# statistics

##### Top 10 statistical concepts for data wizards

“Statistics is the grammar of science”, Karl Pearson

In the world of data science, there is a secret language that benefits those who understand it. Do you want to know what makes a data expert efficient? It’s having a profound understanding of the data. Unfortunately, you can’t have a friendly conversation with the data, but don’t worry, we have the next best solution.

Here are the top ten statistical concepts that you must have in your arsenal.  Whether you’re a budding data scientist, a seasoned professional, or merely intrigued by the inner workings of data-driven decision-making, prepare for an enthralling exploration of the statistical principles that underpin the world of data science.

## 10 statistical concepts you should know

### 1. Descriptive statistics:

Starting with the most fundamental and essential statistical concept, descriptive statistics. Descriptive statistics are the specific methods and measures that describe the data. It’s like the foundation of your building. It is a sturdy groundwork upon which further analysis can be constructed. Descriptive statistics can be broken down into measures of central tendency and measures of variability.

• Measure of Central Tendency:

Central Tendency is defined as “the number used to represent the center or middle of a set of data values”. It is a single value that is typically representative of the whole data. They help us understand where the “average” or “central” point lies amidst a collection of data points.

There are a few techniques to find the central tendency of the data, namely “Mean” (average), “Median” (middle value when data is sorted), and “Mode” (most frequently occurring values).

• Measures of variability:

Measures of variability describe the spread, dispersion, and deviation of the data. In essence, they tell us how much each value point deviates from the central tendency. A few measures of variability are “Range”, “Variance”, “Standard Deviation”, and “Quartile Range”. These provide valuable insights into the degree of variability or uniformity in the data.

### 2. Inferential statistics:

Inferential statistics enable us to draw conclusions about the population from a sample of the population. Imagine having to decide whether a medicinal drug is good or bad for the general public. It is practically impossible to test it on every single member of the population.

This is where inferential statistics comes in handy. Inferential statistics employ techniques such as hypothesis testing and regression analysis (also discussed later) to determine the likelihood of observed patterns occurring by chance and to estimate population parameters.

This invaluable tool empowers data scientists and researchers to go beyond descriptive analysis and uncover deeper insights, allowing them to make data-driven decisions and formulate hypotheses about the broader context from which the data was sampled.

### 3. Probability distributions:

Probability distributions serve as foundational concepts in statistics and mathematics, providing a structured framework for characterizing the probabilities of various outcomes in random events. These distributions, including well-known ones like the normal, binomial, and

Poisson distributions offer structured representations for understanding how data is distributed across different values or occurrences.

Much like navigational charts guiding explorers through uncharted territory, probability distributions function as reliable guides through the landscape of uncertainty, enabling us to quantitatively assess the likelihood of specific events.

They constitute essential tools for statistical analysis, hypothesis testing, and predictive modeling, furnishing a systematic approach to evaluate, analyze, and make informed decisions in scenarios involving randomness and unpredictability. Comprehension of probability distributions is imperative for effectively modeling and interpreting real-world data and facilitating accurate predictions.

### 4. Sampling methods:

We now know inferential statistics help us make conclusions about the population from a sample of the population. How do we ensure that the sample is representative of the population? This is where sampling methods come to aid us.

Sampling methods are a set of methods that help us pick our sample set out of the population. Sampling methods are indispensable in surveys, experiments, and observational studies, ensuring that our conclusions are both efficient and statistically valid. There are many types of sampling methods. Some of the most common ones are defined below.

• Simple Random Sampling: A method where each member of the population has an equal chance of being selected for the sample, typically through random processes.
• Stratified Sampling: The population is divided into subgroups (strata), and a random sample is taken from each stratum in proportion to its size.
• Systematic Sampling: Selecting every “kth” element from a population list, using a systematic approach to create the sample.
• Cluster Sampling: The population is divided into clusters, and a random sample of clusters is selected, with all members in selected clusters included.
• Convenience Sampling: Selection of individuals/items based on convenience or availability, often leading to non-representative samples.
• Purposive (Judgmental) Sampling: Researchers deliberately select specific individuals/items based on their expertise or judgment, potentially introducing bias.
• Quota Sampling: The population is divided into subgroups, and individuals are purposively selected from each subgroup to meet predetermined quotas.
• Snowball Sampling: Used in hard-to-reach populations, where participants refer researchers to others, leading to an expanding sample.

### 5. Regression analysis:

Regression analysis is a statistical method that helps us quantify the relationship between a dependent variable and one or more independent variables. It’s like drawing a line through data points to understand and predict how changes in one variable relate to changes in another.

Regression models, such as linear regression or logistic regression, are used to uncover patterns and causal relationships in diverse fields like economics, healthcare, and social sciences. This technique empowers researchers to make predictions, analyze cause-and-effect connections, and gain insights into complex phenomena.

### 6. Hypothesis testing:

Hypothesis testing is a key statistical method used to assess claims or hypotheses about a population using sample data. It’s like a process of weighing evidence to determine if there’s enough proof to support a hypothesis.

Researchers formulate a null hypothesis and an alternative hypothesis, then use statistical tests to evaluate whether the data supports rejecting the null hypothesis in favor of the alternative.

This method is crucial for making informed decisions, drawing meaningful conclusions, and assessing the significance of observed effects in various fields of research and decision-making.

