Bayes Theorem Example Essays For Scholarships

Sample Scholarship Essays


If you’re applying for a scholarship, chances are you are going to need to write an essay. Very few scholarship programs are based solely on an application form or transcript. The essay is often the most important part of your application; it gives the scholarship committee a sense of who you are and your dedication to your goals. You’ll want to make sure that your scholarship essay is the best it can possibly be.

Unless specified otherwise, scholarship essays should always use the following formatting:

  • Double spaced
  • Times New Roman font
  • 12 point font
  • One-inch top, bottom, and side margins

Other useful tips to keep in mind include:

  1. Read the instructions thoroughly and make sure you completely understand them before you start writing.
  2. Think about what you are going to write and organize your thoughts into an outline.
  3. Write your essay by elaborating on each point you included in your outline.
  4. Use clear, concise, and simple language throughout your essay.
  5. When you are finished, read the question again and then read your essay to make sure that the essay addresses every point.

For more tips on writing a scholarship essay, check out our Eight Steps Towards a Better Scholarship Essay .


The Book that Made Me a Journalist

Prompt: Describe a book that made a lasting impression on you and your life and why.

It is 6 am on a hot day in July and I’ve already showered and eaten breakfast. I know that my classmates are all sleeping in and enjoying their summer break, but I don’t envy them; I’m excited to start my day interning with a local newspaper doing investigative journalism. I work a typical 8-5 day during my summer vacation and despite the early mornings, nothing has made me happier. Although it wasn't clear to me then, looking back on my high school experiences and everything that led to me to this internship, I believe this path began with a particularly savvy teacher and a little book she gave me to read outside of class.

I was taking a composition class, and we were learning how to write persuasive essays. Up until that point, I had had average grades, but I was always a good writer and my teacher immediately recognized this. The first paper I wrote for the class was about my experience going to an Indian reservation located near my uncle's ranch in southwest Colorado. I wrote of the severe poverty experienced by the people on the reservation, and the lack of access to voting booths during the most recent election. After reading this short story, my teacher approached me and asked about my future plans. No one had ever asked me this, and I wasn't sure how to answer. I said I liked writing and I liked thinking about people who are different from myself. She gave me a book and told me that if I had time to read it, she thought it would be something I would enjoy. I was actually quite surprised that a high school teacher was giving me a book titled Lies My Teacher Told Me. It had never occurred to me that teachers would lie to students. The title intrigued me so much that on Friday night I found myself staying up almost all night reading, instead of going out with friends.

In short, the book discusses several instances in which typical American history classes do not tell the whole story. For example, the author addresses the way that American history classes do not usually address about the Vietnam War, even though it happened only a short time ago. This made me realize that we hadn't discussed the Vietnam War in my own history class! The book taught me that, like my story of the Indian reservation, there are always more stories beyond what we see on the surface and what we’re taught in school. I was inspired to continue to tell these stories and to make that my career.

For my next article for the class, I wrote about the practice of my own high school suspending students, sometimes indefinitely, for seemingly minor offenses such as tardiness and smoking. I found that the number of suspensions had increased by 200% at my school in just three years, and also discovered that students who are suspended after only one offense often drop out and some later end up in prison. The article caused quite a stir. The administration of my school dismissed it, but it caught the attention of my local newspaper. A local journalist worked with me to publish an updated and more thoroughly researched version of my article in the local newspaper. The article forced the school board to revisit their “zero tolerance” policy as well as reinstate some indefinitely suspended students.I won no favors with the administration and it was a difficult time for me, but it was also thrilling to see how one article can have such a direct effect on people’s lives. It reaffirmed my commitment to a career in journalism.

This is why I’m applying for this scholarship. Your organization has been providing young aspiring journalists with funds to further their skills and work to uncover the untold stories in our communities that need to be reported. I share your organization’s vision of working towards a more just and equitable world by uncovering stories of abuse of power. I have already demonstrated this commitment through my writing in high school and I look forward to pursuing a BA in this field at the University of Michigan Ann Arbor. With your help, I will hone my natural instincts and inherent writing skills. I will become a better and more persuasive writer and I will learn the ethics of professional journalism.

I sincerely appreciate the committee’s time in evaluating my application and giving me the opportunity to tell my story. I look forward to hearing from you soon.

Scholarship Essay Do's and Don'ts

Do:Follow the prompt and other instructions exactly. You might write a great essay but it may get your application rejected if you don’t follow the word count guidelines or other formatting requirements.
DON'T:Open your essay with a quote. This is a well-worn strategy that is mostly used ineffectively. Instead of using someone else’s words, use your own.
DON'T:Use perfunctory sentences such as, “In this essay, I will…”
DO:Be clear and concise. Make sure each paragraph discusses only one central thought or argument.
DON'T:Use words from a thesaurus that are new to you. You may end up using the word incorrectly and that will make your writing awkward. Keep it simple and straightforward. The point of the essay is to tell your story, not to demonstrate how many words you know.

