almoststochastic.com
almost stochastic: Batch MLE for the GARCH(1,1) model
http://www.almoststochastic.com/2014/06/batch-mle-for-garch11-model.html
A blog on probability. Batch MLE for the GARCH(1,1) model. In this post, we derive the batch MLE procedure for the GARCH model in a more principled way than the last GARCH post. The derivation presented here is simple and concise. There are some stability constraints for this model: begin{align*} alpha beta leq 1, , , alpha geq 0 , , beta geq 0 , , c 0 end{align*}. Batch MLE for GARCH). Read $x {1:n}$ and initialize $ theta 1$. Simulate $v {1:n} { theta j}$:. Batch MLE for the GARCH(1,1) model.
almoststochastic.com
almost stochastic: August 2013
http://www.almoststochastic.com/2013_08_01_archive.html
A blog on probability. In this post, we review the sequential importance sampling-resampling for state space models. These algorithms are also known as particle filters. We give a derivation of these filters and their application to the general state space models. Labels: monte carlo methods. Math ∩ Programming. There are some enterprises in which a careful disorderliness is the true method." (Moby Dick, chapter 82). By Ömer Deniz Akyıldız.
almoststochastic.com
almost stochastic: Probabilistic models of nonnegative matrix factorisation
http://www.almoststochastic.com/2014/07/probabilistic-models-of-nonnegative.html
A blog on probability. Probabilistic models of nonnegative matrix factorisation. I wrote this post last year. I thought it is good to publish this here. Here, we give a brief review of probabilistic models of nonnegative matrix factorisation (NMF). We mainly list the papers which are important to gain intuition and sketch the main ideas without too much mathematical detail. Probabilistic models of nonnegative matrix factorization. 5(2):111–126, June 1994. 401(6755):788–791, October 1999. 5] C Fevotte and...
almoststochastic.com
almost stochastic: Sequential importance sampling-resampling
http://www.almoststochastic.com/2013/08/sequential-importance-sampling.html
A blog on probability. In this post, we review the sequential importance sampling-resampling for state space models. These algorithms are also known as particle filters. We give a derivation of these filters and their application to the general state space models. In this previous post. As we will use the sequential importance sampling (SIS) algorithms for hidden Markov models (HMMs), we define them in a nutshell. Note that by an HMM, we mean a general state-space model. At time $n = 1$. Approximate the ...
almoststochastic.com
almost stochastic: January 2014
http://www.almoststochastic.com/2014_01_01_archive.html
A blog on probability. Convergence of gradient descent algorithms. In this post, I review the convergence proofs of gradient algorithms. Our main reference is: Leon Bottou, Online learning and stochastic approximations. I rewrite the proofs described in Bottous paper but with more details about the points which are subtle to me. I tried to write the proofs as clear as possible so as to make them accessible to everyone. Convergence of gradient descent algorithms. Math ∩ Programming. By Ömer Deniz Akyıldız.
almoststochastic.com
almost stochastic: November 2013
http://www.almoststochastic.com/2013_11_01_archive.html
A blog on probability. Fatou's lemma and monotone convergence theorem. In this post, we deduce Fatous lemma and monotone convergence theorem (MCT) from each other. Young's, Hölder's and Minkowski's Inequalities. In this post, we prove Youngs, Holders and Minkowskis inequalities with full details. We prove Hölders inequality using Youngs inequality. Then we prove Minkowskis inequality by using Hölder. Fatous lemma and monotone convergence theorem. Youngs, Hölders and Minkowskis Inequalities.
christofides.wordpress.com
Δημήτρης Χριστοφίδης | Αποδείξεις από το βιβλίο
https://christofides.wordpress.com/author/demetres
Αποδείξεις από το βιβλίο. Ιστολόγιο μαθηματικών του Δημήτρη Χριστοφίδη. Author Archives: Δημήτρης Χριστοφίδης. Course Leader in Mathematics at UCLan Cyprus. Σεπτεμβρίου 5, 2014. Οι ερωτήσεις που μας απασχολούν στην ακρότατη συνολοθεωρία (extremal set theory) είναι του πιο κάτω τύπου: Έχουμε ένα, συνήθως πεπερασμένο, σύνολο . Έχουμε επίσης κάποια υποσύνολα του τα οποία ικανοποιούν κάποιες ιδιότητες. Συνήθως οι ιδιότητες που ικανοποιούν έχουν να κάνουν … Συνέχεια ανάγνωσης →. 05D05 - Extremal Set Theory.
coloquiooleis.wordpress.com
Pablo Lessa | Coloquio Oleis
https://coloquiooleis.wordpress.com/author/pablolessa
Los seguidores de Manolo. Que m* es esto? Problema de la Semana. Notas de Caminatas al azar. On Miércoles 24, junio, 2015. Hace poco tuve la suerte de dar un cursito en una escuela para estudiantes de grado en la universidad Notre Dame (Indiana, EEUU). Escribo este artículo para divulgar las notas (en inglés) que preparé para el curso que están disponibles acá. Aprovecho también para dar una idea de que se trató el asunto. Comenzamos con el Teorema de Pòlya que dice que una caminata al azar simple en.
mathblog.brettwitty.net
How to construct finite fields | BrettW's Mathematical Musings
http://mathblog.brettwitty.net/2011/01/how-to-construct-finite-fields
BrettW's Mathematical Musings. Algebra, combinatorics and algorithms – oh my! How to construct finite fields. On January 24, 2011. As a primer to some of the finite fields stuff I’ve been talking about (and will talk about a lot more), I thought it’d be nice if we had a few concrete examples to play with. Let’s go! So let’s get some ground rules set:. Abelian groups will typically be written with addition. As the operator. General groups will use multiplication. Will always be a prime. A finite field on.
