# Summary

- Historical terrorist attack deaths suggest the probability of a
__terrorist__attack causing__human extinction__is astronomically low, 4.35*10^-15 per year according to my preferred estimate. - One may well update to a much higher extinction risk after accounting for inside view factors. However, extraordinary evidence would be required to move up sufficiently many orders of magnitude for an
__AI__or__bio__terrorist attack to have a decent chance of causing human extinction. - I think it would be great if Open Philanthropy published the results of their efforts to quantify biorisk if/once they are available.
- In the realm of the more anthropogenic
__AI__,__bio__and__nuclear____outside view__is a major reason leading to overly high risk. I encourage readers to check David’s series__exaggerating the risks__, which includes subseries on__climate__,__AI__and__bio__risk.

# Introduction

I listened to Kevin Esvelt’s stories __on__ The 80,000 Hours Podcast about how bioterrorism may kill billions. They sounded plausible, but at the same time I thought I should account for the __outside view__, which I knew did not favour terrorism being a global catastrophic risk. So I decided to look into historical terrorist attack deaths to estimate a prior probability for a __terrorist__ attack causing __human extinction__.

# Methods

Firstly, I retrieved data for the deaths in the 202 k terrorist attacks between January 1970 and June 2021 on the __Global Terrorism Database__ (GTB). Then I computed some historical stats for such deaths.

Secondly, I relied on the Python library __fitter__ to find the distributions which best fit to the top 1 %:

- Terrorist attack deaths.
- Logarithm of the terrorist attack deaths as a fraction of the global
__population__^{[1]}.

I fitted the distributions to the 1 % most deadly attacks because I am interested in the right tail, which __may__ decay faster than suggested by the less extreme points. __fitter__ tries all the types of __distributions__ in SciPy, 111 on 13 November 2023. For each type of distribution, the best fit is that with the lowest residual sum of squares (__RSS__), respecting the sum of the squared differences between the actual and predicted probability density function (__PDF__). I set the number of bins to define the PDF to the __square root__ of the number of data points, and left the maximum time to find the best fit parameters to the default value in __fitter__ of 30 s.

I estimated the probability of the terrorist attack deaths as a fraction of the global population being at least 10^-10, 10^-9, …, and 100 % multiplying:

- 1 %, which is the probability of the attack being in the right tail.
- Probability of the deaths as a fraction of the global population being at least 10^-10, 10^-9, …, and 100 % if the attack is in the right tail, which I got using the best fit parameters outputted by
__fitter__.

I obtained the annual probability of terrorist attack extinction from 1 - (1 - “probability of the terrorist attack deaths as a fraction of the global population being at least 100 %”)^“terrorist attacks per year”.

I aggregated probabilities from different best fit distributions using the median. I did not use:

- The mean because it ignores information from extremely low predictions, and overweights outliers.
- The
__geometric mean of odds__nor the geometric mean because many probabilities were 0.

The calculations are in __this__ Sheet and __this__ Colab.

# Results

The results are in the __Sheet__.

## Historical terrorist attacks stats

### Terrorist attacks basic stats

Statistic | Terrorist attack deaths | Terrorist attack deaths as a fraction of the global population | Terrorist attack deaths in a single calendar year |
---|---|---|---|

Mean | 2.43 | 3.74*10^-10 | 9.63 k |

Minimum | 0 | 0 | 173 |

5th percentile | 0 | 0 | 414 |

Median | 0 | 0 | 7.09 k |

95th percentile | 10 | 1.53*10^-9 | 31.1 k |

99th percentile | 30 | 4.74*10^-9 | 41.8 k |

Maximum | 1.70 k | 2.32*10^-7 | 44.6 k |

### Terrorist attacks by severity

Terrorist attack deaths | Terrorist attacks | Terrorist attacks per year | |
---|---|---|---|