### 7. Data visualizations:

Data visualization is the art and science of representing complex data in a visual and comprehensible form. It’s like translating the language of numbers and statistics into a graphical story that anyone can understand at a glance.

Effective data visualization not only makes data more accessible but also allows us to spot trends, patterns, and outliers, making it an essential tool for data analysis and decision-making. Whether through charts, graphs, maps, or interactive dashboards, data visualization empowers us to convey insights, share information, and gain a deeper understanding of complex datasets.

Check out some of the most important plots for Data Science here.

### 8. ANOVA (Analysis of variance):

Analysis of Variance (ANOVA) is a statistical technique used to compare the means of two or more groups to determine if there are significant differences among them. It’s like the referee in a sports tournament, checking if there’s enough evidence to conclude that the teams’ performances are different.

ANOVA calculates a test statistic and a p-value, which indicates whether the observed differences in means are statistically significant or likely occurred by chance.

This method is widely used in research and experimental studies, allowing researchers to assess the impact of different factors or treatments on a dependent variable and draw meaningful conclusions about group differences. ANOVA is a powerful tool for hypothesis testing and plays a vital role in various fields, from medicine and psychology to economics and engineering.

### 9. Time Series analysis:

Time series analysis is a specialized field of statistics and data science that focuses on studying data points collected, recorded, or measured over time. It’s like examining the historical trajectory of a variable to understand its patterns and trends.

Time series analysis involves techniques for data visualization, smoothing, forecasting, and modeling to uncover insights and make predictions about future values.

This discipline finds applications in various domains, from finance and economics to climate science and stock market predictions, helping analysts and researchers understand and harness the temporal patterns within their data.

### 10. Bayesian statistics:

Bayesian statistics is a branch of statistics that takes a unique approach to probability and inference. Unlike classical statistics, which use fixed parameters, Bayesian statistics treat probability as a measure of uncertainty, updating beliefs based on prior information and new evidence.

It’s like continually refining your knowledge as you gather more data. Bayesian methods are particularly useful when dealing with complex, uncertain, or small-sample data, and they have applications in fields like machine learning, Bayesian networks, and decision analysis

October 16, 2023
##### 17 most influential equations simplified

The world we live in is defined by numbers and equations. From the simplest calculations to the most complex scientific theories, equations are the threads that weave the fabric of our understanding.

In this blog, we will step on a journey through the corridors of mathematical and scientific history, where we encounter the most influential equations that have shaped the course of human knowledge and innovation.

These equations are not mere symbols on a page; they are the keys that unlocked the mysteries of the universe, allowed us to build bridges that span great distances, enabled us to explore the cosmos, and even predicted the behavior of financial markets.

Get into the worlds of geometry, physics, mathematics, and more, to uncover the stories behind these 17 equations. From Pythagoras’s Theorem to the Black-Scholes Equation, each has its own unique tale, its own moment of revelation, and its own profound impact on our lives.

## Geometry and trigonometry:

### 1. Pythagoras’s theorem

Formula: a^2 + b^2 = c^2

Pythagoras’s Theorem is a mathematical formula that relates the lengths of the three sides of a right triangle. It states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Example:

Suppose you have a right triangle with two sides that measure 3 cm and 4 cm. To find the length of the hypotenuse, you would use the Pythagorean Theorem:

a^2 + b^2 = c^2

3^2 + 4^2 = c^2

9 + 16 = c^2

25 = c^2

c = 5

Therefore, the hypotenuse of the triangle is 5 cm.

Pythagoras’s Theorem is used in many different areas of work, including construction, surveying, and engineering. It is also used in everyday life, such as when measuring the distance between two points or calculating the height of a building.

## Mathematics:

### 2. Logarithms

Formula: log(a, b) = c

Logarithms are a mathematical operation that is used to solve exponential equations. They are also used to scale numbers and compress data.

Example: Suppose you want to find the value of x in the following equation:2^x = 1024You can use logarithms to solve this equation by taking the logarithm of both sides:log(2^x, 2) = log(1024, 2)x * log(2, 2) = 10 * log(2, 2)x = 10Therefore, the value of x is 10.Logarithms are used in many different areas of work, including finance, engineering, and science.

They are also used in everyday life, such as when calculating interest rates or converting units.

### 3. Calculus

Calculus is a branch of mathematics that deals with rates of change. It is used to solve problems in many different areas of work, including physics, engineering, and economics.

One of the most important concepts in calculus is the derivative. The derivative of a function measures the rate of change of the function at a given point.

Another important concept in calculus is the integral. The integral of a function is the sum of the infinitely small areas under the curve of the function.

Example:

Suppose you have a function that represents the distance you have traveled over time. The derivative of this function would represent your speed. The integral of this function would represent your total distance traveled.

Calculus is a powerful tool that can be used to solve many different types of problems. It is used in many different areas of work, including science, engineering, and economics.

### 4. Chaos theory

Chaos theory is a branch of mathematics that studies the behavior of dynamic systems. It is used to model many different types of systems, such as the weather, the stock market, and the human heart.

One of the most important concepts in chaos theory is the butterfly effect. The butterfly effect states that small changes in the initial conditions of a system can lead to large changes in the long-term behavior of the system.

Example:

Suppose you have a butterfly flapping its wings in Brazil. This could cause a small change in the atmosphere, which could eventually lead to a hurricane in Florida.

Chaos theory is used in many different areas of physics, engineering, and economics. It is also used in everyday life, such as when predicting the weather and managing financial risks.

