Understanding Statistical Models and Mathematical Models from Pluralsight

This course covers important techniques from both mathematical and statistical modeling, including the use of ordinary differential equations to model deterministic systems, classic local search and simulated annealing to explore large search spaces.

Data science and data modeling are fast emerging as crucial capabilities that every enterprise and every technologist and it us important to choose the type of model most appropriate to your use-case. In this course, Understanding Statistical Models and Mathematical Models, you will gain the ability to differentiate between mathematical models and statistical models and pick the right type of model for your scenario.

First, you will learn the important characteristics of mathematical and statistical models and their applications. Next, you will discover how classic mathematical models find wide applicability in solving differential equations and modeling deterministic systems.

Then, you will also learn how statistical models are great for modeling systems with randomness, using business-based use-cases from risk management, and the use of Monte Carlo simulations. Finally, you will round out your knowledge performing hypothesis testing using T-tests and Z-tests on real-world data.

When you’re finished with this course, you will have the skills and knowledge to use powerful techniques from both mathematical and statistical modeling, including solving simple ordinary differential equations, the use of simulated annealing and classic hill climbing, as well as hypothesis testing and statistical tests such as the T-test.

What's inside

Syllabus

Course Overview

Understanding Statistical and Mathematical Models

Case Studies on Statistical and Mathematical Models

Applying Mathematical Models in R

Applying Statistical Models in R

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Suitable for beginners who need to distinguish between mathematical and statistical models and pick the right one for their use-case

Appropriate for students seeking to explore real-world applications of mathematical and statistical models, like risk management simulations

Well-suited for learners interested in solving differential equations, using simulated annealing, and performing hypothesis testing

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Understanding Statistical Models and Mathematical Models with these activities:

Statistical and Mathematical Modeling Resource Collection

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Compile a repository of useful resources such as articles, tutorials, and datasets related to statistical and mathematical modeling.

Browse courses on Statistical Models

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Search for and identify relevant resources online.
Organize the resources into a structured and easy-to-navigate collection.

Review Calculus

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Solidify your understanding of basic mathematical concepts, which will serve as the foundation for this course's lessons.

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Start by reviewing your notes from a previous calculus course or use an online resource to refresh your memory on the basics.
Practice solving simple calculus problems to build your confidence.
Focus on understanding the underlying concepts rather than just memorizing formulas.

Review Calculus

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Reinforce the fundamentals of calculus, essential for understanding mathematical models.

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Revisit the concept of derivatives, integrals, and limits.
Practice solving calculus problems involving functions and equations.

Ten other activities

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Solving Ordinary Differential Equations

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Gain proficiency in solving differential equations commonly encountered in mathematical modeling.

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Follow video tutorials on solving ODEs using different methods.
Attempt solving a variety of ODEs with varying complexities.

Explore Differential Equation Tutorials

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Gain a deeper understanding of the concepts you'll encounter in the course, such as solving differential equations.

Browse courses on Differential Equations

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Find online tutorials or videos that provide clear explanations and examples of differential equations.
Follow along with the tutorials, taking notes and practicing the techniques shown.
Try applying what you've learned to solve simple differential equations.

Attend a Study Group for Hypothesis Testing

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Engage with peers, share your understanding, and reinforce your learning of hypothesis testing.

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Find a study group or organize one with classmates who are also taking the course.
Prepare for the session by reviewing the relevant course material on hypothesis testing.
Actively participate in the discussion, asking questions and sharing your insights.

Develop a Cheat Sheet of Key Concepts

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Create a resource that will help you quickly recall and review important information throughout the course.

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Identify the most important formulas, theorems, and definitions covered in the course.
Create a visually appealing cheat sheet that organizes these key concepts in a logical way.
Use colors, diagrams, and other visual elements to enhance memorability.

Simulated Annealing and Hill Climbing

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Explore the concepts and applications of simulated annealing and hill climbing, used in solving complex optimization problems.

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Watch video tutorials to understand the principles of simulated annealing and hill climbing.
Implement these algorithms in a coding environment to solve optimization problems.

Data Science Workshop for Real-World Applications

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Participate in a hands-on workshop to apply statistical and mathematical modeling techniques to solve real-world problems.

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Attend the workshop and actively participate in the hands-on exercises.
Collaborate with other participants to develop solutions and share insights.

Simulate Annealing to Solve Problems

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Develop your problem-solving skills and reinforce your understanding of simulated annealing, a key technique in this course.