Minimum | Maximum | ||

0 | Infinity | 202 k | 3.92 k |

0 | 1 | 101 k | 1.97 k |

1 | 10 | 89.5 k | 1.74 k |

10 | 100 | 10.8 k | 210 |

100 | 1 k | 235 | 4.56 |

1 k | 10 k | 4 | 0.0777 |

10 k | Infinity | 0 | 0 |

__Tail distribution__ of the terrorist attack deaths

## Terrorist attacks tail risk

Below are the median RSS, __coefficient of determination__^{[2]} (R^2), probability of terrorist attack deaths as a fraction of the global population being at least 10^-10, 10^-9, …, and 100 %, and annual probability of a terrorist attack causing human extinction. The medians are taken across the best, top 10, and top 100 distributions according to 3 fitness criteria, lowest RSS^{[3]}, Akaike information criterion (__AIC__), and Bayesian information criterion (__BIC__). My preferred estimate is the median taken across the 10 distributions with lowest RSS, which is the default fitness criterion in __fitter__, fitted to the top 1 % logarithm of the terrorist attack deaths as a fraction of the global population. The results for AIC and BIC are identical^{[4]}. Null values may be exactly 0 if they concern bounded distributions, or just sufficiently small to be rounded to 0 due to finite precision. I also show the annual probability of terrorist attack extinction as a function of R^2.

### Best fit to the top 1 % terrorist attack deaths

Distributions | Median RSS | Median R^2 |
---|---|---|

Best (RSS) | 1.87*10^-6 | 99.6 % |

Top 10 (RSS) | 9.26*10^-6 | 98.0 % |

Top 100 (RSS) | 1.03*10^-4 | 78.1 % |

Best (AIC) | 4.71*10^-4 | 0 |

Top 10 (AIC) | 4.65*10^-4 | 1.21 % |

Top 100 (AIC) | 8.77*10^-5 | 81.4 % |

Best (BIC) | 4.71*10^-4 | 0 |

Top 10 (BIC) | 4.65*10^-4 | 1.21 % |

Top 100 (BIC) | 8.77*10^-5 | 81.4 % |

Distributions | Median probability of terrorist attack deaths as a fraction of the global population being at least... | |||

10^-10 | 10^-9 | 10^-8 | 10^-7 | |

Best (RSS) | 1.00 % | 9.94*10^-3 | 9.89*10^-4 | 2.15*10^-6 |

Top 10 (RSS) | 1.00 % | 1.00 % | 1.43*10^-3 | 2.21*10^-7 |

Top 100 (RSS) | 1.00 % | 1.00 % | 2.10*10^-3 | 9.00*10^-7 |

Best (AIC) | 1.00 % | 1.00 % | 9.71*10^-3 | 5.44*10^-3 |

Top 10 (AIC) | 9.95*10^-3 | 9.94*10^-3 | 9.18*10^-3 | 5.20*10^-3 |

Top 100 (AIC) | 1.00 % | 1.00 % | 2.10*10^-3 | 1.52*10^-6 |

Best (BIC) | 1.00 % | 1.00 % | 9.71*10^-3 | 5.44*10^-3 |

Top 10 (BIC) | 9.95*10^-3 | 9.94*10^-3 | 9.18*10^-3 | 5.20*10^-3 |

Top 100 (BIC) | 1.00 % | 1.00 % | 2.10*10^-3 | 1.52*10^-6 |

Distributions | Median probability of terrorist attack deaths as a fraction of the global population being at least... | |||

10^-6 | 0.001 % | 0.01 % | 0.1 % | |

Best (RSS) | 4.64*10^-9 | 1.00*10^-11 | 2.17*10^-14 | 4.66*10^-17 |

Top 10 (RSS) | 3.60*10^-12 | 3.05*10^-17 | 0 | 0 |

Top 100 (RSS) | 0 | 0 | 0 | 0 |

Best (AIC) | 0 | 0 | 0 | 0 |

Top 10 (AIC) | 0 | 0 | 0 | 0 |

Top 100 (AIC) | 0 | 0 | 0 | 0 |

Best (BIC) | 0 | 0 | 0 | 0 |

Top 10 (BIC) | 0 | 0 | 0 | 0 |

Top 100 (BIC) | 0 | 0 | 0 | 0 |

Distributions | Median probability of terrorist attack deaths as a fraction of the global population being at least... |
Median annual probability of terrorist attack extinction | ||

