Bayesian inference | Computational statistics
Integrated nested Laplace approximations (INLA) is a method for approximate Bayesian inference based on Laplace's method. It is designed for a class of models called latent Gaussian models (LGMs), for which it can be a fast and accurate alternative for Markov chain Monte Carlo methods to compute posterior marginal distributions. Due to its relative speed even with large data sets for certain problems and models, INLA has been a popular inference method in applied statistics, in particular spatial statistics, ecology, and epidemiology. It is also possible to combine INLA with a finite element method solution of a stochastic partial differential equation to study e.g. spatial point processes and species distribution models. The INLA method is implemented in the R-INLA R package. (Wikipedia).
C81 More complex Laplace tranformations
Building on the initial set of Laplace transforms to more complex expressions.
From playlist Differential Equations
C75 Introduction to the Laplace Transform
Another method of solving differential equations is by firs transforming the equation using the Laplace transform. It is a set of instructions, just like differential and integration. In fact, a function is multiplied by e to the power negative s times t and the improper integral from ze
From playlist Differential Equations
Differential Equations | Laplace Transform of a Piecewise Function
We find the Laplace transform of a piecewise function using the unit step function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Laplace Transform
Laplace Transformation: t*e^-at
Englische Version: Heute besprechen wir die Laplace Transformation einer Zeiteinheit t multipliziert mit der Exponentialfunktion.
From playlist Laplace Transformation
Discrete Laplace Equation | Lecture 62 | Numerical Methods for Engineers
Derivation of the discrete Laplace equation using the central difference approximations for the partial derivatives. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscr
From playlist Numerical Methods for Engineers
Introduction to Laplace transforms
Free ebook https://bookboon.com/en/partial-differential-equations-ebook A basic introduction to the Laplace transform. We define it and show how to calculate Laplace transforms from the definition. We also discuss inverse transforms and how to use a table of transforms. Such ideas have
From playlist Partial differential equations
Differential Equations | The Laplace Transform of a Derivative
We establish a formula involving the Laplace transform of the derivative of a function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Laplace Transform
Macdonald processes II - Alexei Borodin
Alexei Borodin Massachussetts Institute of Technology October 9, 2013 Our goal is to explain how certain basic representation theoretic ideas and constructions encapsulated in the form of Macdonald processes lead to nontrivial asymptotic results in various `integrable'; probabilistic probl
From playlist Mathematics
Solve differential equation with laplace transform, example 2
inverse laplace transform, inverse laplace transform example, blakcpenredpen
From playlist Solve Differential Equations with Laplace Transform (Nagle's Sect7.5)
Monte Carlo Geometry Processing
Project Page: http://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/index.html
From playlist Research
C80 Solving a linear DE with Laplace transformations
Showing how to solve a linear differential equation by way of the Laplace and inverse Laplace transforms. The Laplace transform changes a linear differential equation into an algebraical equation that can be solved with ease. It remains to do the inverse Laplace transform to calculate th
From playlist Differential Equations
Live CEOing Ep 279: Calculus & Algebra Features for WL 12.1
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Calculus & Algebra Features for WL 12.1.
From playlist Behind the Scenes in Real-Life Software Design
Anthony Nouy: Adaptive low-rank approximations for stochastic and parametric equations [...]
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Numerical Analysis and Scientific Computing
Probabilistic methods in statistical physics for extreme statistics... - 18 September 2018
http://crm.sns.it/event/420/ Probabilistic methods in statistical physics for extreme statistics and rare events Partially supported by UFI (Université Franco-Italienne) In this first introductory workshop, we will present recent advances in analysis, probability of rare events, search p
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Jeff Calder: "Discrete regularity for graph Laplacians"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop IV: Stochastic Analysis Related to Hamilton-Jacobi PDEs "Discrete regularity for graph Laplacians" Jeff Calder - University of Minnesota, Twin Cities Abstract: The spectrum of the graph Laplacian plays an important role in data science,
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Antonietta Mira: Big data for health: a Bayesian spatio-temporal analysis for predicting ...
Abstract: The term ‘Public Access Defibrillation’ (PAD) is referred to programs based on the placement of Automated External Defibrillators (AED) in key locations along cities’ territory together with the development of a training plan for users (first responders). PAD programs are conside
From playlist Probability and Statistics
Sushanta Dattagupta - Dissipative quantum systems (5)
PROGRAM: BANGALORE SCHOOL ON STATISTICAL PHYSICS - V DATES: Monday 31 Mar, 2014 - Saturday 12 Apr, 2014 VENUE: Raman Research Institute, Bangalore PROGRAM LINK: http://www.icts.res.in/program/BSSP2014 This advanced level school was started in 2010 at the Raman Research Institute, Banga
From playlist Bangalore School on Statistical Physics - V
Angela Kunoth: 25+ Years of Wavelets for PDEs
Abstract: Ingrid Daubechies' construction of orthonormal wavelet bases with compact support published in 1988 started a general interest to employ these functions also for the numerical solution of partial differential equations (PDEs). Concentrating on linear elliptic and parabolic PDEs,
From playlist Numerical Analysis and Scientific Computing
Julie Rowlett: A Polyakov formula for sectors
Abstract: Polyakov's formula expresses a difference of zeta-regularized determinants of Laplace operators, an anomaly of global quantities, in terms of simple local quantities. Such a formula is well known in the case of closed surfaces (Osgood, Philips, & Sarnak 1988) and surfaces with sm
From playlist Women at CIRM
3 Properties of Laplace Transforms: Linearity, Existence, and Inverses
The Laplace Transform has several nice properties that we describe in this video: 1) Linearity. The Laplace Transform of a linear combination is a linear combination of Laplace Transforms. This will be very useful when applied to linear differential equations 2) Existence. When functions
From playlist Laplace Transforms and Solving ODEs