Speech & Language Blog

Bayesian parameter estimation The previous post  introduced the basic concept of Bayesian parameter estimation. If you haven't read it, please check that post before this one. When Bayesian estimation is not simple There are two cases when Bayesian estimation is tractable. The simplest is when a prior distribution is a conjugate prior. Computing the normalising constant of a single or low-dimensional parameter of \( \theta \) is also tractable with a grid approximation. In this post, I will stick to the Pikachu encounter rate example like in the previous post too. Imagine we have analysed 10 routes, each with its own Pikachu encounter rate: \[ \boldsymbol{\theta} = [\theta_1, \dots, \theta_{10}], \quad \theta_k \in [0, 1] \] On each route \( k \), we observed \( n_k \) Pikachu out of \( N_k \) Pokemon, so the likelihood is a product of Binomials, \( P(D|\boldsymbol{\theta}) \propto \prod_{k=1}^{10} \theta_...

Acoustic Signal I had a hard time understanding basics of digital signal processing. I think that the reason was the fact that sounds were not visible. There is a way to "see" the sound, though. This YouTube video for example demonstrates that special cameras make the sound visible.   The sound is the virbation of particles in the air. Something invisible surrounding us rapidly moves back and forth. And our ears can hear this movement. I am writing this post to cover very basics of digital signal processing that I was very slow to understand. I will write concepts of Analogue-to-Digital conversion, sampling and Nyquist frequency. Analogue vs Digital Apart from the sound not usually visible to us, I think that I initially mixed up the concept of the digital signal with the analogue signal. I was still new to the idea that computers represent everything in discrete numbers. Two important things: An anal...