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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

By : Ranja Sarkar, Dr. Ranja Sarkar
4.1 (7)
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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

4.1 (7)
By: Ranja Sarkar, Dr. Ranja Sarkar

Overview of this book

Mathematical modeling is the art of transforming a business problem into a well-defined mathematical formulation. Its emphasis on interpretability is particularly crucial when deploying a model to support high-stake decisions in sensitive sectors like pharmaceuticals and healthcare. Through this book, you’ll gain a firm grasp of the foundational mathematics underpinning various machine learning algorithms. Equipped with this knowledge, you can modify algorithms to suit your business problem. Starting with the basic theory and concepts of mathematical modeling, you’ll explore an array of mathematical tools that will empower you to extract insights and understand the data better, which in turn will aid in making optimal, data-driven decisions. The book allows you to explore mathematical optimization and its wide range of applications, and concludes by highlighting the synergetic value derived from blending mathematical models with machine learning. Ultimately, you’ll be able to apply everything you’ve learned to choose the most fitting methodologies for the business problems you encounter.
Table of Contents (16 chapters)
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1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

Markov Chain Monte Carlo

MCMC is a method of random sampling from a target population/distribution defined by high-dimensional probability definition. It is a large-scale statistical method that draws samples randomly from a complex probabilistic space to approximate the distribution of attributes over a range of future states. It helps gauge the distribution of a future outcome and the sample averages help approximate expectations. A Markov chain is a graph of states over which a sampling algorithm takes a random walk.

The most known MCMC algorithm is perhaps Gibbs sampling. The algorithms are nothing but different methodologies for constructing the Markov chain. The most general MCMC algorithm is Metropolis-Hastings and has flexibility in many ways. These two algorithms will be discussed in the next subsections.

Gibbs sampling algorithm

In Gibbs sampling, the probability of the next sample in the Markov chain is calculated as the conditional probability of the prior sample...

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