It includes various cases and practice problems related to Binomial, Poisson & Normal Distributions. Detailed information on where tp use which probability.
It includes various cases and practice problems related to Binomial, Poisson & Normal Distributions. Detailed information on where tp use which probability.
A Probability Distribution is a way to shape the sample data to make predictions and draw conclusions about an entire population. It refers to the frequency at which some events or experiments occur. It helps finding all the possible values a random variable can take between the minimum and maximum statistically possible values.
A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution. Suppose we flip a coin two times and count the number of heads (successes).
Testing of hypothesis - large sample testParag Shah
Different type of test which are used for large sample has been included in this presentation. Steps for each test and a case study is included for concept clarity and practice.
A Probability Distribution is a way to shape the sample data to make predictions and draw conclusions about an entire population. It refers to the frequency at which some events or experiments occur. It helps finding all the possible values a random variable can take between the minimum and maximum statistically possible values.
A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution. Suppose we flip a coin two times and count the number of heads (successes).
Testing of hypothesis - large sample testParag Shah
Different type of test which are used for large sample has been included in this presentation. Steps for each test and a case study is included for concept clarity and practice.
This talk on Bayesian statistics is tailored especially for biologists and ecologists. The main points are to highlight what the particular benefit to use Bayesian is in comparison to frequentist statistics and to understand the essence for practical application for scientific purposes.
Chris Stuccio - Data science - Conversion Hotel 2015Webanalisten .nl
Slides of the keynote by Chris Stuccio (USA) at Conversion Hotel 2015, Texel, the Netherlands (#CH2015): "What’s this all about data science? Explain baysian statistics to me as a kid – what should I know?" http://conversionhotel.com
What should we expect from reproducibiliryStephen Senn
Is there really a reproducibility crisis and if so are P-values to blame? Choose any statistic you like and carry out two identical independent studies and report this statistic for each. In advance of collecting any data, you ought to expect that it is just as likely that statistic 1 will be smaller than statistic 2 as vice versa. Once you have seen statistic 1, things are not so simple but if they are not so simple, it is that you have other information in some form. However, it is at least instructive that you need to be careful in jumping to conclusions about what to expect from reproducibility. Furthermore, the forecasts of good Bayesians ought to obey a Martingale property. On average you should be in the future where you are now but, of course, your inferential random walk may lead to some peregrination before it homes in on “the truth”. But you certainly can’t generally expect that a probability will get smaller as you continue. P-values, like other statistics are a position not a movement. Although often claimed, there is no such things as a trend towards significance.
Using these and other philosophical considerations I shall try and establish what it is we want from reproducibility. I shall conclude that we statisticians should probably be paying more attention to checking that standard errors are being calculated appropriately and rather less to inferential framework.
This presentation discusses the following topics:
Basic features of R
Exploring R GUI
Data Frames & Lists
Handling Data in R Workspace
Reading Data Sets & Exporting Data from R
Manipulating & Processing Data in R
A study on “Diagnosis Test of Diabetics and Hypertension by AI”, Presentation slides for International Conference on "Life Sciences: Acceptance of the New Normal", St. Aloysius' College, Jabalpur, Madhya Pradesh, India, 27-28 August, 2021
A study on “impact of artificial intelligence in covid19 diagnosis”Dr. C.V. Suresh Babu
A study on “Impact of Artificial Intelligence in COVID-19 Diagnosis”, Presentation slides for International Conference on "Life Sciences: Acceptance of the New Normal", St. Aloysius' College, Jabalpur, Madhya Pradesh, India, 27-28 August, 2021
A study on “impact of artificial intelligence in covid19 diagnosis”Dr. C.V. Suresh Babu
Although the lungs are one of the most vital organs in the body, they are vulnerable to infection and injury. COVID-19 has put the entire world in an unprecedented difficult situation, bringing life to a halt and claiming thousands of lives all across the world. Medical imaging, such as X-rays and computed tomography (CT), is essential in the global fight against COVID-19, and newly emerging artificial intelligence (AI) technologies are boosting the power of imaging tools and assisting medical specialists. AI can improve job efficiency by precisely identifying infections in X-ray and CT images and allowing further measurement. We focus on the integration of AI with X-ray and CT, both of which are routinely used in frontline hospitals, to reflect the most recent progress in medical imaging and radiology combating COVID-19.