Browse courses on Simulated annealing

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Identify a problem that can be solved using simulated annealing.
Implement a simulated annealing algorithm in your preferred programming language.
Run the algorithm on the problem and analyze the results.

Hypothesis Testing with Statistical Software

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Develop confidence in using statistical software for conducting hypothesis testing and analyzing data.

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Review the basics of hypothesis testing and statistical inference.
Use statistical software to perform t-tests and z-tests on sample data.
Interpret the results of the hypothesis tests and draw meaningful conclusions.

Design and Run a Monte Carlo Simulation

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Gain hands-on experience with a fundamental statistical technique used for modeling complex systems.

Browse courses on Monte Carlo Simulation

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Choose a real-world problem that can be modeled using a Monte Carlo simulation.
Design and implement the simulation in your preferred programming language.
Run the simulation and analyze the results to draw meaningful conclusions.

Contribute to a Statistical Modeling Repository

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Immerse yourself in the field by contributing to a repository, gaining valuable experience and deepening your knowledge.

Browse courses on Statistical Modeling

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Identify an open-source statistical modeling repository that aligns with your interests.
Review the repository's documentation and guidelines to understand its structure and contribution process.
Choose an area where you can make a meaningful contribution based on your skills and knowledge.

Career center

Learners who complete Understanding Statistical Models and Mathematical Models will develop knowledge and skills that may be useful to these careers:

Data Scientist

To begin your career as a Data Scientist, you need a solid knowledge base in statistical and mathematical modeling, which this course will help you build. You'll learn techniques for solving differential equations, simulating annealing, and hypothesis testing, all of which are essential for success in this field. Whether you're a recent graduate or looking for a career change, this course will provide you with the skills and knowledge you need to start your journey as a Data Scientist.

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Statistician

Statisticians use mathematical and statistical models to collect, analyze, interpret, and present data. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use statistical models to model systems with randomness and perform hypothesis testing using real-world data. This course is a great way to get started in the field of statistics.

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Operations Research Analyst

Operations Research Analysts use mathematical and statistical models to improve the efficiency of systems. This course will provide you with the skills you need to succeed in this role. You'll learn how to use mathematical models to solve complex problems and make better decisions. This course is a great way to get started in the field of operations research.

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Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use statistical models to analyze risk and return and make better investment decisions.

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Risk Manager

Risk Managers use mathematical and statistical models to identify, assess, and manage risk. This course will provide you with the skills you need to succeed in this role. You'll learn how to use statistical models to analyze risk and make better decisions. This course is a great way to get started in the field of risk management.

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Actuary

Actuaries use mathematical and statistical models to assess the financial risks associated with insurance policies. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use statistical models to analyze risk and make better decisions. This course is a great way to get started in the field of actuarial science.

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Financial Analyst

Financial Analysts use mathematical and statistical models to analyze financial data and make investment decisions. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use statistical models to analyze risk and return and make better investment decisions.

See salaries and explore the career path for Financial Analyst

Market Researcher

Market Researchers use mathematical and statistical models to collect, analyze, and interpret data about consumer behavior. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use statistical models to analyze data and make better decisions. This course is a great way to get started in the field of marketing research.

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Data Analyst

Data Analysts use mathematical and statistical models to collect, analyze, and interpret data. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use statistical models to analyze data and make better decisions. This course is a great way to get started in the field of data analysis.

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Operations Manager

Operations Managers use mathematical and statistical models to improve the efficiency of systems. This course will provide you with the skills you need to succeed in this role. You'll learn how to use mathematical models to solve complex problems and make better decisions.

See salaries and explore the career path for Operations Manager

Business Analyst

Business Analysts use mathematical and statistical models to analyze data and make recommendations for improving business processes. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use statistical models to analyze data and make better decisions. This course is a great way to get started in the field of business analysis.

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Software Engineer

Software Engineers use mathematical and statistical models to design and develop software systems. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use mathematical models to solve complex problems and make better decisions. This course is a great way to get started in the field of software engineering.

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Computer Scientist

Computer Scientists use mathematical and statistical models to design and develop computer systems. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use mathematical models to solve complex problems and make better decisions. This course is a great way to get started in the field of computer science.

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Economist

Economists use mathematical and statistical models to analyze economic data and make recommendations for economic policy. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use statistical models to analyze data and make better decisions. This course is a great way to get started in the field of economics.

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Mathematician

Mathematicians use mathematical and statistical models to solve complex problems. This course will provide you with the foundation you need to succeed in this role. You'll learn how to use mathematical models to solve complex problems and make better decisions.

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