Learn about the Top 7 Statistical Techniques

## Physics:

### 5. Law of gravity

Formula: F = G * (m1 * m2) / r^2

The law of gravity is a physical law that describes the gravitational force between two objects. It states that the force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

Example:

Suppose you have two objects, each with a mass of 1 kg. The gravitational force between the two objects would be 6.67 x 10^-11 N.

If you double the distance between the two objects, the gravitational force between them would be halved.

The law of gravity is used in many different areas of work, including astronomy, space exploration, and engineering. It is also used in everyday life, such as when calculating the weight of an object or the trajectory of a projectile.

## Complex Numbers

### 6.The square root of minus one

Formula: i = sqrt(-1)

The square root of minus one is a complex number that is denoted by the letter i. It is defined as the number that, when multiplied by itself, equals -1.

Example:

i * i = -1

The square root of minus one is used in many different areas of mathematics, physics, and engineering. It is also used in everyday life, such as when calculating the voltage and current in an electrical circuit.

Read the Top 10 Statistics Books for Data Science

## Geometry and Topology

### 7. Euler’s formula for Polyhedra

Formula: V – E + F = 2

Euler’s formula for polyhedra is a mathematical formula that relates the number of vertices, edges, and faces of a polyhedron. It states that the number of vertices minus the number of edges plus the number of faces is always equal to 2.

### Example:

Suppose you have a cube. A cube has 8 vertices, 12 edges, and 6 faces. If you plug these values into Euler’s formula, you get:

V – E + F = 2

8 – 12 + 6 = 2

Therefore, Euler’s formula is satisfied.

## Statistics and Probability:

### 8. Normal distribution

Formula: f(x) = exp(-(x-mu)^2/(2sigma^2)) / sqrt(2pi*sigma^2)
The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetrical and bell-shaped. It is used to model many different natural phenomena, such as human height, IQ scores, and measurement errors.
Example: Suppose you have a class of 30 students, and you want to know the average height of the students. You measure the height of each student and create a histogram of the results. You will likely find that the histogram is bell-shaped, with most of the students clustered around the average height and fewer students at the extremes.
This is because the height of humans is normally distributed. The normal distribution is used in many different areas of work, including statistics, finance, and engineering. It is also used in everyday life, such as when predicting the likelihood of a certain event happening.

### 9. Information theory

Formula: H(X) = -∑p(x) log2(p(x))

Information theory is a branch of mathematics that studies the transmission and processing of information. It was developed by Claude Shannon in the mid-20th century.

One of the most important concepts in information theory is entropy. Entropy is a measure of the uncertainty in a message. The higher the entropy of a message, the more uncertain it is.

Example:

Suppose you have a coin. The entropy of the coin is 1 bit, because there are two equally likely outcomes: heads or tails.

If you flip the coin and it lands on heads, the entropy of the coin is 0, because there is only one possible outcome: heads.

Information theory is used in many different areas of communication, computer science, and statistics. It is also used in everyday life, such as when designing data compression algorithms and communication protocols.

## Physics and Engineering:

### 10. Wave equation

Formula: ∂^2u/∂t^2 = c^2 * ∂^2u/∂x^2

The wave equation is a differential equation that describes the propagation of waves. It is used to model many different types of waves, such as sound waves, light waves, and water waves.

Example:

Suppose you throw a rock into a pond. The rock will create a disturbance in the water that will propagate outwards in the form of a wave. The wave equation can be used to model the propagation of this wave.

The wave equation is used in many different areas of physics, engineering, and computer science. It is also used in everyday life, such as when designing sound systems and optical devices.

Learn about Top Machine Learning Algorithms for Data Science

### 11. Fourier transform

Formula: F(u) = ∫ f(x) * exp(-2pii*ux) dx

The Fourier transform is a mathematical operation that transforms a function from the time domain to the frequency domain. It is used to analyze signals and images.

Example:

Suppose you have a sound recording. The Fourier transform of the sound recording can be used to identify the different frequencies that are present in the recording. This information can then be used to compress the recording or to remove noise from the recording.

The Fourier transform is used in many different areas of science and engineering. It is also used in everyday life, such as in digital signal processing and image processing.

### 12. Navier-Stokes equation

Formula: ρ * (∂u/∂t + (u ⋅ ∇)u) = -∇p + μ∇^2u + F

The Navier-Stokes equations are a system of differential equations that describe the motion of fluids. They are used to model many different types of fluid flow, such as the flow of air around an airplane wing and the flow of blood through the body.

Example:

Suppose you are designing an airplane wing. You can use the Navier-Stokes equations to simulate the flow of air around the wing and to determine the lift and drag forces that the wing will experience.

The Navier-Stokes equations are used in many different areas of engineering, such as aerospace engineering, mechanical engineering, and civil engineering. They are also used in physics and meteorology.

### 13. Maxwell’s equations

Formula: ∇⋅E = ρ/ε0 | ∇×E = -∂B/∂t | ∇⋅B = 0 | ∇×B = μ0J + μ0ε0∂E/∂t

Maxwell’s equations are a set of four equations that describe the behavior of electric and magnetic fields. They are used to model many different phenomena, such as the propagation of light waves and the operation of electrical devices.

Example:

Suppose you are designing a generator. You can use Maxwell’s equations to simulate the flow of electric and magnetic fields in the generator and to determine the amount of electricity that the generator will produce.

