Updating probabilities with data and moments

What are their chances of going all the way, if they win their first game of the playoffs this Friday? I have a chance to apply Bayesian probability theory!My childhood and young adulthood consisted of them repeatedly snatching defeat from the jaws of victory.In the process, we will be develop sharper tail bounds than the ones based on the inequalities of Markov and Chebychev.Join the Quantcademy private membership portal that caters to the rapidly-growing retail quant trader community.Read a rigorous yet accessible introduction to the main concepts of probability theory, such as random variables and random vectors, expected value, variance, correlation, conditional probability and conditional expectation.Explore this compendium of common probability distributions, including the binomial, Poisson, uniform, exponential and normal distributions; find step-by-step derivations of the properties of the main probability distributions.One of the key modern areas is that of Bayesian Statistics.

This paper describes a Bayesian statistical model for estimating flood frequency by combining uncertain annual maximum (AMAX) data from a river gauge with estimates of flood peak discharge from various historic sources that predate the period of instrument records.

This chapter provides some general methods for working with sums of random variables, whether discrete or continuous.

We will start with the continuous analog of the convolution formula for the distribution of a sum of two independent discrete random variables.

It refers to a controversial idea of epistemological probability theory: the method of maximum entropy, that was popularised and (arguably) invented by Jaynes.

This principle states that, when choosing probabilities on a discrete hypothesis space, subject to constraints on the probabilities (e.g.

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