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Planners and Searchers

Prompt: In 600 words or less, please tell us about yourself and why you are applying for this scholarship. Please be clear about how this scholarship will help you achieve your personal and professional goals.

Being African, I recognize Africa’s need for home- grown talent in the form of “planners” (assistants with possible solutions) and “searchers” (those with desperate need) working towards international development. I represent both. Coming from Zimbabwe my greatest challenge is in helping to improve the livelihoods of developing nations through sustainable development and good governance principles. The need for policy-makers capable of employing cross-jurisdictional, and cross- disciplinary strategies to solve complex challenges cannot be under-emphasized; hence my application to this scholarship program.

After graduating from Africa University with an Honors degree in Sociology and Psychology, I am now seeking scholarship support to study in the United States at the Master’s level. My interest in democracy, elections, constitutionalism and development stems from my lasting interest in public policy issues. Accordingly, my current research interests in democracy and ethnic diversity require a deeper understanding of legal processes of constitutionalism and governance. As a Master’s student in the US, I intend to write articles on these subjects from the perspective of someone born, raised, and educated in Africa. I will bring a unique and much-needed perspective to my graduate program in the United States, and I will take the technical and theoretical knowledge from my graduate program back with me to Africa to further my career goals as a practitioner of good governance and community development.

To augment my theoretical understanding of governance and democratic practices, I worked with the Zimbabwe Election Support Network (ZESN) as a Programs Assistant in the Monitoring and Observation department. This not only enhanced my project management skills, but also developed my skills in research and producing communication materials. ZESN is Zimbabwe’s biggest election observation organization, and I had the responsibility of monitoring the political environment and producing monthly publications on human rights issues and electoral processes. These publications were disseminated to various civil society organizations, donors and other stakeholders. Now I intend to develop my career in order to enhance Africa’s capacity to advocate, write and vote for representative constitutions.

I also participated in a fellowship program at Africa University, where I gained greater insight into social development by teaching courses on entrepreneurship, free market economics, and development in needy communities. I worked with women in rural areas of Zimbabwe to setup income-generating projects such as the jatropha soap-making project. Managing such a project gave me great insight into how many simple initiatives can transform lives.

Your organization has a history of awarding scholarships to promising young students from the developing world in order to bring knowledge, skills and leadership abilities to their home communities. I have already done some of this work but I want to continue, and with your assistance, I can. The multidisciplinary focus of the development programs I am applying to in the US will provide me with the necessary skills to creatively address the economic and social development challenges and develop sound public policies for Third World countries. I thank you for your time and consideration for this prestigious award.

Scholarship Essay Do's and Don'ts

DO:Research the organization and make sure you understand their mission and values and incorporate them into your essay.
DO:Focus on your strengths and turn in any problems or weaknesses into a success story.
DO:Use actual, detailed examples from your own life to backup your claims and arguments as to why you should receive the scholarship.
DO:Proofread several times before finally submitting your essay.
DON'T:Rehash what is already stated on your resume. Choose additional, unique stories to tell sell yourself to the scholarship committee.
DON'T:Simply state that you need the money. Even if you have severe financial need, it won’t help to simply ask for the money and it may come off as tacky.

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Saving the Manatees

Prompt: Please give the committee an idea of who you are and why you are the perfect candidate for the scholarship.

It is a cliché to say that I’ve always known what I want to do with my life, but in my case it happens to be true. When I first visited Sea World as a young child, I fell in love with marine animals in general. Specifically, I felt drawn to manatees. I was compelled by their placid and friendly nature. I knew then and there that I wanted to dedicate my life to protecting these beautiful creatures.

Since that day in Orlando, I have spent much of my spare time learning everything there is to know about manatees. As a junior high and high school student, I attempted to read scholarly articles on manatees from scientific journals. I annoyed my friends and family with scientific facts about manatees-- such as that they are close relatives of elephants--at the dinner table. I watched documentaries, and even mapped their migration pattern on a wall map my sister gave me for my birthday.

When I was chosen from hundreds of applicants to take part in a summer internship with Sea World, I fell even more in love with these gentle giants. I also learned a very important and valuable lesson: prior to this internship, I had imagined becoming a marine biologist, working directly with the animals in their care both in captivity and in the wild. However, during the internship, I discovered that this is not where my strengths lie. Unfortunately, I am not a strong student in science or math, which are required skills to become a marine biologist. Although this was a disheartening realization, I found that I possess other strengths can still be of great value to manatees and other endangered marine mammals: my skills as a public relations manager and communicator. During the internship, I helped write new lessons and presentations for elementary school groups visiting the park and developed a series of fun activities for children to help them learn more about manatees as well as conservation of endangered species in general. I also worked directly with the park’s conservation and communication director, and helped develop a new local outreach program designed to educate Floridians on how to avoid hitting a manatee when boating. My supervisor recommended me to the Save the Manatee Foundation so in addition to my full-time internship at Sea World, I interned with the Save the Manatee Foundation part-time. It was there that I witnessed the manatee rescue and conservation effort first hand, and worked directly with the marine biologists in developing fund-raising and awareness-raising campaigns. I found that the foundation’s social media presence was lacking, and, using skills I learned from Sea World, I helped them raise over $5,000 through a Twitter challenge, which we linked to the various social media outlets of the World Wildlife Federation.

