**Python** has emerged as a powerhouse in the realm of data science, and its application in statistics is no exception. Its versatility, readability, and supportive community make it a top choice for students and professionals alike.

**Why Use Python for Statistics?**

Python’s intuitive syntax and extensive libraries have propelled it to the forefront of statistical computing. Whether you’re a seasoned statistician or just beginning your journey, Python provides a user-friendly and robust environment for your analytical needs.

**Advantages of Python**

**Versatility:**Python’s capabilities extend far beyond statistics, making it an ideal language for various data-driven tasks. From web development to machine learning, Python’s versatility allows you to seamlessly integrate statistical analysis into broader projects.**Readability:**Python’s clear and concise syntax promotes code readability, making it easier to understand and maintain your statistical analyses. This readability fosters collaboration and reduces the likelihood of errors.**Open-Source Community:**Python boasts a vibrant and supportive open-source community, providing a wealth of resources, libraries, and support forums. This collaborative environment ensures that you have access to the latest tools and guidance for your statistical endeavors.

**Comparison with Other Statistical Software**

While Python shines in statistics, other specialized software options exist, each with strengths and weaknesses. Let’s compare Python with two prominent contenders: R and SAS.

Feature | Python | R | SAS |
---|---|---|---|

Purpose | General-purpose programming language with strong data science capabilities. | Specifically designed for statistical computing and data visualization. | Comprehensive statistical software suite commonly used in industries like healthcare, finance, and government. |

Learning Curve | Relatively easy to learn, especially for beginners with some programming experience. | Can be more challenging for beginners, particularly those without a statistical background. | Steep learning curve, often requiring specialized training. |

Cost | Open-source and free to use. | Open-source and free to use. | Proprietary software, typically requiring expensive licenses, making it less accessible to individuals and smaller organizations. |

Libraries | Extensive collection of libraries for statistics, data visualization, and machine learning. | Rich ecosystem of packages specifically designed for statistical analysis and graphics. | Offers a wide range of statistical procedures and modules, but its library may not be as extensive or rapidly evolving as Python’s. |

Community | Large and active community, providing ample support and resources. | Strong community of statisticians and data scientists. | Large user base, but the community may be more focused on enterprise solutions. |

Industry Use | Widely used in various industries, including tech, finance, and healthcare. | Popular in academia and research, as well as industries with a strong statistical focus. | Prevalent in industries with strict regulatory requirements and a legacy of using SAS, such as pharmaceuticals and clinical research. |

Visualization | Offers powerful visualization libraries like Matplotlib and Seaborn. | Known for its high-quality statistical graphics and data visualization capabilities. | Provides comprehensive graphing and reporting features, but its visualization capabilities may not be as flexible or aesthetically pleasing as Python’s. |

### When to Choose Python for Statistical Analysis

Python emerges as a compelling choice for statistical analysis in various scenarios:

**Beginners:**Python’s gentle learning curve and readable syntax make it an excellent entry point for those new to statistics and programming.**Data Scientists:**Python’s versatility allows data scientists to seamlessly integrate statistical analysis into broader data science workflows, encompassing machine learning, data visualization, and more.**Open-Source Advocates:**Python’s open-source nature ensures cost-effectiveness and access to a vast community of developers and resources.

https://www.geeksforgeeks.org/python-for-data-science/

**Getting Started with Python for Statistics**

Embarking on your statistical journey with Python is remarkably accessible. Here’s a roadmap to guide your initial steps:

### Setting Up Your Python Environment

**Python Installation:**Begin by downloading and installing the latest version of Python from the official Python website.**Package Management:**Utilize package managers like pip or conda to effortlessly install and manage the necessary Python libraries for statistical analysis.

