The post explains how to compute entries of the inverse of a sparse symmetric positive definite matrix that correspond to the non-zero elements of the original matrix. It also discusses the motivation behind computing certain elem...
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The post is about building a block sparse matrix in Eigen using C++. The author explains the process and challenges of building the matrix and provides code examples. The post is not an interview and requires knowledge of C++, Eig...
The text discusses the Laplace approximation, sparse autodiff, and manipulating the jaxpr intermediate representation to make logistic regression produce autodiff code. It also compares the Laplace approximation to MCMC and discus...
The text discusses diffusion models and their application in sampling from arbitrary distributions. It explains the concept of measure transport and its relation to normalizing flows. It also delves into the use of inverse problem...
The text discusses the theory and practical applications of Markovian Gaussian processes, focusing on the art of fitting Gaussian process models and the use of the Markov property and efficient sparse matrix computations to reduce...
The text discusses the author's journey into sparse matrices and the challenges faced in implementing the sparse Cholesky factorisation in a JAX-traceable way. The author explains the limitations of JAX and the control flow constr...
The text discusses the Markov chain Monte Carlo (MCMC) algorithm and the impact of having the wrong acceptance probability. It explores the consequences of using an approximate acceptance probability instead of the correct one, an...
The text discusses the example of Robins and Ritov, focusing on the Bayesian and the Ancillary Coin. It explores the problem, introduces a version that does not trigger the counterexample, and discusses the challenges in construct...
The text discusses Gaussian processes and the process of defining Gaussian processes. It explains the need to understand approximation properties of a certain class of GPs and the process of computing Penalised Complexity (PC) pri...
Eliza and Mark conducted a study on aged Barbary macaques to replicate a previous study's findings. They found that the monkeys did not lose interest in novel stimuli as they aged, contradicting the previous study's results. They ...
The text discusses the concept of penalised complexity priors in the context of setting prior distributions. It explains the idea of flexibility parameters and how to use them to penalise complexity in models. The author provides ...
The text discusses the importance of importance sampling in estimating expectations of a target probability distribution. It explains the use of Monte Carlo to estimate the second integral and the importance sampling estimator. It...
The text is part six of an ongoing series on making sparse linear algebra differentiable in JAX. It discusses the implementation of differentiation rules for JAX primitives and the Jacobian-vector product. The author also talks ab...
The text is part five of a series on implementing differentiable sparse linear algebra in JAX. It discusses the process of adding a primitive to JAX, including reading the docs, implementing a call with abstract types, implementin...
The text is the fourth post in a series where the author tries to implement autodiffable sparse matrices into JAX to speed up some model classes in PyMC. The author outlines the problem, works through a basic python implementation...
The text is part three of a series of posts aiming to look at how sparse Cholesky factorisations work, how JAX works, and how to marry the two with the ultimate aim of putting a bit of sparse matrix support into PyMC. The author d...
The text is about the Cholesky factorisation of a symmetric positive definite matrix. It explains the algorithm for constructing the Cholesky factorisation and discusses the sparsity structure of the Cholesky factor. It also cover...
The text discusses the author's project to implement models inside Stan, focusing on Bayesian models and using sparse linear algebra to make things fast and scalable. The author is motivated by the lack of implementation of lesson...
The text discusses the challenges of comparing computational methods in statistics, particularly in the context of simulation studies. The author shares their experiences in numerical analysis and statistics, highlighting the comp...
The text discusses the dependence of sparsity priors on the design, the implications of priors on the one- and two-dimensional quantities of interest, and the need for design dependence in Gaussian processes. It also touches on th...