Deep Research and Development

Markov Chain Monte Carlo (MCMC) is a technique for generating a sample from a distribution, and it works even if all you have is a non-normalized representation of the distribution. Why does a data scientist care about this? Well, in a Bayesian analysis a non-normalized form of the posterior distribution is super easy to come by, being just the product of likelihood and prior - so MCMC can be used to sample from (essentially simulate) a Bayesian posterior. In python one of the most widely used packages for doing exactly this is called PyMC . What is Markov chain Monte Carlo A Markov Chain is a sequence of RVs {X} each of which will have an observed value from the state space of possible values, {x}. A Markov Process is a sequence of such RVs where the distribution of the initial RV's value is specified (Π0) as well as a Transition Rule (P) which gives the probability to transition from one state to another, P(i,j)=P(Xn+1=xj|Xn=xi), for all pairs of states. Notice P doe...

Introduction We'll start our Python for Data Scientists series with NumPy , short for Numerical Python, which is the foundational package for scientific computing in Python. One of its primary purposes with regards to data analysis is as the primary container for data to be passed between algorithms. For numerical data, NumPy arrays are a much more efficient way of storing and manipulating data than the other built-in Python data structures. Also, libraries written in a lower-level language, such as C or Fortran, can operate on the data stored in a NumPy array without copying any data. Here are some of the things it provides: A fast and efficient multidimensional array object ndarray Functions for performing element-wise computations arrays Tools for reading and writing array-based data sets to disk Linear algebra operations, Fourier transform, and random number generation Tools for integrating connecting C, C++, and Fortran code to Python  Knowing Numpy is fundam...