cesarosum

If you're not shy of a few swear words, Nat's What I Reckon has some great recipes that are straightforward. Here's link to his bolognese - https://www.youtube.com/watch?v=Sw_Ze9zIafM

vim + vim-latex ;-)

Thanks for sharing this. I feel seen :)

Agreed, not knowing measure theory never stopped me from computing a conditional expectation. Some courses and books overemphasize rigor in probability and, while it obviously has its place, I've seen newcomers to the field become obsessed with doing everything via measure theory. Further to your point, volume two of Feller is pretty light on measure theory IIRC.

I do think that there's some merit in sticking with probability on discrete spaces for a while. Once you start dealing with continuous spaces, soon you're talking measure theory and you can wade deep into the technical details and miss some understanding of what's going on. I go back and forth on this as I think it's largely down to the reader to figure out what works for them, but I think probability is one of those fields where developing intuition early on is a must if you want to go further.

> it's simply a dumb idea.

Agreed. It's laughable. Dave Chappelle even parodied a similar concept (The Love Contract) on Chappelle's Show.

edit: the idea was actually called The Love Contract.

+1 for Andrews & Arnolds.

> Is Figure 8 an unconditional empirical CDF of inter-arrival times?

My understanding is that it's the inter-arrival times after some cleaning and resampling. If I've understood correctly, when they resampled the data, they did so uniformly between the neighbours of the points they omitted, which would actually make the data appear more like an exponential distribution.

> Especially considering its purpose. Maybe it would have been more accurate to say "there's a mixture of two Poissons: the bulk and the network disruption".

Could be. Could also follow a power law or a phase type distribution.

> But this isn't physics. We want to know how useful the approximation is, and whether there is a similarly tractable one with better predictive power.

It's worse, it's math :-) I take your point though, it all comes down to what you're trying to do. If inter-arrival times did follow an exponential distribution with parameter $\lambda$, then we'd have finite variance and I'd be pretty confident that I could build a performant predictive model. The presence of a heavy right tail makes me think otherwise.

It's definitely not a homogenous Poisson process, mainly because of the random changes to mining difficulty and propagation delays. There's a good paper here looking at block arrival times and fitting some different models - https://arxiv.org/pdf/1801.07447.pdf

To the programmer, developer or casual visitor looking at this and wondering whether it's worth the time and effort to dig into this, it is. Most of what's covered here can be understood with undergrad calculus, and will give you a solid basis for understanding and modelling random phenomena you may encounter in your studies, work or hobby.

Fun fact to get you started, Nakamoto suggested in the original Bitcoin paper that blocks would be added to the Bitcoin blockchain according to a homogenous Poisson process (spoiler alert: it's definitely not).

Regardless of whether the collection of the data was incidental or not, this is a huge breach of public trust given the assurances made by the Australian government.

For shame.

Disclaimer: I am one of the devs at Peergos.

You should definitely check out Peergos - https://peergos.org.

To point 3 - Protect what matters most - please do check out Peergos (https://peergos.org). We provide private and secure online storage that collects no metadata and is not dependent on DNS or TLS.

Disclaimer: I am one of the Peergos devs.

Disclaimer: I am one of the Peergos devs.

Yes, you should check out Peergos - https://peergos.org. Self-hosting details are on our GitHub page - https://github.com/Peergos/Peergos

I hear you. Here in the UK we have an unelected consultant to the Prime Minister who is pushing for a loosening of data privacy laws. The right to privacy is politicised to suit the agendas of politicians and big tech alike.

Long term, I do hope laws and regulation will catch up. I know some incredible people in the space and their work and commitment is inspiring. It's unsatisfying though to think that the effects will only be reactive and recourse provided after years of ongoing privacy invasion at mass scale. To me, that's where technology comes in and we should advocate and use products and solutions that respect our privacy (e.g. Qwant).

For what it's worth, I'm one of the developers of Peergos - https://peergos.org - a secure storage solution that puts user privacy and control of data first. We're currently in alpha and looking for users to test it out and give feedback. If it interests you at all, I would really appreciate your views on the product and what we're trying to create.

Equating privacy and privilege is not helpful. It is true that the privileged in our society wield more capability to enact protect and enact change for themselves and others in society, and privacy may not be top of mind when ranked against more immediate concerns such as those you have listed, but that doesn't change the fact that privacy is a universal human right and essential to our dignity and the functioning of society. It is something to be valued and upheld for everyone, not dismissed as a concern for the privileged alone.

+1 for mentioning Carissa Véliz. Her podcasts are really good as well - https://www.carissaveliz.com/podcasts.

It saddens me to read this sentiment. I agree there is a huge uphill battle to fight here to change the current situation, but there are a) plenty of people who value their privacy and are willing to make changes to the products and technologies they use in order to preserve their rights, and b) developers creating technology, tools and products that will protect your online privacy.

> Should there even be a contrived concept of property in the digital universe?

Absolutely. Property in law designates rights. Frequently multiple different types of rights are bundled and coexist. This enables the same physical property to be the subject of several and often competing interests e.g. ownership, possession, custody, freehold, leasehold, legal and equitable interests. Having a property right means being able to exclude others from that property to a greater or lesser extent. This may then be modified in different legal contexts but not radically. The statement holds true grosso modo. Online property rights are modelled on traditional property rights without need for more. The discussion of online property is normally about rights of transferring, managing etc. or rights in the manner of acquisition, dealing, disposal etc. Of course this refers to physical assets, but since property is rights and these are created and managed digitally it is online property ipso facto.