Maxwell’s equations are used in many different areas of physics and engineering. They are also used in everyday life, such as in the design of electrical devices and communication systems.

### 14. Second Law of thermodynamics

Formula: dS ≥ 0

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. Entropy is a measure of the disorder of a system.

Example:

Suppose you have a cup of hot coffee. The coffee is initially ordered, with the hot molecules at the top of the cup and the cold molecules at the bottom of the cup. Over time, the coffee will cool down and the molecules will become more disordered. This is because the second law of thermodynamics requires the total entropy of the system to increase over time.

The second law of thermodynamics is used in many different areas of physics, engineering, and economics. It is also used in everyday life, such as when designing power plants and refrigerators.

## Physics and Cosmology:

### 15. Relativity

Formula: E = mc^2

Relativity is a branch of physics that studies the relationship between space and time. It was developed by Albert Einstein in the early 20th century. One of the most famous equations in relativity is E = mc^2, which states that energy and mass are equivalent. This means that energy can be converted into mass and vice versa.

Example: Suppose you have a nuclear reactor. The nuclear reactor converts nuclear energy into mass. This is because the nuclear reactor converts the energy of the nuclear binding force into mass. Relativity is used in many different areas of physics, astronomy, and engineering. It is also used in everyday life, such as in the design of GPS systems and particle accelerators.

### 16. Schrödinger’s equation

Formula: iℏ∂ψ/∂t = Hψ

Schrödinger’s equation is a differential equation that describes the behavior of quantum mechanical systems. It is used to model many different types of quantum systems, such as atoms, molecules, and electrons.

Example:

Suppose you have a hydrogen atom. The Schrödinger equation can be used to calculate the energy levels of the hydrogen atom and the probability of finding the electron in a particular region of space.

Schrödinger’s equation is used in many different areas of physics, chemistry, and materials science. It is also used in the development of new technologies, such as quantum computers and quantum lasers.

## Finance and Economics:

### 17. Black-Scholes equation

Formula: ∂C/∂t + ½σ^2S^2∂^2C/∂S^2 – rC = 0

The Black-Scholes equation is a differential equation that describes the price of a European option. A European option is a financial contract that gives the holder the right, but not the obligation, to buy or sell an asset at a certain price on a certain date.

The Black-Scholes equation is used to price options and to develop hedging strategies. It is one of the most important equations in finance.

Example:

Suppose you are buying a call option on a stock. The Black-Scholes equation can be used to calculate the price of the call option. This information can then be used to decide whether or not to buy the call option and to determine how much to pay for it.

The Black-Scholes equation is used by many different financial institutions, such as investment banks and hedge funds. It is also used by individual investors to make investment decisions.

## Share your favorite equation with us!

Mathematics and science are not just abstract concepts but the very foundations upon which our modern world stands. These 17 equations have not only changed the way we see the world but have also paved the way for countless innovations and advancements.

From the elegance of Euler’s Formula for Polyhedra to the complexity of Maxwell’s Equations, from the order of Normal Distribution to the chaos of Chaos Theory, each equation has left an indelible mark on the human story.

They have transcended their origins and become tools that shape our daily lives, drive technological progress, and illuminate the mysteries of the cosmos.

As we continue to explore, learn, and discover, let us always remember the profound impact of these equations and the brilliant minds behind them. They remind us that the pursuit of knowledge knows no bounds and that the world of equations is a realm of infinite wonder and possibility.

Let us know in the comments in case we missed any!

September 19, 2023
##### Unleashing success: Mastering the 10 must-have skills for data analysts in 2023

Are you interested in learning more about the essential skills for data analysts to succeed in today’s data-driven world?

You are in luck if you have a knack for working with numbers and handling datasets. The good news is that you don’t need to be an engineer, scientist, or programmer to acquire the necessary data analysis skills. Whether you’re located anywhere in the world or belong to any profession, you can still develop the expertise needed to be a skilled data analyst.

## Who are data analysts?

Data analysts are professionals who use data to identify patterns, trends, and insights that help organizations make informed decisions. They collect, clean, organize, and analyze data to provide valuable insights to business leaders, enabling them to make data-driven decisions.

The profession of data analysis is gaining momentum for several reasons. First, the amount of data available to organizations has grown exponentially in recent years, creating a need for professionals who can make sense of it. Second, advancements in technology, such as big data and machine learning, have made it easier and more efficient to analyze data. Finally, businesses are realizing the importance of making data-driven decisions to remain competitive in today’s market.

As we move further into the age of data-driven decision-making, the role of the data analyst continues to evolve and expand. In 2023, data analysts will be expected to have a wide range of skills and knowledge to be effective in their roles.

## 10 essential skills for data analysts to have in 2023

Here are 10 essential skills for data analysts to have in 2023:

### 1. Data Visualization:

Topping the list of skills for data analysts data visualization stands first. Data visualization is the process of presenting data in a visual format such as charts, graphs, or maps. Data analysts need to be able to effectively communicate their findings through visual representations of data.

They should be proficient in using tools like Tableau, PowerBI, or Python libraries like Matplotlib and Seaborn to create visually appealing and informative dashboards. Data analysts should also understand design principles such as color theory and visual hierarchy to create effective visualizations. Effective data visualization allows stakeholders to quickly understand complex data and draw actionable insights from it.