### Essential Python Libraries for Statistics

**NumPy:**The cornerstone of numerical computing in Python, NumPy provides support for arrays, matrices, and a plethora of mathematical functions.**Pandas:**Built atop NumPy, Pandas introduces DataFrames, powerful data structures for efficient data manipulation, cleaning, and analysis.

https://www.w3schools.com/python/python_ml_getting_started.asp

- SciPy: SciPy builds upon NumPy, offering a rich collection of scientific computing routines, including statistical analysis, optimization, and signal processing.
- Matplotlib: The foundation of data visualization in Python, Matplotlib enables you to create a wide array of static, interactive, and animated visualizations.
- Seaborn: Based on Matplotlib, Seaborn provides a higher-level interface for creating visually appealing and informative statistical graphics, simplifying the process of generating insightful plots.
- Introduction to Jupyter NotebooksJupyter Notebooks provide an interactive and collaborative environment for data exploration, analysis, and visualization. Their cell-based structure allows you to execute code snippets independently, fostering experimentation and facilitating the sharing of results.

https://jupyter.org/

## Data Preparation and Exploration with Pandas

Pandas, with its versatile DataFrame structure, takes center stage in data preparation and exploration. Let’s delve into its key functionalities:

### Importing Data from Various Sources

Before embarking on any statistical analysis, the crucial first step involves importing your data into Python. Pandas excels in this domain, seamlessly handling a variety of data sources and formats. Let’s explore how to import data from common sources:

**1. CSV Files (Comma-Separated Values)**

CSV files are ubiquitous for storing tabular data. Pandas provides the `read_csv()`

function to effortlessly import them:

```
import pandas as pd
```*# Importing data from a CSV file*
df = pd.read_csv('data.csv')
*# Displaying the first few rows of the DataFrame*
print(df.head())

**Key Parameters for **`read_csv()`

:

`read_csv()`

:`filepath_or_buffer`

: The path to your CSV file.`sep`

: The separator used in your CSV file (default is ‘,’).`header`

: Row number to use as column names (default is 0).`names`

: List of column names to use, especially if your CSV lacks headers.`index_col`

: Column to use as the DataFrame’s index (optional).

**2. Excel Spreadsheets (.xls, .xlsx)**

Excel files are widely used. Pandas uses the `read_excel()`

function to import data from Excel files:

```
import pandas as pd
```*# Importing data from an Excel file*
df = pd.read_excel('data.xlsx', sheet_name='Sheet1')
*# Displaying the DataFrame*
print(df)

**Key Parameters for **`read_excel()`

:

`read_excel()`

:`io`

: The path to your Excel file.`sheet_name`

: The name of the sheet you want to import (default is 0, importing the first sheet). You can also pass a list of sheet names to import multiple sheets.`header`

: Row number to use as column names (default is 0).`names`

: List of column names to use (similar to`read_csv()`

).`index_col`

: Column to use as the DataFrame’s index (optional).

**3. Databases (SQL Databases)**

For data residing in SQL databases, Pandas integrates seamlessly with libraries like SQLAlchemy to establish connections and retrieve data using SQL queries.

**Example using SQLAlchemy:**

```
import pandas as pd
from sqlalchemy import create_engine
```*# Database connection details*
db_url = 'dialect+driver://username:password@host:port/database' *# Replace with your database details*
*# Create an engine to connect to the database*
engine = create_engine(db_url)
*# SQL query to retrieve data*
query = "SELECT * FROM customers;"
*# Read data from the database into a DataFrame*
df = pd.read_sql(query, engine)
*# Display the DataFrame*
print(df)

**Explanation:**

**Import Libraries:**Import`pandas`

and`create_engine`

from`sqlalchemy`

.**Database Connection:**Define the database URL with your credentials and database name.**Create Engine:**Use`create_engine()`

to establish a connection to the database.**SQL Query:**Write your SQL query to select the desired data.**Read Data:**Utilize`pd.read_sql()`

, passing the query and the engine, to execute the query and load the results into a Pandas DataFrame.

By mastering these data importing techniques, you’ll be well-prepared to load data from diverse sources into Pandas DataFrames, setting the stage for insightful statistical analysis.

## Statistical Modeling and Hypothesis Testing

With your data cleansed and prepped, the journey into the heart of statistical analysis begins: **statistical modeling** and **hypothesis testing**. This phase unveils hidden patterns, empowers predictions, and extracts meaningful inferences from your data.

### Probability Distributions and Statistical Tests

A cornerstone of statistical inference lies in understanding **probability distributions**. These mathematical functions describe the likelihood of different outcomes in a random event. Common distributions like the normal, binomial, and Poisson distribution each model distinct data types and phenomena.