1 % | 10 % | 100 % | ||

Best (RSS) | 0 | 0 | 0 | 0 |

Top 10 (RSS) | 0 | 0 | 0 | 0 |

Top 100 (RSS) | 0 | 0 | 0 | 0 |

Best (AIC) | 0 | 0 | 0 | 0 |

Top 10 (AIC) | 0 | 0 | 0 | 0 |

Top 100 (AIC) | 0 | 0 | 0 | 0 |

Best (BIC) | 0 | 0 | 0 | 0 |

Top 10 (BIC) | 0 | 0 | 0 | 0 |

Top 100 (BIC) | 0 | 0 | 0 | 0 |

### Best fit to the top 1 % logarithm of the terrorist attack deaths as a fraction of the global population

Distributions | Median RSS | Median R^2 |
---|---|---|

Best (RSS) | 0.113 | 98.4 % |

Top 10 (RSS) | 0.123 | 98.2 % |

Top 100 (RSS) | 0.654 | 90.5 % |

Best (AIC) | 6.88 | 0 |

Top 10 (AIC) | 6.87 | 1.77*10^-3 |

Top 100 (AIC) | 0.654 | 90.5 % |

Best (BIC) | 6.88 | 0 |

Top 10 (BIC) | 6.87 | 1.77*10^-3 |

Top 100 (BIC) | 0.654 | 90.5 % |

Distributions | ||||

10^-10 | 10^-9 | 10^-8 | 10^-7 | |

Best (RSS) | 1.00 % | 1.00 % | 2.75*10^-3 | 3.48*10^-5 |

Top 10 (RSS) | 1.00 % | 1.00 % | 2.74*10^-3 | 3.65*10^-5 |

Top 100 (RSS) | 1.00 % | 1.00 % | 2.89*10^-3 | 6.85*10^-5 |

Best (AIC) | 1.00 % | 1.00 % | 8.08*10^-3 | 2.16*10^-3 |

Top 10 (AIC) | 1.00 % | 1.00 % | 7.18*10^-3 | 2.40*10^-3 |

Top 100 (AIC) | 1.00 % | 1.00 % | 2.89*10^-3 | 6.81*10^-5 |

Best (BIC) | 1.00 % | 1.00 % | 8.08*10^-3 | 2.16*10^-3 |

Top 10 (BIC) | 1.00 % | 1.00 % | 7.18*10^-3 | 2.40*10^-3 |

Top 100 (BIC) | 1.00 % | 1.00 % | 2.89*10^-3 | 6.81*10^-5 |

Distributions | ||||

10^-6 | 0.001 % | 0.01 % | 0.1 % | |

Best (RSS) | 4.21*10^-7 | 5.09*10^-9 | 6.15*10^-11 | 7.44*10^-13 |

Top 10 (RSS) | 4.46*10^-7 | 5.26*10^-9 | 6.05*10^-11 | 6.85*10^-13 |

Top 100 (RSS) | 4.19*10^-8 | 5.65*10^-11 | 2.34*10^-14 | 4.11*10^-17 |

Best (AIC) | 0 | 0 | 0 | 0 |

Top 10 (AIC) | 0 | 0 | 0 | 0 |

Top 100 (AIC) | 3.95*10^-8 | 5.22*10^-11 | 1.09*10^-14 | 1.55*10^-17 |

Best (BIC) | 0 | 0 | 0 | 0 |

Top 10 (BIC) | 0 | 0 | 0 | 0 |

Top 100 (BIC) | 3.95*10^-8 | 5.22*10^-11 | 1.09*10^-14 | 1.55*10^-17 |

Distributions |
Median annual probability of terrorist attack extinction | |||

1 % | 10 % | 100 % | ||

Best (RSS) | 9.00*10^-15 | 1.09*10^-16 | 1.11*10^-18 | 4.35*10^-15 |

Top 10 (RSS) | 7.71*10^-15 | 8.66*10^-17 | 1.11*10^-18 | 4.35*10^-15 |

Top 100 (RSS) | 5.55*10^-19 | 0 | 0 | 0 |

Best (AIC) | 0 | 0 | 0 | 0 |

Top 10 (AIC) | 0 | 0 | 0 | 0 |

Top 100 (AIC) | 0 | 0 | 0 | 0 |

Best (BIC) | 0 | 0 | 0 | 0 |

Top 10 (BIC) | 0 | 0 | 0 | 0 |

Top 100 (BIC) | 0 | 0 | 0 | 0 |

# Discussion

Historical terrorist attack deaths suggest the probability of a terrorist attack causing human extinction is astronomically low. According to my preferred estimate, the median taken across the 10 distributions with lowest RSS fitted to the top 1 % logarithm of the terrorist attack deaths as a fraction of the global population, the annual probability of human extinction caused by a terrorist attack is 4.35*10^-15. Across all my 18 median estimates, it is 4.35*10^-15 for 2, and 0 for the other 16. For context, in the Existential Risk Persuasion Tournament (__XPT__), superforecasters and domain experts^{[5]} predicted a probability of an engineered pathogen causing human extinction by 2100 of 0.01 % and 1 %, which are much higher than the implied by my prior estimates.