### 2. Programming

Programming is a crucial skill for data analysts. They should be proficient in languages like Python, R or SQL to effectively analyze data and create custom scripts to automate data processing and analysis. Data analysts should be able to manipulate data using programming constructs such as loops, conditional statements, and functions.

They should also be familiar with data structures such as arrays and lists, and be able to use libraries and packages such as NumPy, Pandas, or dplyr to process and manipulate data. In the skills for data analysts list, programming skills are essential since they enable data analysts to create automated workflows that can process large volumes of data quickly and efficiently, freeing up time to focus on higher-value tasks such as data modeling and visualization.

### 3. Statistics

Possessing the right skills for data analysts is essential for success in this field. A strong foundation in statistics is crucial to applying statistical methods and models to analysis, including concepts like hypothesis testing, regression, and clustering analysis.

In addition, data analysts must have a thorough understanding of probability and statistics to identify patterns in data, eliminate biases and logical errors, and generate accurate results. These abilities are critical to becoming a skilled data analyst and making informed decisions based on data analysis.

### 4. Data cleaning and preparation

Data cleaning and preparation is the process of transforming raw data into a format that is suitable for analysis. This involves identifying and correcting errors, removing duplicates, handling missing values, and restructuring data.

Data analysts should be proficient in using tools like Excel, OpenRefine or Python libraries like Pandas to clean and preprocess data. They should be able to identify patterns and outliers in data and use their knowledge of statistical analysis to handle them appropriately. In addition, they should be able to create automated data-cleaning pipelines to ensure data is clean and consistent for future analysis.

### 5. Data modeling

Data modeling is the process of creating a conceptual representation of data and its relationships to support business decisions. This involves creating models that can be used to predict future outcomes based on historical data. Data analysts should have a strong understanding of concepts such as classification, regression, and time-series analysis.

They should be able to choose the appropriate model for a specific problem and evaluate the performance of the model. Data analysts should also have the ability to implement models using tools like Python’s sci-kit-learn library, R’s caret package, or IBM SPSS.

### 6. Data security

Data security is the process of protecting data from unauthorized access, use, disclosure, disruption, modification, or destruction. Data analysts should have a strong understanding of data security and privacy to ensure the data they work with is secure and compliant with regulations such as GDPR, CCPA, or HIPAA. They should be able to identify potential security risks and take measures to mitigate them.

This may include using encryption techniques to protect sensitive data, implementing access controls to restrict access to data, and ensuring that data is stored and transmitted securely. Additionally, data analysts should be familiar with legal and ethical issues surrounding data privacy and be able to ensure compliance with relevant laws and regulations.

### 7. Communication

Data analysts should be able to communicate their findings in a clear and concise manner to non-technical stakeholders. They should be able to translate complex data insights into actionable insights for decision-makers.

### 8. Critical thinking

Data analysts should have strong critical thinking skills to be able to analyze and interpret data to identify trends and patterns that may not be immediately apparent.

Data analysts should have a strong understanding of the business domain they work in to be able to effectively apply data analysis to business problems and make data-driven decisions.

### 10. Continuous learning

Data analysts should be committed to continuous learning and staying up-to-date with new tools, techniques, and technologies. They should be willing to invest time and effort into learning new skills and technologies to stay competitive.

In conclusion, data analysts in 2023 will need to have a diverse skill set that includes technical, business, and soft skills. They should be proficient in data visualization, programming, statistics, data modeling, and data cleaning and preparation. In addition, they should have strong communication, critical thinking, and business acumen skills.

Finally, they should be committed to continuous learning and staying up-to-date with new tools and technologies. By developing these skills, data analysts can add value to their organizations and stay competitive in the job market.

April 18, 2023
##### Master the top 7 statistical techniques for better data analysis

Get ahead in data analysis with our summary of the top 7 must-know statistical techniques. Master these tools for better insights and results.

While the field of statistical inference is fascinating, many people have a tough time grasping its subtleties. For example, some may not be aware that there are multiple types of inference and that each is applied in a different situation. Moreover, the applications to which inference can be applied are equally diverse.

For example, when it comes to assessing the credibility of a witness, we need to know how reliable the person is and how likely it is that the person is lying. Similarly, when it comes to making predictions about the future, it is important to factor in not just the accuracy of the forecast but also whether it is credible.

Counterfactual causal inference:

Counterfactual causal inference is a statistical technique that is used to evaluate the causal significance of historical events. Exploring how historical events may have unfolded under small changes in circumstances allows us to assess the importance of factors that may have caused the event. This technique can be used in a wide range of fields such as economics, history, and social sciences. There are multiple ways of doing counterfactual inference, such as Bayesian Structural Modelling.

Overparametrized models and regularization:

Overparametrized models are models that have more parameters than the number of observations. These models are prone to overfitting and are not generalizable to new data. Regularization is a technique that is used to combat overfitting in overparametrized models. Regularization adds a penalty term to the loss function to discourage the model from fitting the noise in the data. Two common types of regularization are L1 and L2 regularization.

Generic computation algorithms:

Generic computation algorithms are a set of algorithms that can be applied to a wide range of problems. These algorithms are often used to solve optimization problems, such as gradient descent and conjugate gradient. They are also used in machine learning, such as support vector machines and k-means clustering.

Robust inference:

Robust inference is a technique that is used to make inferences that are not sensitive to outliers or extreme observations. This technique is often used in cases where the data is contaminated with errors or outliers. There are several robust statistical methods such as the median and the Huber M-estimator.

