Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

The entropy score of an observed outcome that has been given a probability forecast p is defined to be -log p. If p is derived from a probability model and there is a background model for which the ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

French mathematician and astronomer, Pierre-Simon Laplace brought forth the first major treatise on probability that combined calculus and probability theory in 1812. A single roll of the dice can be ...

A mathematician who developed formulas to make random processes more predictable and helped to solve an iconic model of complex phenomena has won the 2024 Abel Prize, one of the field’s most coveted ...

This is a preview. Log in through your library . Abstract We obtain an asymptotic formula for the persistence probability in the positive real line of a random polynomial arising from evolutionary ...

The early success of physics comes mainly from solving direct or forward problems in which the physical state of a system can be described from a well-defined physical model and from governing ...