### Basics of Integration using Monte Carlo

Recently, someone asked me about Monte Carlo. So, I thought I should write this post to provide a basic introduction of performing integration using Monte Carlo. "Why integration?", you asked. Well, this is because integration is one of the main operations done in computing the posterior probability distributions used in machine learning and probabilistic filtering (e.g. Bayes filter). For example, consider the typical posterior probability expression in the Bayes filtering context, \(p(x_{t} \mid y_{1:t})\), i.e. the probability of hidden state \(x_{t}\) given the observed sequence of measurements up to the current time point \(y_{1:t}\), $$p(x_{t} \mid y_{1:t}) = \frac{p(y_{t} \mid x_{t}) p(x_{t} \mid y_{1:t-1})}{p(y_{t} \mid y_{1:t-1})}$$ The \(p(x_{t} \mid y_{1:t-1})\) is of particular interest. It can be seen as the prediction of \(x_{t}\) from previous observations \(y_{1:t-1}\) and can be expressed as $$p(x_{t} \mid y_{1:t-1}) = \int p(x_{t} \mid x_{t-1}) p(x_{t-1}

hi,, what about ubuntu 12.04? can i use this way?

ReplyDeleteFor 12.04, everything's the same. But you HAVE to use Oibaf's PPA instead of mine.

Delete$ dpkg --list | grep vdpau

ReplyDeleteii libvdpau1:amd64 0.4.1-8 amd64 Video Decode and Presentation API for Unix (libraries)

ii libvdpau1-gallium-drivers:amd64 9.1.3-7ubuntu0.3ppa1~raring1 amd64 VDPAU Gallium3D video acceleration drivers

ii vdpauinfo 0.0.6-1 amd64 Video Decode and Presentation API for Unix (vdpauinfo utility)

$ uname -a; cat /etc/lsb-release

Linux phong 3.10.10-031010-generic #201308291422 SMP Thu Aug 29 18:24:39 UTC 2013 x86_64 x86_64 x86_64 GNU/Linux

DISTRIB_ID=Ubuntu

DISTRIB_RELEASE=13.04

DISTRIB_CODENAME=raring

DISTRIB_DESCRIPTION="Ubuntu 13.04"

$ dmesg|grep VERDE

[ 14.727922] [drm] initializing kernel modesetting (VERDE 0x1002:0x683F 0x1043:0x0459).

[ 15.149522] [drm] Loading VERDE Microcode

$ vdpauinfo

display: :0 screen: 0

Failed to open VDPAU backend libvdpau_nvidia.so: cannot open shared object file: No such file or directory

Error creating VDPAU device: 1

What am I getting wrong here?

The backend selection for the radeonsi vdpau drivers in mesa 9.1.3.x is most likely not implemented properly. I recommend using packages from Oibaf's PPA.

Delete