Bootstrapping and simulation-based inference:

Bootstrapping and simulation-based inference are techniques that are used to estimate the precision of sample statistics and to evaluate and compare models. Bootstrapping is a resampling technique that is used to estimate the sampling distribution of a statistic by resampling the data with replacement.

Simulation-based inference is a method that is used to estimate the sampling distribution of a statistic by generating many simulated samples from the model.

Multilevel models:

Multilevel models are a class of models that are used to account for the hierarchical structure of data. These models are often used in fields such as education, sociology, and epidemiology. They are also known as hierarchical linear models, mixed-effects models, or random coefficient models.

Adaptive Decision Analysis is a statistical technique that is used to make decisions under uncertainty. It involves modeling the decision problem, simulating the outcomes of the decision and updating the decision based on the new information. This method is often used in fields such as finance, engineering, and healthcare.

## Which statistical techniques are most used by you?

This article discusses most of the statistical methods that are used in quantitative fields. These are often used to infer causal relationships between variables.

The primary goal of any statistical way is to infer causality from observational data. It is usually difficult to achieve this goal for two reasons. First, observational data may be noisy and contaminated by errors. Second, variables are often correlated. To correctly infer causality, it is necessary to model these correlations and to account for any biases and confounding factors.

As statistical techniques are often implemented using specific software packages, the implementations of each method often differ. This article first briefly describes the papers and software packages that are used in the following sections. It then describes the most common statistical techniques and the best practices that are associated with each technique.

February 7, 2023
##### Top 10 statistics books for data science

In this blog, we will introduce you to the highly rated data science statistics books on Amazon. As you read the blog, you will find 5 books for beginners and 5 books for advanced-level experts. We will discuss what’s covered in each book and how it helps you to scale up your data science career.

## Advanced statistics books for data science

### 1. Naked Statistics: Stripping the Dread from the Data – By Charles Wheelan

The book unfolds the underlying impact of statistics on our everyday life. It walks the readers through the power of data behind the news.

Mr. Wheelan begins the book with the classic Monty Hall problem. It is a famous, seemingly paradoxical problem using Bayes’ theorem in conditional probability. Moving on, the book separates the important ideas from the arcane technical details that can get in the way. The second part of the book interprets the role of descriptive statistics in crafting a meaningful summary of the underlying phenomenon of data.

Wheelan highlights the Gini Index to show how it represents the income distribution of the nation’s residents and is mostly used to measure inequality. The later part of the book clarifies key concepts such as correlation, inference, and regression analysis explaining how data is being manipulated in order to tackle thorny questions. Wheelan’s concluding chapter is all about the amazing contribution that statistics will continue to make to solving the world’s most pressing problems, rather than a more reflective assessment of its strengths and weaknesses.

### 2. Bayesian Methods For Hackers – Probabilistic Programming and Bayesian Inference, By Cameron Davidson-Pilon

We mostly learn Bayesian inference through intensely complex mathematical analyses that are also supported by artificial examples. This book comprehends Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib.

Davidson-Pilon focused on improving learners’ understanding of the motivations, applications, and challenges in Bayesian statistics and probabilistic programming. Moreover, this book brings a much-needed introduction to Bayesian methods targeted at practitioners. Therefore, you can reap the most benefit from this book if you have a prior sound understanding of statistics. Knowing about prior and posterior probabilities will give an added advantage to the reader in building and training the first Bayesian model.

Read this blog if you want to learn in detail about statistical distributions

The second part of the book introduces the probabilistic programming library for Python through a series of detailed examples and intuitive explanations, with recent core developments and the popularity of the scientific stack in Python, PyMC is likely to become a core component soon enough. PyMC does have dependencies to run, namely NumPy and (optionally) SciPy. To not limit the user, the examples in this book will rely only on PyMC, NumPy, SciPy, and Matplotlib. This book is filled with examples, figures, and Python code that make it easy to get started solving actual problems.

### 3. Practical Statistics for Data Scientists – By Peter Bruce and Andrew Bruce

This book is most beneficial for readers that have some basic understanding of R programming language and statistics.

The authors penned the important concepts to teach practical statistics in data science and covered data structures, datasets, random sampling, regression, descriptive statistics, probability, statistical experiments, and machine learning. The code is available in both Python and R. If an example code is offered with this book, you may use it in your programs and documentation.

The book defines the first step in any data science project that is exploring the data or data exploration. Exploratory data analysis is a comparatively new area of statistics. Classical statistics focused almost exclusively on inference, a sometimes-complex set of procedures for drawing conclusions about large populations based on small samples.

To apply the statistical concepts covered in this book, unstructured raw data must be processed and manipulated into a structured form—as it might emerge from a relational database—or be collected for a study.

### 4. Advanced Engineering Mathematics by Erwin Kreyszig

Advanced Engineering Mathematics is a textbook for advanced engineering and applied mathematics students. The book deals with calculus of vector, tensor and differential equations, partial differential equations, linear elasticity, nonlinear dynamics, chaos theory and applications in engineering.

Advanced Engineering Mathematics is a textbook that focuses on the practical aspects of mathematics. It is an excellent book for those who are interested in learning about engineering and its role in society. The book is divided into five sections: Differential Equations, Integral Equations, Differential Mathematics, Calculus and Probability Theory. It also provides a basic introduction to linear algebra and matrix theory. This book can be used by students who want to study at the graduate level or for those who want to become engineers or scientists.