#### Common Statistical Tests in Python

Test Name | Description | Applications | Python Implementation |
---|---|---|---|

t-test | Compares the means of two groups. | Determining if there’s a significant difference in average height between men and women. | `scipy.stats.ttest_ind()` |

Chi-square test | Examines relationships between categorical variables. | Assessing if there’s an association between smoking habits (yes/no) and lung cancer incidence (yes/no). | `scipy.stats.chi2_contingency()` |

ANOVA | Compares means of three or more groups. | Investigating if there’s a difference in average exam scores among students taught with different teaching methods (e.g., lecture, online, blended). | `statsmodels.formula.api.ols()` or `scipy.stats.f_oneway()` |

Correlation | Measures the strength and direction of a linear relationship between two continuous variables. | Analyzing the relationship between hours of study and exam performance. | `scipy.stats.pearsonr()` or `pandas.DataFrame.corr()` |

Mann-Whitney U test | Compares distributions of two groups when data is not normally distributed. | Comparing customer satisfaction ratings (on an ordinal scale) between two different product designs. |

### Implementing Machine Learning Algorithms

Machine learning, a powerful subfield of artificial intelligence, has become an indispensable tool for statistical analysis. Python, with its rich ecosystem of machine learning libraries, provides a robust platform for implementing various algorithms.

#### Scikit-learn: Your Machine Learning Toolkit

Scikit-learn (`sklearn`

) is a widely used Python library for machine learning, offering a consistent and user-friendly interface for numerous algorithms.

##### Supervised Learning

In supervised learning, we train models on labeled data (input-output pairs) to make predictions on unseen data. Common supervised learning algorithms include:

**Linear Regression:**Predicts a continuous target variable based on a linear relationship with input features.**Logistic Regression:**Used for binary classification, predicting the probability of an instance belonging to a particular class.**Decision Trees:**Build tree-like structures to model decisions based on input features.**Support Vector Machines (SVMs):**Construct hyperplanes to effectively separate data points into different classes.**Naive Bayes:**Applies Bayes’ theorem with the assumption of independence among features.

##### Unsupervised Learning

Unsupervised learning deals with unlabeled data, aiming to discover hidden patterns and structures. Key algorithms include:

**Clustering:**Groups similar data points together based on their characteristics.**K-Means Clustering:**Partitions data into ‘k’ clusters by minimizing the distance between data points and cluster centroids.**Hierarchical Clustering:**Builds a hierarchy of clusters, either agglomerative (bottom-up) or divisive (top-down).

**Dimensionality Reduction:**Reduces the number of input features while preserving important information.**Principal Component Analysis (PCA):**Transforms data into a new coordinate system, capturing maximum variance in fewer dimensions.

**Example: Building a Simple Linear Regression Model with Scikit-learn**Let’s predict exam scores based on hours studied using linear regression:

```
import numpy as np
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
```*# Sample data*
X = np.array([2, 4, 6, 8, 10]).reshape(-1, 1) *# Hours studied (input feature)*
y = np.array([60, 70, 75, 85, 90]) *# Exam scores (target variable)*
*# Split data into training and testing sets*
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
*# Create a linear regression model*
model = LinearRegression()
*# Train the model*
model.fit(X_train, y_train)
*# Make predictions on the test set*
y_pred = model.predict(X_test)
*# Evaluate the model*
mse = mean_squared_error(y_test, y_pred)
print(f"Mean Squared Error: {mse:.2f}")

This code snippet demonstrates a typical machine learning workflow:

**Data Preparation:**Load and prepare your data, ensuring features are in the correct format.**Splitting Data:**Divide your data into training and testing sets to evaluate model performance on unseen data.**Model Selection:**Choose an appropriate machine learning algorithm based on your task (regression, classification, clustering, etc.).**Model Training:**Fit the chosen model to your training data, allowing it to learn patterns.**Model Evaluation:**Assess the model’s performance using appropriate metrics (e.g., mean squared error for regression, accuracy for classification).

## Advanced Topics and Applications

As you delve deeper into the world of statistics with Python, you’ll encounter more specialized techniques and applications tailored to specific types of data and analytical goals. Let’s explore some of these advanced areas:

### Time Series Analysis with Statsmodels

Time series data, characterized by observations collected over time, requires specialized methods to analyze trends, seasonality, and make forecasts. Statsmodels, a powerful Python library, provides a comprehensive toolkit for time series analysis.

