump's chance of securing the Republican nomination.
I guess this is such a fluid and dynamic situation that perhaps it's a bit too early to call a definitive outcome. But I'm sure we'll be bombarded with predictions in the next few months...
Thursday, 30 June 2016
Friday, 17 June 2016
Workshop on Infectious Disease Modelling in Public Health Policy: Current status and challenges (yet, again)
I've written about this a couple of times already (here and here). We've finalised the speakers line up (see here for the latest information) and I think this is a very exciting programme! (I know you may think "well, he would say that, wouldn't he?" $-$ and you're probably right... But I do think that the line up is really interesting!).
Anyway, although the registration list on Eventbrite is formally close, I think we do have some places available $-$ so if you would like to go, send me an email (details on the website)!
Anyway, although the registration list on Eventbrite is formally close, I think we do have some places available $-$ so if you would like to go, send me an email (details on the website)!
My week at ISBA (2)
I should add to my previous post that while there have been many very good talks, I thought two were incredibly good: David Spiegelhalter's Foundational lecture on Monday and Adrian Raftery's talk in a session on Bayesian Demography that was very interesting overall. I'm not sure whether slides will be made available, but if they are, you should definitely check them out!
In particular, Adrian's talk was about the application of Bayesian hierarchical methods to formally account for and quantify uncertainty in population projections (I think this is the relevant paper). He started his talk by showing a screenshot from the BBC website reporting on Boris Johnson's claim that if the UK stays within the EU, its population will "increase to 80 millions" (from the current level of around 65 millions).
As Adrian pointed out, it wasn't clear what time frame was Johnson referring to. However, I'd say unsurprisingly, his model showed that this event had virtually no chance of happening within the next 5 years and at most around 40% chance of happening in a period of 25 years [I am citing the numbers by memory, so the details may be slightly different, although they are most definitely in the right ball-park!].
In particular, Adrian's talk was about the application of Bayesian hierarchical methods to formally account for and quantify uncertainty in population projections (I think this is the relevant paper). He started his talk by showing a screenshot from the BBC website reporting on Boris Johnson's claim that if the UK stays within the EU, its population will "increase to 80 millions" (from the current level of around 65 millions).
As Adrian pointed out, it wasn't clear what time frame was Johnson referring to. However, I'd say unsurprisingly, his model showed that this event had virtually no chance of happening within the next 5 years and at most around 40% chance of happening in a period of 25 years [I am citing the numbers by memory, so the details may be slightly different, although they are most definitely in the right ball-park!].
My week at ISBA
I've spent the last few days in beautiful Sardinia for the ISBA world conference. The place is outstanding, really beautiful, although it's kind of weird that there is no real town along the cost for miles and miles. Leaving Cagliari and driving for over 50km, you only come across a massive oil refinery and the town of Pula. There are many resorts (some super high-end, like the one where the conference is, some more like very nice camping sites with tents or bungalows replaced by nice apartments), but no real town. I felt that was a bit weird as I wasn't used to things like that, in Italy $-$ but it may well be that I am just ignorant about my own country and there's tons of places like that...
As for the conference, my last ISBA was 10 years ago $-$ that was the last one of the original "Valencia meetings". Even then, it felt like a big conference, but that was nowhere near the level it has reached now (I think there are over 700 people here!). This means there are several parallel sessions and lots of heterogeneity in the topics. Also, the schedule is quite packed with talks from 9am to 7.30pm (with some breaks throughout) and then poster sessions after dinner. I was impressed by how well the organisation has worked: I've not seen a single session running late!
My talk is later today; I'll be talking about our work on the RDD $-$ I've planned a rather high-level talk, showing some of the general themes we've developed and giving broad examples, rather than going to the details. Luckily, we do have a few papers on these so hopefully I'll be able to point people to the relevant references.
More importantly, I'll have to rush off just after my talk (which isn't great) so that I won't miss my flight home $-$ I've tried to plan everything ahead, so I've put petrol in the car, checked out the hotel, etc. I'll give the talk with my fingers crossed, just in case...