The text provides a self-contained introduction to advanced mathematical concepts and methods in applied mathematics. It covers topics such as integral calculus, partial differentiation, vector calculus and its applications to physics, Hamiltonian systems and their stability analysis, functional analysis, classical mechanics and its applications to engineering problems.

The book includes a large number of problems at the end of each chapter that helps students develop their understanding of the material covered in the chapter.

### 5. Computer Age Statistical Inference by Bradley Efron and Trevor Hastie

Computer Age Statistical Inference is a book aimed at data scientists who are looking to learn about the theory behind machine learning and statistical inference. The authors have taken a unique approach in this book, as they have not only introduced many different topics, but they have also included a few examples of how these ideas can be applied in practice.

The book starts off with an introduction to statistical inference and then progresses through chapters on linear regression models, logistic regression models, statistical model selection, and variable selection. There are several appendices that provide additional information on topics such as confidence intervals and variable importance. This book is great for anyone looking for an introduction to machine learning or statistics.

Computer Age Statistical Inference is a book that introduces students to the field of statistical inference in a modern computational setting. It covers topics such as Bayesian inference and nonparametric methods, which are essential for data science. In particular, this book focuses on Bayesian classification methods and their application to real world problems. It discusses how to develop models for continuous and discrete data, how to evaluate model performance, how to choose between parametric and nonparametric methods, how to incorporate prior distributions into your model, and much more.

## 5 Beginner level statistics books for data science

### 6. How to Lie with Statistics by Darrell Huff

How to Lie with Statistics is one of the most influential books about statistical inference. It was first published in 1954 and has been translated into many languages. The book describes how to use statistics to make your most important decisions, like whether to buy a house, how much money to give to charity, and what kind of mortgage you should take out. The book is intended for laymen, as it includes illustrations and some mathematical formulas. It’s full of interesting insights into how people can manipulate data to support their own agendas.

The book is still relevant today because it describes how people use statistics in their daily lives. It gives an understanding of the types of questions that are asked and how they are answered by statistical methods. The book also explains why some results seem more reliable than others.

The first half of the book discusses methods of making statistical claims (including how to make improper ones) and illustrates these using examples from real life. The second half provides a detailed explanation of the mathematics behind probability theory and statistics.

A common criticism of the book is that it focuses too much on what statisticians do rather than why they do it. This is true — but that’s part of its appeal!

### 7. Head-first Statistics: A Brain-Friendly Guide Book by Dawn Griffiths

If you are looking for a book that will help you understand the basics of statistics, then this is the perfect book for you. In this book, you will learn how to use data and make informed decisions based on your findings. You will also learn how to analyze data and draw conclusions from it.

This book is ideal for those who have already completed a course in statistics or have studied it in college. Griffiths has given an overview of the different types of statistical tests used in everyday life and provides examples of how to use them effectively.

The book starts off with an explanation of statistics, which includes topics such as sampling, probability, population and sample size, normal distribution and variation, confidence intervals, tests of hypotheses and correlation.

After this section, the book goes into more advanced topics such as regression analysis, hypothesis testing etc. There are also some chapters on data mining techniques like clustering and classification etc.

The author has explained each topic in detail for the readers who have little knowledge about statistics so they can follow along easily. The language used throughout this book is very clear and simple which makes it easy to understand even for beginners.

### 8. Think Stats By Allen B. Downey

Think Stats is a great book for students who want to learn more about statistics. The author, Allen Downey, uses simple examples and diagrams to explain the concepts behind each topic. This book is especially helpful for those who are new to mathematics or statistics because it is written in an easy-to-understand manner that even those with a high school degree can understand.

The book begins with an introduction to basic counting, addition, subtraction, multiplication and division. It then moves on to finding averages and making predictions about what will happen if one number changes. It also covers topics like randomness, sampling techniques, sampling distributions and probability theory.

The author uses real-world examples throughout the book so that readers can see how these concepts apply in their own lives. He also includes exercises at the end of each chapter so that readers can practice what they’ve learned before moving on to the next section of the book. This makes Think Stats an excellent resource for anyone looking for tips on improving their math skills or just wanting to brush up on some statistical basics!

### 9. An Introduction To Statistical Learning With Applications In R By Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani

Statistical learning with applications in R is a guide to advanced statistical learning. It introduces modern machine learning techniques and their applications, including sequential decision-making, Gaussian mixture models, boosting, and genetic programming. The book covers methods for supervised and unsupervised learning, as well as neural networks. The book also includes chapters on Bayesian statistics and deep learning.

It begins with a discussion of correlation and regression analysis, followed by Bayesian inference using Markov chain Monte Carlo methods. The authors then discuss regularization techniques for regression models and introduce boosting algorithms. This section concludes with an overview of neural networks and convolutional neural networks (CNNs). The remainder of the book deals with topics such as kernel methods, support vector machines (SVMs), regression trees (RTs), naive Bayes classifiers, Gaussian processes (GP), gradient ascent methods, and more.

This statistics book is recommended to researchers willing to learn about statistical machine learning but do not have the necessary expertise in mathematics or programming languages

### 10. Statistics in Plain English By Timothy C. Urdan

Statistics in Plain English is a writing guide for students of statistics. Timothy in his book covered basic concepts with examples and guidance for using statistical techniques in the real world. The book includes a glossary of terms, exercises (with solutions), and web resources.