I do not think __anthropics__ are confounding the results. There would be no one to do this analysis if a terrorist attack had caused human extinction in the past, but there would be for less severe large scale attacks, and there have not been any. The most deadly attack since 1970 on GTB only killed 1.70 k people. As a side note, the most deadly __bioterrorist incident__ only killed 200 people (over 5 years).

Interestingly, some best fit distributions led to an annual probability of human extinction caused by a terrorist attack higher than 10 % (see last 2 graphs), which is unreasonably high. In terms of the best fit distributions to:

- The top 1 % terrorist attack deaths, a
__lognormal__results in 45.1 %^{[6]}(R^2 = 14.5 %). - The logarithm of the top 1 % terrorist attack deaths as a fraction of the global population (the following are ordered by descending R^2):
- A
__half-Cauchy__results in 39.5 % (R^2 of 94.8 %). - A
__skew-Cauchy__results in 39.4 % (94.8 %). - A
__log-Laplace__results in 28.8 % (90.8 %). - A
__Lévi__results in 96.2 % (77.9 %). - A
__noncentral F-distribution__results in 58.0 % (77.8 %). - A
__Cauchy__results in 15.1 % (70.7 %). - A
__von Mises__results in 100 % (66.4 %). - A
__F-distribution__results in 66.4 % (65.5 %).

- A

Nonetheless, I have no reason to put lots of weight into the distributions above, so I assume it makes sense to rely on the median. In addition, according to __extreme value theory__, the right tail __should__ follow a __generalised Pareto__, whose respective best fit to:

- The top 1 % terrorist attack deaths results in an annual probability of human extinction caused by a terrorist attack of 0 (R^2 of 94.5 %).
- The logarithm of the top 1 % terrorist attack deaths as a fraction of the global population results in 0 (98.1 %).

Of course, no one is arguing that terrorist attacks with the current capabilities pose a meaningful extinction risk. The claim is that the world may become __vulnerable__ if advances in AI and bio make super destructive technology much more widely accessible. One may well update to a much higher extinction risk after accounting for inside view factors, and indirect effects of terrorist attacks (like precipitating wars). However, extraordinary evidence would be required to move up sufficiently many orders of magnitude for an __AI__ or __bio__ terrorist attack to have a decent chance of causing human extinction. On the other hand, extinction may be caused via other routes, like a big war or accident.

I appreciate it is often difficult to present compelling evidence for high terrorism risk due to __infohazards__, even if these __hinder__ good epistemics. However, there are ways of quantifying terrorism risk which mitigate them. From Open Philanthropy’s __request__ for proposal to quantify __biorisk__:

One way of estimating biological risk that we do not recommend is ‘threat assessment’—investigating various ways that one could cause a biological catastrophe. This approach may be valuable in certain situations, but the information hazards involved make it inherently risky. In our view, the harms outweigh the benefits in most cases.

A second, less risky approach is to abstract away most biological details and instead consider general ‘base rates’. The aim is to estimate the likelihood of a biological attack or accident using historical data and base rates of analogous scenarios, and of risk factors such as warfare or terrorism.

As far as know, there is currently no publicly available detailed model of tail biorisk. I think it would be great if Open Philanthropy published the results of their efforts to quantify biorisk if/once they are available. The request was published about 19 months ago, and the respective __grants__ were announced 17 months ago. Denise Melchin asked 12 months ago whether the results would be published, but there has been no reply.

In general, I agree with David Thorstad that Toby Ord’s __guesses__ for the existential risk between 2021 and 2120 given in __The Precipice__ are very high. In the realm of the more anthropogenic __AI__, __bio__ and __nuclear____ __risk, I personally think underweighting the __outside view__ is a major reason leading to overly high risk. I encourage readers to check David’s series __exaggerating the risks__, which includes subseries on __climate__, __AI__ and __bio__ risk.