And I will reciprocate with this interesting paper on privacy in the context of war - https://www.cambridge.org/core/journals/ethics-and-internati...

Thanks for posting those links. I admit I haven't got around to reading Solove's work yet, but a friend gave a brief explanation of his taxonomy to me a while back. From memory, there's a key diagram covering activities that are affected by privacy like data collection, processing and dissemination. I'll follow those links and have a read.

To the author's opening sentence - I also feel the definition of privacy can be difficult to pin down. I tend to think about privacy as a necessary prerequisite in most contexts to being authentic and truthful - consider what you would say about your employer in a public form versus what you would say to your partner or friend. It gets more complicated in online spaces, particularly when encryption enters. As social creatures, we have been evolving the nature of our non-digital interactions for a much longer time and we shouldn't expect that we can simply design ways of interacting that preserve the complicated nuances of real-life social interaction. However, as more of our activities move online, we can and must do better.

The company I work for builds enterprise software, so the key question that has to be addressed is "does this solve the business problem?". Most of what I review are implementations of some form of standard supervised learning model that has been tweaked for performance at scale, but I also see unsupervised learning, causal modeling, optimisation and some statistical analyses. As such, the criteria changes depending on the particular problem and I'm afraid I can't give detailed examples. However, in the case of an implementation of a standard supervised learning model, some common criteria are:

1. Is the statement of the business problem well-defined with a clear outcome that can be measured? Does it change for different clients?

2. Where is the data sourced from? Who or what created the labels? Any known discrepancies or errors (systematic or random)? Is it standard across clients?

3. Is the model appropriate for a) the problem to be solved b) the data available for training and validation?

4. Is the model performant with regards to the specified performance metrics? What's the cost of a false positive/negative?

5. How often will the model be re-trained? What's the justification?

6. Has the model been validated on data that is out of sample (usually includes out of time and out of population)?

7. Have biases in the data been identified? What has been done to address this?

8. What assumptions have been made about the data? Have these been tested?

9. What second-order effects do you anticipate will result from putting this model into production? Will these affect the data being collected and used to re-train the model?

A lot of my job involves reviewing other people's models and their implementation including the code and the data to train the models. If the author or team has put together a mathematical description, that's usually a good sign that they've done things with a degree of consideration and capability. However, I do have to remind myself not to fall for the mistake of conflating mathematical proficiency with correspondence to a "correct" model of the real world. The circuit breaker for me is to test my thinking and assessment with someone else. We're all suckers for something.

[EDIT] Grammar.

I believe one of the biggest barriers to personal advancement is self-perception, in particular, the difficulty in imagining yourself in a role that is not your current one or some version of it within a company or industry hierarchy. For what it’s worth, I’ve managed to enlarge that self-perception and change jobs by a) asking good friends and professional colleagues for their honest views on what I’m good at and where my shortcomings are and b) networking outside my professional circle to understand how my role is perceived in terms of what constitutes success (personally and for a company) and how others succeed in non-engineering (e.g. sales, management) roles. You will probably be surprised at the answers and, I hope, see that there are many more options out there for you once you see yourself as more than just your job title.

So it would seem one can now effectively use Peergos as a front-end to manage identity and permissions on S3?

I suffered from mild bruxism about 10 years ago and have had several bouts of TMJD where I couldn’t close one side of my jaw. For me, the key has been poor posture induced by stress; these bouts coincide with heavy laptop and mobile phone use (neck angle forward and down). What fixed it for me was switching to a good desktop set-up whenever possible and self-treatment via Kelly Starrett’s Becoming A Supple Leopard (there is whole section in the second edition on neck and jaw). He has good general advice in this video as well - https://youtu.be/kfg_e6YG37U

I haven’t used the mouthguard now in probably 5 or more years.

rollulus gave a good summary of Laplace transforms and what they do. For some more context, they appear regularly in applied probability (e.g. finance, insurance, physical models including dams). A typical problem is dealing with sums of non-negative random variables. Let's say you want the distribution of n independent copies of a non-negative random variable with distribution function F. The hard way is the n-fold convolution or essentially evaluating an n-dimensional integral. The easy way is using the Laplace transform of F and simply raising it to the power of n.

The result isn't always invertible analytically, but you can almost always invert it numerically and this is why techniques like the one outlined in the paper are so important.

This is a fantastic post and I thoroughly recommend reading it and the 2019 paper that summarises all their work for several reasons:

1. Very clear exposition of previous work and their own.

2. Clear evaluation metrics.

3. They've even made it easy for you to replicate their work and results.

I think a lot of the features that the author is describing exist already on some decentralised apps like Mastodon. Yet surprisingly she never mentions the word 'decentralised.'

Some practices and advice that I gained from my time doing a PhD in mathematics:

1. Find a time of day to read and work on problems that works for you and make it interruption-free. For me it was up at 6AM and working until 9 or 10AM with no phone or laptop. If you can do longer or fit in another session, go for it.

2. I found that I process new material in the background, so either going to the gym or taking a long walk gave my mind the break and mental space to process what it had just ingested.

3. In mathematics, it's common to present the most terse, stripped-down version of a result which can rob it of the background and context. I found it was often helpful to find the author's previous work, PhD thesis or talks in order to understand how they got to their result.

4. Don't be afraid to get a little side-tracked or obsessed with something that's not directly related to what you're currently working on. Part of training to be a mathematician is learning the ability to hold seemingly unrelated concepts in your head for long periods of time until the connection becomes apparent. Learn to love difficult things!