#### Key Concepts:

**Trend:**A long-term upward or downward movement in the data.**Seasonality:**Recurring patterns that occur at fixed intervals (e.g., daily, monthly, yearly).**Cyclical Variations:**Fluctuations that don’t follow fixed intervals and are often influenced by external factors.

#### Statsmodels Functionality:

**ARIMA Models (Autoregressive Integrated Moving Average):**Versatile models for capturing a wide range of time series patterns.**SARIMA Models (Seasonal ARIMA):**Extend ARIMA models to explicitly account for seasonality.**Exponential Smoothing Methods:**Suitable for data with less pronounced trends and seasonality.

**Example: Simple Time Series Forecasting with ARIMA**

```
import pandas as pd
from statsmodels.tsa.arima.model import ARIMA
from sklearn.metrics import mean_squared_error
```*# Sample time series data (e.g., monthly sales)*
data = [10, 12, 15, 14, 18, 22, 20, 25, 28, 26, 30, 35]
index = pd.date_range('2023-01-01', periods=len(data), freq='M')
df = pd.DataFrame({'sales': data}, index=index)
*# Split data into train and test sets*
train_data = df[:-3]
test_data = df[-3:]
*# Fit an ARIMA(5,1,0) model*
model = ARIMA(train_data['sales'], order=(5, 1, 0))
model_fit = model.fit()
*# Forecast future values*
predictions = model_fit.predict(start=len(train_data), end=len(df)-1)
*# Evaluate the model*
rmse = mean_squared_error(test_data['sales'], predictions, squared=False)
print(f"RMSE: {rmse:.2f}")

### Statistical Inference and Bayesian Analysis

While traditional frequentist statistics focuses on p-values and hypothesis testing, Bayesian analysis offers a different perspective, incorporating prior beliefs and updating them based on observed data.

#### Bayesian Concepts:

**Prior Distribution:**Represents your initial beliefs about the parameter you’re estimating.**Likelihood Function:**Describes the probability of observing the data given a specific parameter value.**Posterior Distribution:**Combines the prior and likelihood to provide an updated belief about the parameter after observing the data.

#### Bayesian Libraries in Python:

**PyMC3:**A powerful and flexible library for probabilistic programming in Python.**PyStan:**An interface to the Stan probabilistic programming language.

**Example: Estimating a Proportion with PyMC3**Let’s say we want to estimate the proportion of people who prefer a new product design over an old one based on survey data.

```
import pymc3 as pm
import numpy as np
```*# Sample data (number of successes and total trials)*
successes = 75
trials = 100
*# Define the model*
with pm.Model() as model:
*# Prior distribution for the proportion (uniform between 0 and 1)*
p = pm.Uniform("p", 0, 1)
*# Likelihood function (binomial distribution)*
observations = pm.Binomial("observations", n=trials, p=p, observed=successes)
*# Sample from the posterior distribution*
trace = pm.sample(2000, tune=1000)
*# Analyze the posterior distribution*
pm.summary(trace)

This code uses PyMC3 to define a Bayesian model, sample from the posterior distribution, and provide summaries of the estimated proportion and its uncertainty.

## Data Analysis Pipelines and Automation

As data analyses grow in complexity, it becomes essential to organize your code efficiently and automate repetitive tasks. This is where data analysis pipelines and automation come into play.

### Organizing Python Code for Reusability and Scalability

#### Functions: The Building Blocks of Reusable Code

Functions allow you to encapsulate a specific task or computation within a reusable block of code. This promotes code organization, readability, and reduces redundancy.

```
def calculate_summary_stats(data):
"""Calculates mean, median, and standard deviation of a numerical list.
Args:
data: A list of numerical values.
Returns:
A tuple containing the mean, median, and standard deviation.
"""
mean = np.mean(data)
median = np.median(data)
std = np.std(data)
return mean, median, std
```*# Example usage*
data = [10, 15, 12, 18, 14]
mean, median, std = calculate_summary_stats(data)
print(f"Mean: {mean:.2f}, Median: {median:.2f}, Standard Deviation: {std:.2f}")

#### Modules and Packages: Organizing Larger Projects

For more extensive projects, organize your code into modules (Python files) and packages (collections of modules) to create a logical structure and improve maintainability.