# Acknowledgements

Thanks to Anonymous Person 1 and Anonymous Person 2 for feedback on the draft.

^{^}__fitter__has trouble finding good distributions if I do not use the logarithm, presumably because the optimisation is harder / fails with smaller numbers.^{^}^{^}Equivalent to lowest R^2.

^{^}Although the results I present are identical, the rankings for AIC and BIC are not exactly the same.

^{^}The sample drew heavily from the Effective Altruism (EA) community: about 42% of experts and 9% of superforecasters reported that they had attended an EA meetup.

^{^}In addition, the best fit

__normal-inverse Gaussian__to the top 1 % terrorist attack deaths results in 100 % (R^2 = 86.0 %). I did not mention this in the main text because there must be an error in__fitter__(or, less likely, in SciPy's norminvgauss) for this case. The respective cumulative distribution function (__CDF__) increases until terrorist attack deaths as a fraction of the global population of 10^-7, but then unexpectedly drops to 0, which cannot be right.

Hi Vasco, nice post thanks for writing it! I haven't had the time to look into all your details so these are some thoughts written quickly.

I worked on a project for Open Phil quantifying the likely number of terrorist groups pursuing bioweapons over the next 30 years, but didn't look specifically at attack magnitudes (I appreciate the push to get a public-facing version of the report published - I'm on it!). That work was as an independent contractor for OP, but I now work for them on the GCR Cause Prio team. All that to say these are my own views, not OP's.

I think this is a great post grappling with the empirics of terrorism. And I agree with the claim that the history of terrorism implies an extinction-level terrorist attack is unlikely. However, for similar reasons to Jeff Kaufman, I don't think this strongly undermines the existential threat from non-state actors. This is for three reasons, one methodological and two qualitative:

So overall, compared to the threat model of future bio x-risk, I think the empirical track record of bioterrorism is too weak (point 1), and the broader terrorism track record is based on actors with very different motivations (point 2) using very different attack modalities (point 3). The latter two points are grounded in a particular worldview - that within coming years/decades biotechnology will enable biological weapons with catastrophic potential. I think that worldview is certainly contestable, but I think the track record of terrorism is not the most fruitful line of attack against it.

On a meta-level, the fact that XPT superforecasters are so much higher than what your model outputs suggests that they also think the right reference class approach is OOMs higher. And this is despite my suspicion that the XPT supers are too low and too indexed on past base-rates.

You emailed asking for reading recommendations - in lieu of my actual report (which will take some time to get to a publishable state), here's my structured bibliography! In particular I'd recommend Binder & Ackermann 2023 (CBRN Terrorism) and McCann 2021 (Outbreak: A Comprehensive Analysis of Biological Terrorism).

Great points, and thanks for the reading suggestions, Ben! I am also happy to know you plan to publish a report describing your findings.

I qualitatively agree with everything you have said. However, I would like to see a detailed quantitative model estimating AI or bio extinction risk (which handled well infohazards). Otherwise, I am left wondering about how much higher extinction risk will become accounting not only for increased capabilities, but also increased safety.

To clarify, my best guess is also many OOMs higher than the headline number of my post. I think XPT's superforecaster prediction of 0.01 % human extinction risk due an engineered pathogen by 2100 (Table 3) is reasonable.

However, I wonder whether superforecasters are overestimating the risk because their nuclear extinction risk by 2100 of 0.074 % seems way too high. I estimated a 0.130 % chance of a nuclear war before 2050 leading to an injection of soot into the stratosphere of at least 47 Tg, so around 0.39 % (= 0.00130*75/25) before 2100. So, for the superforecasters to be right, extinction conditional on at least 47 Tg would have to be around 20 % (= 0.074/0.39) likely. This appears extremely pessimistic. From Xia 2022 (see top tick in the 3rd bar from the right in Fig. 5a):

This scenario is the most optimistic in Xia 2022, but it is pessimist in a number of ways (search for "High:" here):

rationing.So 20 % chance of extinction conditional on at least 47 Tg does sound very high to me, which makes me think superforecasters are overestimating nuclear extinction risk quite a lot. This in turn makes me wonder whether they are also overestimating other risks which I have investigated less.

