The two most popular Markov chain Monte Carlo sampling algorithms are Gibbs sampling and Metropolis Hastings. These algorithms produce Markov chains. Numbers inside a Markov chain are dependent on only the previous number. In the context of sampling, we check the probability of the proposed value based on only the probability of the current value,… Continue reading Introduction to Bayesian Statistics, Part 3
Mathematical modeling is a relatively new field. You may be more aware of a subfield of biology called bioinformatics or computational biology. These tend to deal with larger data sets, studying them using more algorithmic methods. Computational biology also refers to mathematical biology, or an even mixture of mathematics and computer science as applied to… Continue reading Why do we need mathematical modeling in biology?
Games of chance are often people’s first exposure to statistics. Settlers of Catan is a game that revolves around the probability distribution of two independent 6-sided die rolls. The game consists of hexagons with one of four possible resources available. These hexagons are normally in a random configuration. Each hexagon receives a random number token.… Continue reading Random Chance in Settlers of Catan
Bayesian vs frequentist statistics Source: Er, about those other approaches, hold off until a balanced appraisal is in
How can we identify a good mathematical model? Over focusing on one aspect of modeling (fitting, inference) may not be the best approach. Here are 6 qualities that defines a good model: Reflects data accurately Not overly complex Has predictive power Consistent with general knowledge of the system Can be studied mathematically Can be simulated… Continue reading What makes a model good?
I am replacing a small Radeon 5450 graphics card with a CUDA capable GTX 1050 Ti that I can use for GPU computing. Please ignore my terrible cable management. I will fix it one day... Overview of the steps mentioned here: Set up work area Remove screws around installation area Remove the card and identify the… Continue reading How To Install a Graphics Card
As I discussed in my post on sensitive parameters, optimizing parameter values may sometimes be difficult for reasons other than a poorly defined model. Initial parameter values have a high impact on the ability of the optimizer to find a solution, unless you are using a global optimizer. The solution is iterative curve fitting. What… Continue reading Iterative curve fitting of biological systems
There are two broad categories of models: statistical and mathematical. Statistical Models Statistical models are a subset of mathematical models. I am dividing them into two broad categories, although it is a fairly arbitrary distinction. Models to Identify Relationships Statistical models may be used to find relationships between inputs and outputs of a system. These… Continue reading Different Types of Models: Mathematical and Statistical
Programming elements that are used to perform basic mathematical calculations include: Arrays Matrices Equations or Simple functions Math functions See my previous post about the first two here. This post will deal with the latter two. Equations or Simple functions The simplest problem to be solved via programming would be the solution to a single… Continue reading Basic Mathematical Biology Programming Part II
Programming elements that are used to perform basic mathematical calculations include: Arrays Matrices Equations or Simple functions Math functions This post will deal with the first two. Arrays Sets are common in mathematical biology : response values, independent values, time units, gene or protein names. These sets can be expressed as arrays. The two most… Continue reading Basic Mathematical Biology Programming Part I