If you have taken a statistics class it may have included stuff like basic measure theory. Lebesgue measures and integrals and their relations to other means of integration. If your course was math heavy (like mine was) it may have included Carathéodory's extension theorem and even basics of operator theory on Hilbert spaces, Fourier transforms etc. Most of this mathematical tooling would be devoted to a proof of one of the most important theorems on which most of statistics is based - central limit theorem (CLT).  Central limit theorem states that for a broad class of what we in math cal ..read more

As I child I've been raised as a catholic and I vividly remember what it was like to believe in God and all the divine entities. It does bring certain amount of comfort to our lives, removes loneliness, gives a broader sense to existence. At some point however I started questioning the things I was told and eventually became more of a deist and at this point pretty much an atheist. I don't claim to know the answer to life universe and everything (except that it is 42!), in fact although I much prefer rational and objectivist approach to reality, I believe science as we know is still barely scr ..read more

Back in a very distant past, perhaps over 2 billion years ago, a wonderful thing happened: a strand of nucleic acid found itself encapsulated in a little protein bubble, along with a few other ingredients sufficient for it to replicate. This in fact may have happened millions of times before, each time dying out after a few generations. But one such bubble that appeared that day in the primordial sea was going to survive, this was the one which was going to make it and launch an incredible evolutionary process lasting until this day. A process that managed to create incredibly complex beings i ..read more

Statisticians like to insist that correlation should not be confused with causation. Most of us intuitively understand this actually not a very subtle difference. We know that correlation is in many ways weaker than causal relationship. A causal relationship invokes some mechanics, some process by which one process influences another. A mere correlation simply means that two processes just happened to exhibit some relationship, perhaps by chance, perhaps influenced by yet another unobserved process, perhaps by an entire chain of unobserved and seemingly unrelated processes.  When we rely ..read more

For some reason, people love to be scared. People also love to spook other people, that gives them the sense of advantage, power. And in the hyper-stimulated era of social media and numerous dopamine shots per hour this dynamics takes on a completely new scale. It turns into a psychotic rumbling between complete and unquestionable excitement only to turn in minutes to fear mongering utter dystopia. This has been going on with Artificial Intelligence over the last decade and it became almost painfully absurd. Social media "influencers" ride this bipolar mania to their advantage while normal peo ..read more

I was raised in a rational family, with strong belief in science. When I got my masters degree a was pretty much convinced that we generally know everything about the world and that science is more or less a complete endeavor. By the time I got my PhD however, my confidence dropped quite significantly. Now almost 13 years after my PhD defense, my view is that science is actually a rather fragile thread we use to hold together and explain various mysteries in the world. And that is not to say science is not the right method - it is! But I now view science as any other social activity, being inf ..read more

In the modern era of computers and data science, there is a ton of things discussed that are of "statistical" nature. Data science essentially is glorified statistics with a computer, AI is deeply statistical at its very core, we use statistical analysis for pretty much everything from economy to biology. But what actually is it? What exactly does it mean that something is statistical?  The short story of statistics I don't want to get into the history of statistical studies, but rather take a birds eye view on the topic. Let's start with a basic fact: we live in a complex world which pro ..read more

It's time for another post in the Tesla FSD series, which is a part of a general self driving car debacle discussed in this blog since 2016 [1,2,3,4,5,6,7]. In summary, the thesis of this blog is that AI hasn't reached the necessary understanding of physical reality to become truly autonomous and hence the contemporary AI contraptions cannot be trusted with important decisions such as those risking human life in cars. In various posts I go into detail of why I think that is the case [1,2,3,4,5,6] and in others I propose various approaches to get out if this pickle [1,2,3]. In short my claim is ..read more

There is a never ending discussion, which very concisely can be summarized in this tweet below: And frankly any time I see similar exchanges (and I see a lot of them) I get mildly irritated. Let me get to the essence.  Computer analogy Computers have been undoubtably the shaping invention of the recent century and hence they have became a strong theme in our culture. Since the theory on which computers have been built is a branch of mathematics, by definition an abstract discipline, computers have also had a major impact on philosophy. We learned for example that everything we can write a ..read more

The pandemic has largely overwhelmed the news cycle over the past year and hence influencing and largely deflating the AI hype train. There were a few developments though which I'd consider significant. Some of them very well predicted by articles in this blog, and some surprising. Let's jump right in.  Million Robotaxis in wonderland Since it is 2021 after all, the most immediate AI flop is related to Tesla robotaxis or rather lack thereof. Elon Musk promised that Tesla would achieve L5 autonomy by the end of 2020 back in April 2019 when he needed to raise money [and reiterated in April ..read more