Nitpick. I think you meant bioterrorism, not terrorism which includes more data.

Thanks! Fixed.

I don't know the nuclear field well, so don't have much to add. If I'm following your comment though, it seems like you have your own estimate of the chance of nuclear war raising 47+ Tg of soot, and on the basis of that infer the implied probability supers give to extinction conditional on such a war. Why not instead infer that supers have a higher forecast of nuclear war than your 0.39% by 2100? E.g. a ~1.6% chance of nuclear war with 47+ Tg and a 5% chance of extinction conditional on it. I may be misunderstanding your comment. Though to be clear, I think it's very possible the supers were not thinking things through in similar detail to you - there were a fair number of questions in the XPT.

I don't think I follow this sentence? Is it that one might expect future advances in defensive biotech/other tech to counterbalance offensive tech development, and that without a detailed quant model you expect the defensive side to be under-counted?

Fair point! Here is another way of putting my point. I estimated a probability of 3.29*10^-6 for a 50 % population loss due to the climatic effects of nuclear war before 2050, so around 0.001 % (= 3.29*10^-6*75/25) before 2100. Superforecasters' 0.074 % nuclear extinction risk before 2100 is 74 times my risk for a 50 % population loss due to climatic effects. My estimate may be off to some extent, and I only focussed on the climatic effects, not the indirect deaths caused by infrastructure destruction, but my best guess has to be many OOMs off for superforecasters prediction to be in the right OOM. This makes me believe superforecasters' are overestimating nuclear extinction risk.

Yes, in the same way that the risk of global warming is often overestimated due to neglecting adaptation.

I expect the defensive side to be under-counted, but not necessarily due to lack of quantitative models. However, I think using quantitative models makes it less likely that the defensive side is under-counted. I have not thought much about this; I am just expressing my intuitions.

How extraordinary does the evidence need to be? You can easily get many orders of magnitude changes in probabilities given some evidence. For example, as of 1900 on priors the probability that >1B people would experience powered flight in the year 2000 would have been extremely low, but someone paying attention to technological developments would have been right to give it a higher probability.

I've written something up on why I think this is likely: Out-of-distribution Bioattacks. Short version: I expect a technological change which expands which actors would try to cause harm.

(Thanks for sharing a draft with me in advance so I could post a full response at the same time instead of leaving "I disagree, and will say why soon!" comments while I waited for information hazard review!)

Thanks for the comment, Jeff!

I have not thought about this in any significant detail, but it is a good question! I think David Thorstad's series exagerating the risks has some relevant context.

Is that a fair comparison? I think the analogous comparison would involve replacing terrorist attack deaths per year by the number of different people travelling by plane per year. So we would have to

assume, in the last 51.5 years, only:Then, analogously to asking about a terrorist attack causig human extinction next year, we would ask about the probability that every single human (or close) would travel by plane next year, which would a priori be astronomically unlikely given the above.

I am glad you did. It is a useful complement/follow-up to my post. I qualitatevely agree with the points you make, although it is still unclear to me how much higher the risk will become.

You are welcome, and thanks for letting me know about that too!

I don't really understand what you're getting at here? Would you be able to spell it out more clearly?

(Or if someone else understands and I'm just missing it, feel free to jump in!)

Sorry for the lack of clarity. Basically, I was trying to point out that the structure of the data we had on people travelling by plane in 1900 (only in 1903) is different from that we have on terrorist attack deaths now. Then I described hypothetical data on travelling by plane with a similar structure to that we have on terrorist attack deaths now.

One could argue no people having travelled by plane until 1900 is analogous to no people having been killed in terrorist attacks, which would set an even lower prior probability of human extinction due to a terrorist attack (I would just be extrapolating based on e.g. 50 or so 0s, respecting 50 or so years of no terrorist attack deaths), whereas apparently 45 % of people in the US travelled by plane in 2015.

However, in the absence of data on people travelling by plane, it would make sense to use other reference class instead of extrapolating based on a bunch of 0s. Once one used an appropriate reference class, it is possible lots of people travelling now by plane does not seem so surprising. In addition, one may be falling prey to hindsight bias to some extent. Maybe so many people travelling by plane (e.g. instead of having more remote work) was not that likely ex ante.