Related papers: Estimating $\pi$ with a Coin
These lecture notes are intended to cover some introductory topics in stochastic simulation for scientific computing courses offered by the IT department at Uppsala University, as taught by the author. Basic concepts in probability theory…
A brief introduction to the technique of Monte Carlo simulations in statistical physics is presented. The topics covered include statistical ensembles random and pseudo random numbers, random sampling techniques, importance sampling, Markov…
Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant…
Analogue to the well-known Langevin Monte Carlo method, in this article we provide a method to sample from a target distribution \(\pi\) by simulating a solution of a stochastic differential equation. Hereby, the stochastic differential…
Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…
This tutorial paper introduces quantum approaches to Monte Carlo computation with applications in computational finance. We outline the basics of quantum computing using Grover's algorithm for unstructured search to build intuition. We then…
This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational…
The objective of Bayesian inference is often to infer, from data, a probability measure for a random variable that can be used as input for Monte Carlo simulation. When datasets for Bayesian inference are small, a principle challenge is…
The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of…
Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + \theta$, $\theta \in [-1/2,1/2]$, $\theta$ unknown but…
Comprehensive and physically consistent model of a tossed coin is presented in terms of geometric algebra. The model clearly shows that there is nothing elementary particle specific in the half-spin quantum mechanical formalism. It also…
We take a fresh look at the classical problem of runs in a sequence of i.i.d.\ coin tosses and derive a general identity/recursion which can be used to compute (joint) distributions of functionals of run types. This generalizes and unifies…
The present work addresses the question how sampling algorithms for commonly applied copula models can be adapted to account for quasi-random numbers. Besides sampling methods such as the conditional distribution method (based on a…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
We present a new method devised to overcome the intrinsic difficulties associated to the numerical simulations of the Tsallis statistics. We use a standard Metropolis Monte Carlo algorithm at a fictitious temperature T', combined with a…
The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…
With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…
In this paper we propose and analyse a method for estimating three quantities related to an Asian option: the fair price, the cumulative distribution function, and the probability density. The method involves preintegration with respect to…
It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…
According to a popular belief, the decimal digits of mathematical constants such as {\pi} behave like statistically independent random variables, each taking the values 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 with equal probability of 1/10. If…