Jingbiao's Blog

「Hinc lucem et pocula sacra」

3M1 Mathematical Methods Tripos Revision

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \newcommand{\norm}[1]{\lVert #1 \rVert} \) Linear Algebra Hermitian Conjugate Transpose: \( M^H = \overline{M...

Posted by Jingbiao on April 10, 2021, 1 minute to read

3F8 Inference Tripos Revision

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \) Algorithms MLE Maximum Likelihood Estimation of parameters: Given data $ y=\{ y_i \}$ and parameter $\theta$, t...

Posted by Jingbiao on April 10, 2021, 3 minutes to read

3F7 Information theory Tripos Revision

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \) Full notes can be viewed over here: rendered version and LaTex Source Code Entropy Calculation of entropy, joint...

Posted by Jingbiao on April 10, 2021, 3 minutes to read

3F4 Data Transmission Tripos Revision

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \) Finding Orthonormal Basis and optimal detection Finding the orthonormal basis for a group of waveform Represent...

Posted by Jingbiao on April 10, 2021, 4 minutes to read

3F3 Statistical Signal Processing Tripos Revision

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \) Full notes can be viewed over here: rendered version and LaTex Source Code Markov Chain Proof of Markov Property...

Posted by Jingbiao on April 10, 2021, 2 minutes to read

3F1 Signals ad Systems Tripos Revision

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \) Transfer Function for discrete system: For a system to have a transfer function, it has to be linear and time...

Posted by Jingbiao on April 10, 2021, 6 minutes to read

3E3 Risk Management Tripos Revision

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \) Markov Chain State Transition Matrix Stationary distribution Properties: Classes: a set of states c...

Posted by Jingbiao on April 10, 2021, 4 minutes to read

3G5 Biomaterial Tripos Revision

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \) Definition/Conceptual of Medical Devices Biocompatibility In terms of bio-safety: The medical device does not cau...

Posted by Jingbiao on April 9, 2021, 6 minutes to read

3G4 Medical imaging Tripos Revision

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \) Medical Imaging Ultrasonic Scan The ultrasound machine is calibrated with a constant speed. If speed mismatch, the...

Posted by Jingbiao on April 9, 2021, 2 minutes to read

Logistic Classification Comparing ML/MAP/Bayesian approches

With PCA and logistic regression

\( \require{amstext} \require{amsmath} \require{amssymb} \require{amsfonts} \newcommand{\eg}{\textit{e}.\textit{g}.} \newcommand{\xb}{\mathbf{x}} \newcommand{\yb}{\mathbf{y}} \newcommand{\xbtn}{\ti...

Posted by Jingbiao on March 14, 2021, 3 minutes to read