The book begins by explaining the difference between descriptive statistics and inferential statistics, which are used to draw conclusions about data. It then covers basic vocabulary such as mean, median, mode, standard deviation, and range.

In Chapter 2, the author explains how to calculate sample sizes that are large enough to make accurate estimates. In Chapters 3–5 he gives examples of how to use various kinds of data: census data on population density; survey data on attitudes toward various products; weather reports on temperature fluctuations; and sports scores from games played by teams over time periods ranging from minutes to seasons. He also shows how to use these data to estimate the parameters for models that explain behavior in these situations.

The last 3 chapters define the use of frequency distributions to answer questions about probability distributions such as whether there’s a significant difference between two possible outcomes or whether there’s a trend in a set of numbers over time or space

## Which data science statistics books are you planning to get?

Build upon your statistical concepts and successfully step into the world of data science. Analyze your knowledge and choose the most suitable book for your career to enhance your data science skills. If you have any more suggestions for statistics books for data science, please share them with us in the comments below.

September 9, 2022
##### Regular expression 101 – A beginner’s guide

A regular expression is a sequence of characters that specifies a search pattern in a text. Learn more about Its common uses in this regex 101 guide.

## What is a regular expression?

A regular expression, or regex for short, is perhaps the most common thing that every data scientist must deal with multiple times in their career, and the frustration is natural because, at a vast majority of universities, this skill is not taught unless you have taken some hard-core Computer Science theory course. Even at times, trying to solve a problem using regular expression can cause multiple issues, which is summed beautifully in this meme:

Making sense and using them can be quite daunting for beginners, but this RegEx 101 blog has got you covered. Regular expressions, in essence, are used to match strings in the text that we want to find. Consider the following scenario:

You are interested in counting the number of occurrences of Pandas in a journal related to endangered species to see how much focus is on this species. You write an algorithm that calculates the occurrences of the word ‘panda.’

However, as you might have noticed, your algorithm will miss the words ‘Panda’ and ‘Pandas.’ In this case, you might argue that a simple if-else condition will also count these words. But imagine, while converting the journal alphabets of every word is randomly capitalized or converted into a lower-case letter. Now, there are the following possibilities

• PaNda
• pAnDaS
• PaNdA

And may more variations as well. Now you must write a lot of if-else conditions and even must write nested if-else conditions as well. What if I tell you that you can do this in one line of code using regular expressions? First, we need to learn some basics before coming back to solve the problem ourselves.

### Square Brackets ([])

The name might sound scary, but it is nothing but the symbol: []. Some people also refer to square brackets as character class – a regular expression jargon word that means that it will match any character inside the bracket. For instance:

 Pattern Matches [Pp]enguin Penguin, penguin [0123456789] (This will match any digit) [0oO] 0, o, O

### Disjunction (|)

The pipe symbol means nothing but either ‘A’ or ‘B’, and it is helpful in cases where you want to select multiple strings simultaneously. For instance:

 Pattern Matches A|B|C A, B, C Black|White Black, White [Bb]lack|[Ww]hite Black, black, White, white

### Question Mark (?)

The question mark symbol means that the character it comes after is optional. For instance:

 Pattern Matches Ab?c Ac, Abc Colou?r Color, Colour

### Asterisk (*)

The asterisk symbol matches with 0 or more occurrences of the earlier character or group. For instance:

 Pattern Matches Sh* (0 or more of earlier character h) S, Sh, Shh, Shhh. (banana)* (0 or more of earlier banana. This will also match with nothing, but most regex engines will ignore it or give you a warning in that case) banana, bananabanana, bananabananabanana.

### Plus (+)

The plus symbol means to match with one or more occurrences of the earlier character or group. For instance:

 Pattern Matches Sh+ (1 or more of earlier character h) Sh, Shh, Shhh. (banana)+ (1 or more of the earlier banana) banana, bananabanana, bananabananabanana.

## Difference between Asterisk (*) and Plus(+)

The difference between the asterisk confuses many people; even the experts sometimes must look at the internet for their differences. However, there is an effortless way to remember the distinction between them.

Imagine you have a number 1, and you multiply it with 0:

1*0 = 0 or more occurrences of earlier character or group.

Now suppose that you have the same number 1, and you add it with 0:1+0 = 1 or more occurrences of an earlier character or group.

It is that simple when you try to understand things intuitively.

### Negation (^)

Negation has two everyday use cases:

1. Inside square brackets, it will search for the negation of whatever is inside the brackets. For instance:

 Pattern Matches [^Aa] It will match with anything that is not A or a [^0123456789] It will match anything that is not a digit

2. It can also be used as an anchor to search for expressions at the start of the line(s) only. For instance:

 Pattern Matches ^Apple It will match with every Apple that is at the start of any line in the text ^(Apple|Banana) It will match with every Apple and Banana that is at the start of any line in the text

### Dollar (\$)

A dollar is used to search for expressions at the end of the line. For instance:

 Pattern Matches \$[0123456789] It will match with any digit at the end of any line in the text. \$([Pp]anda) It will match with every Panda and panda at the end of any line in the text.

## Conclusion

This article covered some of the very basic types of regular expression by using a story-telling approach. Regular expressions are indeed very hard to understand but if one develops an intuitive understanding then they can be easily learned.

June 10, 2022

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