Blog (mostly math)

Hypothesis Testing

Updated: 21/10/25 Ref: “Introduction to Mathematical Statistics” by Hogg, McKean, Craig. “Statistics for Mathematicians” by Panaretos. [Hypothesis Testing] Consider a random variable ${ X }$ with density ${ f(x; \theta) , }$ ${ \theta \in \Omega . }$ Suppose we think ${ \theta \in \Omega _0 }$ or ${ \theta \in \Omega _1 , }$ where ${ \... Read more

Gaussian Errors

Consider the plane ${ \mathbb{R} ^2 . }$ Consider the origin ${ (0, 0) . }$ Consider the natural error generating process: The random error vector is ${ \mathcal{E} = (\varepsilon _1, \varepsilon _2) . }$ The components ${ \varepsilon _1, \varepsilon _2 }$ are independent and identically distributed. The distribution of ${ \mathcal{E} }$... Read more

Kernel Density Estimators

Ref: “Data Analysis for Social Scientists” by Duflo, Ellison. Lec-5. Link to the lecture: Link. Scikit-learn’s Density estimation documentation. Link to the page: Link. “Introduction to Mathematical Statistics” by Hogg, McKean, Craig. “Introduction to Nonparametric Estimation” by Tsybakov. “Smoothing methods in Statistics” by Simonoff... Read more

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Life in North Korea. Andhra Pradesh seems to be moving in this direction. They remember but they are not coming out. Read more

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Speculation. How did we learn as infants? We learn by a combination of: innate curiosity, innate drives, mimicking the people around us. We do the same as adults at a subconscious level. Eg: The concept of an anthropomorphic God can be a useful mental device. Eg: Bhakti for Krishna. Namely, love and devotion for Krishna. Surrenderin... Read more