While I know that your organization typically awards scholarships to students planning to major in disciplines directly related to conservation such as environmental studies or zoology, I feel that the public relations side of conservation is just as important as the actual work done on the ground. Whether it is reducing one’s carbon footprint, or saving the manatees, these are efforts that, in order to be successful, must involve the larger public. In fact, the relative success of the environmental movement today is largely due to a massive global public relations campaign that turned environmentalism from something scientific and obscure into something that is both fashionable and accessible to just about anyone. However, that success is being challenged more than ever before--especially here in the US, where an equally strong anti-environmental public relations campaign has taken hold. Therefore, conservationists need to start getting more creative.

I want to be a part of this renewed effort and use my natural abilities as a communicator to push back against the rather formidable forces behind the anti-environmentalist movement. I sincerely hope you will consider supporting this non-traditional avenue towards global sustainability and conservation. I have already been accepted to one of the most prestigious communications undergraduate programs in the country and I plan to minor in environmental studies. In addition, I maintain a relationship with my former supervisors at Save the Manatee and Sea World, who will be invaluable resources for finding employment upon graduation. I thank the committee for thinking outside the box in considering my application.

Scholarship Essay Do's and Don'ts

DO:Tell a story. Discuss your personal history and why those experiences have led you to apply for these scholarships.
DO:Write an outline. If you’ve already started writing or have a first draft, make an outline based on what you’ve written so far. This will help you see whether your paragraphs flow and connect with one another.
DON'T:Write a generic essay for every application. Adapt your personal statement for each individual scholarship application.
DO:Run spellcheck and grammar check on your computer but also do your own personal check. Spellcheck isn’t perfect and you shouldn't rely on technology to make your essay perfect.

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Sample Essays

Related Content:

Bayes’ theorem was the subject of a detailed article. The essay is good, but over 15,000 words long — here’s the condensed version for Bayesian newcomers like myself:

  • Tests are not the event. We have a cancer test, separate from the event of actually having cancer. We have a test for spam, separate from the event of actually having a spam message.

  • Tests are flawed. Tests detect things that don’t exist (false positive), and miss things that do exist (false negative).

  • Tests give us test probabilities, not the real probabilities. People often consider the test results directly, without considering the errors in the tests.

  • False positives skew results. Suppose you are searching for something really rare (1 in a million). Even with a good test, it’s likely that a positive result is really a false positive on somebody in the 999,999.

  • People prefer natural numbers. Saying “100 in 10,000″ rather than “1%” helps people work through the numbers with fewer errors, especially with multiple percentages (“Of those 100, 80 will test positive” rather than “80% of the 1% will test positive”).

  • Even science is a test. At a philosophical level, scientific experiments can be considered “potentially flawed tests” and need to be treated accordingly. There is a test for a chemical, or a phenomenon, and there is the event of the phenomenon itself. Our tests and measuring equipment have some inherent rate of error.

Bayes’ theorem converts the results from your test into the real probability of the event. For example, you can:

  • Correct for measurement errors. If you know the real probabilities and the chance of a false positive and false negative, you can correct for measurement errors.

  • Relate the actual probability to the measured test probability. Bayes’ theorem lets you relate Pr(A|X), the chance that an event A happened given the indicator X, and Pr(X|A), the chance the indicator X happened given that event A occurred. Given mammogram test results and known error rates, you can predict the actual chance of having cancer.

Anatomy of a Test

The article describes a cancer testing scenario:

  • 1% of women have breast cancer (and therefore 99% do not).
  • 80% of mammograms detect breast cancer when it is there (and therefore 20% miss it).
  • 9.6% of mammograms detect breast cancer when it’s not there (and therefore 90.4% correctly return a negative result).

Put in a table, the probabilities look like this:

How do we read it?

  • 1% of people have cancer
  • If you already have cancer, you are in the first column. There’s an 80% chance you will test positive. There’s a 20% chance you will test negative.
  • If you don’t have cancer, you are in the second column. There’s a 9.6% chance you will test positive, and a 90.4% chance you will test negative.

How Accurate Is The Test?

Now suppose you get a positive test result. What are the chances you have cancer? 80%? 99%? 1%?