As for the conference, my last ISBA was 10 years ago $-$ that was the last one of the original "Valencia meetings". Even then, it felt like a big conference, but that was nowhere near the level it has reached now (I think there are over 700 people here!). This means there are several parallel sessions and lots of heterogeneity in the topics. Also, the schedule is quite packed with talks from 9am to 7.30pm (with some breaks throughout) and then poster sessions after dinner. I was impressed by how well the organisation has worked: I've not seen a single session running late!
My talk is later today; I'll be talking about our work on the RDD $-$ I've planned a rather high-level talk, showing some of the general themes we've developed and giving broad examples, rather than going to the details. Luckily, we do have a few papers on these so hopefully I'll be able to point people to the relevant references.
More importantly, I'll have to rush off just after my talk (which isn't great) so that I won't miss my flight home $-$ I've tried to plan everything ahead, so I've put petrol in the car, checked out the hotel, etc. I'll give the talk with my fingers crossed, just in case...
Friday, 3 June 2016
Large enough probability?
However, I was talking earlier to my "polls guy" Roberto (yes: I have a polls guy) and he's suggested I took a look at Stephen Fisher's blog, who is predicting a 72% chance that the outcome of the referendum will be "remain" (in the EU). I think I'll take that as a good sign.
In the past couple of days, people have put forward the argument that the UK should take their economy back and "do like New Zealand in the 1980s $-$ that was very good for their economy, so surely it'll work for us too". [start rather annoyed irony]Surely the global economy and trading system were exactly what they are today, back in the 1980s, so surely this is super relevant evidence and something we should be basing our judgement on, today...[end rather annoyed irony]
Monday, 23 May 2016
Bayes 2016
As for the more statsy-bits of the conference, as usual I really enjoyed it very much $-$ we always try to make a point of getting talks of high methodological level from both academia and industry, which in my opinion makes for a very nice three days!
In addition, the social part of being at Bayes 20XX is also usually very attractive $-$ and this year has not disappointed. At the end of the first day of the conference, we had a beer-tasting tour $-$ as Emmanuel put it, that was really a study to find the maximum tolerated dose: we were there to determine at what point in the escalation of the beer alcohol percentage we would seriously need to stop (we passed 5% without problems, then worked our way to an 8% and then had to go for dinner after a 10%)...
Anyway, I think the programme was packed with very interesting talks and hopefully, we'll be soon able to upload the presentations! And next year we'll go to Albacete, where Virgilio will play host. In keeping with our grand tradition, several people have been ambushed and as a consequence we do have quite a few candidates to host the next edition in 2018...
Sunday, 22 May 2016
BCEA 2.2-3 is out
I think the newest release of BCEA, our R package to standardise and post-process the output of a health economic model, is now available from CRAN $-$ in fact, the source code is also available here. The package is rather stable, so the changes aren't many, but the few ones are quite substantial, I think. In particular, we've now modified the function evppi, which is used to perform the analysis of the expected value of partial information (incidentally, that's also related to our upcoming short course).
In the last few years this has been a very interesting and fertile area of research within the health economics community, with interesting methods being proposed $-$ this is a nice editorial by Nicky Welton and Howard Thom, while this is (an arxived version of) our own technical review.
BCEA implements all the most recent methods, with particular focus on Strong et al's based on Gaussian Process regression and our own work (just published in Statistics in Medicine), which, building on their work, uses INLA to speed up the computation even further. In addition, we have also included a graphical tool that can be used to describe, at least as a first order approximation, the individual impact of each parameter on the overall uncertainty in the decision-making process. We have called this the info-rank plot, which is basically a generalisation of commonly used (especially when economic evaluations are performed under a frequentist approach) Tornado plots. The info-rank is based on the single-parameter EVPPI and can be used to roughly determine the contribution of each single parameters to the overall value of partial information (of course, because the EVPPI is a highly non-linear function, combinations of parameters are not additive, so some caution is needed here).
In the last few years this has been a very interesting and fertile area of research within the health economics community, with interesting methods being proposed $-$ this is a nice editorial by Nicky Welton and Howard Thom, while this is (an arxived version of) our own technical review.
