Resampling techniques
Imagine that you have a weighted sample of size and you want to obtain another sample of the same size, consisting of the same elements. One way to do that is by doing a miltinomial sampling, where we sample each point (or particle if we deal with particle filters) proportional to its weight. That way,…
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Particle Filters (Part II)
As we saw from the previous blog, the SIS algorithm is degenerate, which simply means that after some observations, relatively small in number, one of the particles achieves a weight close to . A solution has been proposed to sample the particles at each time observation. SIR algorithm The SIR (sequential importance resampling) algorithm can…
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Particle Filters (Part I)
Remember our hidden Markov model for the rabbits and foxes from the previous blog? Well, let us recap quickly. It was a hidden Markov process, the state of which consisted of the number of rabbits and foxes at each integer time step, that we could not observe, but only had access to noisy observations of…
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Markov Chains and Hidden Models
Markov Chains Markov chains are a fairly common, and relatively simple, way to statistically model random processes. They have been used in many different domains, ranging from text generation to financial modeling. Overall, Markov Chains are conceptually quite intuitive, and are very accessible in that they can be implemented without the use of any advanced…
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Linux
Linux is a family of open-source Unix-like operating systems. It is an OS just like Windows, iOS, and Mac OS. In fact, one of the most popular platforms on the planet, Android, is powered by a Linux kernel (more on that later) . An operating system is software that manages all of the hardware resources…
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Network Modelling
Networks and network data analysis have seen one of the largest growth in quantitative sciences recently. While their origins stem mostly from social connections, their applications are more wide spread. One particular example is creating a map of the brain and trying to capture connectivity of different parts of it. Therefore, we introduce networks here:…
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Jacob is Mr. Cool!
I like Mr. Cool posts.