Here’s how I think about it:

  • Ok, we got a positive result. It means we’re somewhere in the top row of our table. Let’s not assume anything — it could be a true positive or a false positive.
  • The chances of a true positive = chance you have cancer * chance test caught it = 1% * 80% = .008
  • The chances of a false positive = chance you don’t have cancer * chance test caught it anyway = 99% * 9.6% = 0.09504

The table looks like this:

And what was the question again? Oh yes: what’s the chance we really have cancer if we get a positive result. The chance of an event is the number of ways it could happen given all possible outcomes:

The chance of getting a real, positive result is .008. The chance of getting any type of positive result is the chance of a true positive plus the chance of a false positive (.008 + 0.09504 = .10304).

So, our chance of cancer is .008/.10304 = 0.0776, or about 7.8%.

Interesting — a positive mammogram only means you have a 7.8% chance of cancer, rather than 80% (the supposed accuracy of the test). It might seem strange at first but it makes sense: the test gives a false positive 9.6% of the time (quite high), so there will be many false positives in a given population. For a rare disease, most of the positive test results will be wrong.

Let’s test our intuition by drawing a conclusion from simply eyeballing the table. If you take 100 people, only 1 person will have cancer (1%), and they’re most likely going to test positive (80% chance). Of the 99 remaining people, about 10% will test positive, so we’ll get roughly 10 false positives. Considering all the positive tests, just 1 in 11 is correct, so there’s a 1/11 chance of having cancer given a positive test. The real number is 7.8% (closer to 1/13, computed above), but we found a reasonable estimate without a calculator.

Bayes’ Theorem

We can turn the process above into an equation, which is Bayes’ Theorem. It lets you take the test results and correct for the “skew” introduced by false positives. You get the real chance of having the event. Here’s the equation:

And here’s the decoder key to read it:

  • Pr(A|X) = Chance of having cancer (A) given a positive test (X). This is what we want to know: How likely is it to have cancer with a positive result? In our case it was 7.8%.
  • Pr(X|A) = Chance of a positive test (X) given that you had cancer (A). This is the chance of a true positive, 80% in our case.
  • Pr(A) = Chance of having cancer (1%).
  • Pr(not A) = Chance of not having cancer (99%).
  • Pr(X|not A) = Chance of a positive test (X) given that you didn’t have cancer (~A). This is a false positive, 9.6% in our case.

Try it with any number:

It all comes down to the chance of a true positive result divided by the chance of any positive result. We can simplify the equation to:

Pr(X) is a normalizing constant and helps scale our equation. Without it, we might think that a positive test result gives us an 80% chance of having cancer.

Pr(X) tells us the chance of getting any positive result, whether it’s a real positive in the cancer population (1%) or a false positive in the non-cancer population (99%). It’s a bit like a weighted average, and helps us compare against the overall chance of a positive result.

In our case, Pr(X) gets really large because of the potential for false positives. Thank you, normalizing constant, for setting us straight! This is the part many of us may neglect, which makes the result of 7.8% counter-intuitive.

Intuitive Understanding: Shine The Light

The article mentions an intuitive understanding about shining a light through your real population and getting a test population. The analogy makes sense, but it takes a few thousand words to get there :).

Consider a real population. You do some tests which “shines light” through that real population and creates some test results. If the light is completely accurate, the test probabilities and real probabilities match up. Everyone who tests positive is actually “positive”. Everyone who tests negative is actually “negative”.

But this is the real world. Tests go wrong. Sometimes the people who have cancer don’t show up in the tests, and the other way around.

Bayes’ Theorem lets us look at the skewed test results and correct for errors, recreating the original population and finding the real chance of a true positive result.

Bayesian Spam Filtering

One clever application of Bayes’ Theorem is in spam filtering. We have

  • Event A: The message is spam.
  • Test X: The message contains certain words (X)

Plugged into a more readable formula (from Wikipedia):

Bayesian filtering allows us to predict the chance a message is really spam given the “test results” (the presence of certain words). Clearly, words like “viagra” have a higher chance of appearing in spam messages than in normal ones.

Spam filtering based on a blacklist is flawed — it’s too restrictive and false positives are too great. But Bayesian filtering gives us a middle ground — we use probabilities. As we analyze the words in a message, we can compute the chance it is spam (rather than making a yes/no decision). If a message has a 99.9% chance of being spam, it probably is. As the filter gets trained with more and more messages, it updates the probabilities that certain words lead to spam messages. Advanced Bayesian filters can examine multiple words in a row, as another data point.

Further Reading

There’s a lot being said about Bayes:

Have fun!

Other Posts In This Series

  1. A Brief Introduction to Probability & Statistics
  2. An Intuitive (and Short) Explanation of Bayes' Theorem
  3. Understanding Bayes Theorem With Ratios
  4. Understanding the Monty Hall Problem
  5. How To Analyze Data Using the Average
  6. Understanding the Birthday Paradox

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