BCEA implements all the most recent methods, with particular focus on Strong et al's based on Gaussian Process regression and our own work (just published in Statistics in Medicine), which, building on their work, uses INLA to speed up the computation even further. In addition, we have also included a graphical tool that can be used to describe, at least as a first order approximation, the individual impact of each parameter on the overall uncertainty in the decision-making process. We have called this the info-rank plot, which is basically a generalisation of commonly used (especially when economic evaluations are performed under a frequentist approach) Tornado plots. The info-rank is based on the single-parameter EVPPI and can be used to roughly determine the contribution of each single parameters to the overall value of partial information (of course, because the EVPPI is a highly non-linear function, combinations of parameters are not additive, so some caution is needed here).
Monday, 9 May 2016
How to be Bayesian and spare yourself a dreadful afternoon with your stupid football team losing the derby
Yesterday was the second-last game of the Italian Serie A; I've been a Sampdoria supported since I was 12 $-$ at that time, they were starting to become one of the best clubs in Serie A (and that was back in the 80's when Serie A was arguably the best league in the world), although they hadn't won anything and didn't have prospects for that season either. But they were a young, good side, playing nicely and so I kind of fell in love with them (and their shirt). Then they did become a very good side, winning the league and a few more trophies $-$ so good timing on my part! But also, then they reverted to some relative mediocrity $-$ of course, once you've decided you support a team, you're stuck with them no matter what.
Anyway, this season has been rather crappy and yesterday it was a crucial game: we were playing the derby against local rival Genoa entering the game with 40 points and two games left in the campaign. Two teams couldn't reach us any more (as they were trailing by over 6 points). But at least one between Carpi and Palermo could still overtake us if we lost our two remaining games and they won all of theirs. Also, Udinese was just one point behind us so they too could overtake us, technically. With three teams being relegated, we weren't statistically safe yet.
So, that's kind of nervous and earlier last week I thought about this a bit. I had a bad feeling about our game, because we've not been great lately (the previous game we were beaten by Palermo) and, clearly, Genoa would try really hard to mess it up for us... But, irrespective of the outcome of the derby, if at least one between Carpi, Palermo and Udinese failed to win their match we would be safe (as there wouldn't be enough points left for them to catch us). Carpi played at home against Lazio, whose season hasn't been great either, but they were already safe and with not much else to fight for, except a strong finish; Palermo were away at Fiorentina, who theoretically were still fighting for a Europa league qualification and so should have something to play for; Udinese were away at Atalanta, who much as Lazio were mathematically safe and with not much to play for.
Although one can make a much more complex model, I reasoned that instead of the actual result, what was only important was the chance that either of the three teams behind us would win and so I set up a model with $ y_{\rm{Car}} \sim \mbox{Bernoulli}(\theta_{\rm{Car}})$, $y_{\rm{Pal}} \sim \mbox{Bernoulli}(\theta_{\rm{Pal}})$ and $y_{\rm{Udi}} \sim \mbox{Bernoulli}(\theta_{\rm{Udi}})$ where the "success" would in fact be the worst possible outcome, ie a win for them.
Then I set up some priors: I reasoned that because they were playing at home, Carpi may have a slightly higher chance of winning the game $-$ I figured something about 35%. Also, I thought (hoped) that Lazio wouldn't be a walkover and so I assumed that 90% of the mass for the chance of Carpi winning their game was around 45%. These can be turned into an informative Beta(15.80107,28.4877) prior $-$ it's fairly easy to work out the parameters of a Beta distribution given the mode (0.35, in this case) and some percentile (0.45 as the 90th percentile, in this case); Christensen et al (page 100) show some theory, while this is some relevant R code.
This is effectively the prior I was assuming:
Anyway, this season has been rather crappy and yesterday it was a crucial game: we were playing the derby against local rival Genoa entering the game with 40 points and two games left in the campaign. Two teams couldn't reach us any more (as they were trailing by over 6 points). But at least one between Carpi and Palermo could still overtake us if we lost our two remaining games and they won all of theirs. Also, Udinese was just one point behind us so they too could overtake us, technically. With three teams being relegated, we weren't statistically safe yet.
