A frequentist interpretation of Bayesian posterior — Assume we have observed N independent and identically distributed (iid) samples X = (x1, … , xN) from an unknown distribution q. A typical question in statistics is “what does the set of samples X tell us about the distribution q?”. Parametric statistical methods assume that q belongs to a…

A theoretical and empirical investigation of the additional information the h-index contains and cannot be found in the total number of citations — To compare researchers with each other¹, we need to have a measure that can represent how influential and successful they have been by a single number. One way to do so is to look at how many times their articles have been cited and count their total number of citations…

A note on how our lives would look like if we could perceive joy only by our errors in predicting rewards. — WARNING: This article is not supposed to be scientifically precise. Rather, it is a playful discussion about an imaginary scenario inspired by scientific findings Dopamine, enjoyment, and reward prediction error It is generally believed that dopamine is what makes us feel happy and pleased, and there is scientific evidence for the release of dopamine at the…

A proof of the existence of the optimal policy for finite MDPs — In a finite Markov Decision Process (MDP), the optimal policy is defined as a policy that maximizes the value of all states at the same time¹. In other words, if an optimal policy exists, then the policy that maximizes the value of state s is the same as the policy…

An introduction to and a comparison between Bayesian and frequentist methods for hypothesis testing — A lady claims that she can find out whether tea or milk is added first to a cup of milk tea, only by tasting it. How can we evaluate her claim? …

In the absence of a distance, “close” and “far” are meaningless. To define these notions over a set of abstract mathematical objects, we need to be able to measure the distance between each pair of them. …

What do we know about the correlation of two random variables given their correlations with a 3rd one? — “X₂ and X₃ both increase when X₁ increases”; if there is a deterministic relation between these variables, then such a statement logically implies that “X₂ increases also when X₃ increases”. …