### Automating Data Cleaning and Analysis Tasks

Many data analysis tasks, such as data cleaning, transformation, and visualization, can be automated using Python scripts.

#### Example: Automating Data Cleaning with Pandas

Let’s say you have a CSV file with missing values that need to be filled and outliers that need to be addressed:

```
import pandas as pd
def clean_data(df):
"""Cleans a DataFrame by filling missing values and handling outliers.
Args:
df: The input DataFrame.
Returns:
The cleaned DataFrame.
"""
```*# Fill missing values in 'age' with the mean*
df['age'] = df['age'].fillna(df['age'].mean())
*# Cap outliers in 'income' at the 95th percentile*
income_cap = df['income'].quantile(0.95)
df['income'] = np.where(df['income'] > income_cap, income_cap, df['income'])
return df
*# Load the data*
df = pd.read_csv('data.csv')
*# Clean the data*
cleaned_df = clean_data(df)
*# Proceed with further analysis using the cleaned DataFrame*
By automating these tasks, you save time, reduce errors, and ensure consistency in your analysis workflow.

## Integrating Python with Other Tools and Environments

Python’s versatility shines when integrated with other tools and environments, extending its capabilities for data visualization, reporting, and collaborative analysis.

### Interactive Visualizations with Plotly and Bokeh

While Matplotlib provides a solid foundation for static visualizations, libraries like Plotly and Bokeh enable the creation of interactive plots, dashboards, and web-based visualizations.

#### Plotly: Interactive Plots and Dashboards

Plotly’s Python library offers a wide range of interactive chart types, from scatter plots and line graphs to heatmaps and 3D visualizations. You can easily embed these interactive plots in Jupyter Notebooks, web applications, or export them as standalone HTML files.

#### Bokeh: Interactive Visualizations for the Web

Bokeh specializes in creating interactive visualizations designed for modern web browsers. It excels in handling large datasets and streaming data, making it suitable for real-time dashboards and data exploration tools.

### Reporting and Sharing Insights with Jupyter Notebooks

Jupyter Notebooks have become a staple for data scientists and analysts, providing an interactive environment to combine code, visualizations, and narrative text. You can easily share your Jupyter Notebooks with colleagues or publish them online as interactive documents.

#### Key Features of Jupyter Notebooks:

**Code Cells:**Execute Python code snippets interactively.**Markdown Cells:**Format text, add headings, lists, and include mathematical equations using Markdown.**Visualizations:**Embed static or interactive plots directly within the notebook.

### Cloud-Based Data Analysis Platforms

Cloud platforms like Google Colab, Amazon SageMaker, and Microsoft Azure Notebooks offer cloud-based Jupyter Notebook environments, providing access to powerful computing resources and pre-installed data science libraries.

#### Advantages of Cloud Platforms:

**Scalability:**Easily scale your computations to handle larger datasets and more demanding analyses.**Collaboration:**Work collaboratively on notebooks with colleagues, much like using shared documents.**Pre-configured Environments:**Start analyzing data quickly with pre-configured environments and libraries.

By leveraging these integrations and tools, you can enhance your data analysis workflow, create compelling visualizations, and seamlessly share your findings with others.

## Best Practices for Robust and Reproducible Data Analysis

Ensuring your data analysis is robust, reproducible, and reliable is paramount, especially as projects grow in complexity and impact. Let’s explore key best practices:

### Version Control with Git and GitHub

**Version control** is essential for tracking changes to your code, collaborating with others, and reverting to previous states when needed.

**Git:**A distributed version control system that allows you to track code changes locally and remotely.**GitHub:**A web-based platform for hosting Git repositories, fostering collaboration and code sharing.

#### Key Benefits:

**Track Changes:**Keep a detailed history of every modification made to your code.**Collaboration:**Work seamlessly with others on the same codebase.**Experimentation:**Create branches to test new ideas without affecting the main codebase.**Reproducibility:**Easily share and reproduce your analysis by providing access to your code repository.

### Documentation: Making Your Analysis Transparent

Thorough documentation is crucial for understanding the steps involved in your analysis, interpreting the results, and ensuring reproducibility.

#### Types of Documentation:

**Code Comments:**Explain the purpose of code sections, functions, and complex logic within your code.**README File:**Provide an overview of your project, instructions for setup and execution, and descriptions of key files and data sources.**Data Dictionary:**Document the variables in your dataset, including their definitions, data types, and any relevant coding schemes.