So, that's kind of nervous and earlier last week I thought about this a bit. I had a bad feeling about our game, because we've not been great lately (the previous game we were beaten by Palermo) and, clearly, Genoa would try really hard to mess it up for us... But, irrespective of the outcome of the derby, if at least one between Carpi, Palermo and Udinese failed to win their match we would be safe (as there wouldn't be enough points left for them to catch us). Carpi played at home against Lazio, whose season hasn't been great either, but they were already safe and with not much else to fight for, except a strong finish; Palermo were away at Fiorentina, who theoretically were still fighting for a Europa league qualification and so should have something to play for; Udinese were away at Atalanta, who much as Lazio were mathematically safe and with not much to play for.
Although one can make a much more complex model, I reasoned that instead of the actual result, what was only important was the chance that either of the three teams behind us would win and so I set up a model with $ y_{\rm{Car}} \sim \mbox{Bernoulli}(\theta_{\rm{Car}})$, $y_{\rm{Pal}} \sim \mbox{Bernoulli}(\theta_{\rm{Pal}})$ and $y_{\rm{Udi}} \sim \mbox{Bernoulli}(\theta_{\rm{Udi}})$ where the "success" would in fact be the worst possible outcome, ie a win for them.
Then I set up some priors: I reasoned that because they were playing at home, Carpi may have a slightly higher chance of winning the game $-$ I figured something about 35%. Also, I thought (hoped) that Lazio wouldn't be a walkover and so I assumed that 90% of the mass for the chance of Carpi winning their game was around 45%. These can be turned into an informative Beta(15.80107,28.4877) prior $-$ it's fairly easy to work out the parameters of a Beta distribution given the mode (0.35, in this case) and some percentile (0.45 as the 90th percentile, in this case); Christensen et al (page 100) show some theory, while this is some relevant R code.
This is effectively the prior I was assuming:
and I thought it was just about reasonable (the dotted vertical lines indicate a rough estimate of the 95% prior credible interval). Then I did something similar to derive the priors for a Palermo and Udinese win $-$ because they were playing away, I figured they would have an average chance of winning of around 20% with 90% of the mass before 40%, which can be turned into a Beta(3.279775,10.1191) prior, looking like this:
Again, I was relatively happy with this and so used these priors in my model, which one could code in R as something like
p.car ~ rbeta(10000,15.80107,28.4877) # P(win) on average .35 and with 95% mass <= .45
p.pal ~ rbeta(10000,3.279775,10.1191) # P(win) on average .2 and with 95% mass <=.4
p.udi ~ rbeta(10000,3.279775,10.1191) # P(win) on average .2 and with 95% mass <=.4
p.safe <- 1-(p.car*p.pal*p.udi)
The most important variable in the model is the probability of Sampdoria being mathematically certain of avoiding relegation, p.safe, which is 1 minus the probability of the worst happening $-$ this assumes independence in the three games for Palermo, Carpi and Udinese; in general that's probably not the best assumption, but in this case they kind of had to win to have a good shot at safety themselves and so I think it's OK to assume independence. The results were kind of reassuring:
$-$ I got an estimated posterior average of 97.8% with a 95% credible interval of 93.8 to 99.7%.
I am not really one to stay at home on a Sunday just to watch the football game (so perhaps I'm not really a footaball fan?) and we'd planned to see some friends, but this reassured me that we shouldn't be in too much trouble, even if we lost the derby. In the event, Kobi wasn't great (possibly as a result of venturing an outing at the seaside on Saturday) and so we stayed at home $-$ but I decided not to bother with watching the game (again: a) a bold move for a real football fan, confident about his team; b) a cowardly move from a real football fan scared of what the outcome may be; c) not a real football fan).
We did lose the derby very badly, but Carpi, Palermo and Udinese all failed to win their games, which means we are safe. I'm glad I didn't watch the game...
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