Basics of Statistics for Everyone 3700-AZ-FAK-ST

These classes are designed to familiarize students with the beauty and usefulness of statistics in every field of knowledge about the complex world.

A significant part (and definitely the most interesting one!) of the area of interest of modern empirical science is the zone of uncertainty and approximations. Thus, such fields of science as quantum physics and gas physics, meteorology, evolutionary biology and ecology, psychology and sociology, despite obvious differences, have much more in common than they divide - because they all describe reality not with certainty, but with uncertainty (i.e. probabilistically or otherwise). statistically speaking). And it is the formal science called statistics (which is part of applied mathematics) that makes these areas of empirical knowledge still a realm of exact science, and not just free extrascientific conjectures. The language of statistics gives us the ability to speak precisely about inaccuracies, to talk confidently about uncertainty. Statistics makes it possible for a modern man to try to understand precisely something that for millennia of human civilization eluded an objective view.
We will start our classes with a look at the general meaning of statistics,

both from the empirical side - in the context of the general axioms of science about the world, and from the formal side, i.e. from the foundations of modern applied mathematics (especially decision theory and game theory). We will also devote a few words here to the history of the alliance between mathematics and the study of empiricism (in this context, we will get acquainted with both the Vienna circle and the tradition of the Lvov-Warsaw school).

Next, we will look at statistics in a little more detail - especially in the context of its elementary division into description and inference.

As part of the statistical description, we will try to understand both statistical approximations (such as the arithmetic mean) and the error measures of these approximations (such as entropy or variance). Next, we will see how the introduction of successive properties to the description of the world can reduce the entropy of the obtained image. We will call such a phenomenon a statistical dependence (correlation) between the property of the world we are interested in (which we will call the dependent variable) and the auxiliary properties (independent variables). By the way, we will note that correlation does not necessarily mean cause and effect.

Finally, as part of statistical inference, we will deal with the description of a certain whole - a certain area of reality (called the universe or population) based on the description of a sample taken from it. We will note here that a large sample does not guarantee correct conclusions.

We will end our classes with a review of errors in the applicability of both statistics and any mathematical formalization to describe the empirical world.