### Testing Your Code: Catching Errors Early

Writing tests for your code helps to identify and correct errors early on, improving the reliability of your analysis.

#### Types of Tests:

**Unit Tests:**Test individual functions or components of your code in isolation.**Integration Tests:**Verify that different parts of your code work together correctly.

#### Python Testing Frameworks:

**pytest:**A popular testing framework known for its conciseness and flexibility.**unittest:**Python’s built-in testing framework.

By incorporating these best practices into your data analysis workflow, you enhance the transparency, reliability, and impact of your work, fostering trust and collaboration in the process.

## Embracing the Power of Data

As we conclude this exploration of data analysis with Python, remember that you’ve embarked on a journey with limitless possibilities. The ability to extract insights, uncover patterns, and make data-driven decisions is a powerful skill set applicable across industries and domains.

### Key Takeaways

**Python’s Versatility:**Python’s rich ecosystem of libraries makes it a versatile language for data cleaning, analysis, visualization, and machine learning.**From Fundamentals to Advanced Techniques:**Start with the basics and gradually build your knowledge to tackle more complex statistical analyses, time series modeling, and machine learning tasks.**The Importance of Best Practices:**Embrace version control, documentation, and testing to ensure your analyses are robust, reproducible, and reliable.**Continuous Learning and Exploration:**The world of data science is constantly evolving—stay curious, embrace new tools and techniques, and never stop learning!

### The Future of Data Analysis

As data continues to proliferate at an unprecedented rate, the demand for skilled data analysts will only continue to grow. By honing your skills, staying curious, and embracing the power of data, you’ll be well-equipped to navigate this exciting landscape and make meaningful contributions to your chosen field.

## Python for Data Analysis: FAQs

**Q1: What are the essential Python libraries for data analysis?**

**A:** Python boasts a rich ecosystem of libraries for data analysis. Some essentials include:

**NumPy:**The foundation for numerical computing, providing support for arrays, matrices, and mathematical functions.**Pandas:**Offers powerful data structures like DataFrames for data manipulation, cleaning, and analysis.**Matplotlib and Seaborn:**Popular libraries for creating static and visually appealing data visualizations.**SciPy:**Extends NumPy with advanced statistical functions, optimization algorithms, and signal processing tools.**Scikit-learn:**The go-to library for machine learning, providing implementations of various algorithms for classification, regression, clustering, and more.

**Q2: What are the advantages of using Python for data analysis?**

**A:** Python offers several advantages for data analysis:

**Easy to Learn:**Python’s syntax is clear, concise, and beginner-friendly.**Vast Community and Resources:**A large and supportive community provides ample documentation, tutorials, and online forums for assistance.**Extensive Libraries:**As mentioned above, Python has a rich ecosystem of specialized libraries for data analysis, visualization, and machine learning.**Open-Source and Free:**Python is free to use, even for commercial purposes, making it accessible to individuals and organizations of all sizes.

**Q3: How do I handle missing data in Python?**

**A:** Pandas provides flexible methods for handling missing data:

Replace missing values with a specific value (e.g., mean, median) or using different interpolation methods.`fillna()`

:Remove rows or columns containing missing values.`dropna()`

:

The best approach depends on the nature of your data and the goals of your analysis.

**Q4: What are some resources for learning Python for data analysis?**

**A:** Numerous online courses, tutorials, and books cater to various skill levels:

**Online Platforms:**Coursera, edX, DataCamp, Codecademy, and Udemy.**Books:**“Python for Data Analysis” by Wes McKinney, “Data Science from Scratch” by Joel Grus, “Hands-On Machine Learning with Scikit-Learn, Keras & TensorFlow” by Aurélien Géron.**Documentation:**The official documentation of libraries like Pandas, NumPy, and Scikit-learn provides comprehensive information and examples.

**Q5: How can I make my data analysis projects reproducible?**

**A:** Reproducibility is crucial for ensuring the reliability and trustworthiness of your analyses:

**Version Control:**Use Git and GitHub to track code changes and collaborate effectively.**Documentation:**Clearly document your code, data sources, and analysis steps.**Virtual Environments:**Create virtual environments to isolate project dependencies and ensure consistent execution across different machines.