A study on “the impact of data analytics in covid 19 health care system”Dr. C.V. Suresh Babu
A Study on “The Impact of Data Analytics in COVID-19 Health Care System”, Presentation slides for International Conference on "Life Sciences: Acceptance of the New Normal", St. Aloysius' College, Jabalpur, Madhya Pradesh, India, 27-28 August, 2021
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
2. Introduction
• Bayes' theorem is also known as Bayes' rule, Bayes' law, or Bayesian
reasoning, which determines the probability of an event with
uncertain knowledge.
• In probability theory, it relates the conditional probability and
marginal probabilities of two random events.
• Bayes' theorem was named after the British mathematician Thomas
Bayes. The Bayesian inference is an application of Bayes' theorem,
which is fundamental to Bayesian statistics.
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3. What is Bayes Theorem?
• Bayes Theorem is a method of calculating conditional probability.
• The traditional method of calculating conditional probability (the
probability that one event occurs given the occurrence of a different
event) is to use the conditional probability formula, calculating the
joint probability of event one and event two occurring at the same
time, and then dividing it by the probability of event two occurring.
• However, conditional probability can also be calculated in a slightly
different fashion by using Bayes Theorem.
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4. • When calculating conditional probability with Bayes theorem, you use the
following steps:
• Determine the probability of condition B being true, assuming that condition
A is true.
• Determine the probability of event A being true.
• Multiply the two probabilities together.
• Divide by the probability of event B occurring.
• This means that the formula for Bayes Theorem could be expressed like this:
P(A|B) = P(B|A)*P(A) / P(B)
• Calculating the conditional probability like this is especially useful when the
reverse conditional probability can be easily calculated, or when calculating
the joint probability would be too challenging.
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5. How?
• It is a way to calculate the value of P(B|A) with the knowledge of
P(A|B)
• Bayes' theorem allows updating the probability prediction of an event
by observing new information of the real world.
• Example: If cancer corresponds to one's age then by using Bayes'
theorem, we can determine the probability of cancer more accurately
with the help of age.
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6. Bayes' theorem
• Bayes' theorem can be derived using product rule and conditional probability of
event A with known event B:
• As from product rule we can write:
• P(A ⋀ B)= P(A|B) P(B) or
• imilarly, the probability of event B with known event A:
• P(A ⋀ B)= P(B|A) P(A)
• Equating right hand side of both the equations, we will get:
• The above equation (a) is called as Bayes' rule or Bayes' theorem. This equation
is basic of most modern AI systems for probabilistic inference.
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8. • It shows the simple relationship between joint and conditional
probabilities. Here,
• P(A|B) is known as posterior, which we need to calculate, and it will be
read as Probability of hypothesis A when we have occurred an evidence B.
• P(B|A) is called the likelihood, in which we consider that hypothesis is true,
then we calculate the probability of evidence.
• P(A) is called the prior probability, probability of hypothesis before
considering the evidence
• P(B) is called marginal probability, pure probability of an evidence.
• In the equation (a), in general, we can write P (B) = P(A)*P(B|Ai), hence the
Bayes' rule can be written as:
• Where A1, A2, A3,........, An is a set of mutually exclusive and exhaustive
events.
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9. Applying Bayes' rule:
• Bayes' rule allows us to compute the single term P(B|A) in terms of
P(A|B), P(B), and P(A).
• This is very useful in cases where we have a good probability of these
three terms and want to determine the fourth one.
• Suppose we want to perceive the effect of some unknown cause, and
want to compute that cause, then the Bayes' rule becomes:
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10. Example #1
Question: what is the probability that a patient has diseases meningitis with a
stiff neck?
Given Data:
• A doctor is aware that disease meningitis causes a patient to have a stiff neck,
and it occurs 80% of the time.
• He is also aware of some more facts, which are given as follows:
• The Known probability that a patient has meningitis disease is 1/30,000.
• The Known probability that a patient has a stiff neck is 2%.
Let a be the proposition that patient has stiff neck and b be the proposition that
patient has meningitis. , so we can calculate the following as:
P(a|b) = 0.8
P(b) = 1/30000
P(a)= .02
Hence, we can assume that 1 patient out of 750 patients has meningitis
disease with a stiff neck.
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11. Example #2:
• Question: From a standard deck of playing cards, a single card is drawn. The probability
that the card is king is 4/52, then calculate posterior probability P(King|Face), which
means the drawn face card is a king card.
• Solution:
• P(king): probability that the card is King= 4/52= 1/13
• P(face): probability that a card is a face card= 3/13
• P(Face|King): probability of face card when we assume it is a king = 1
• Putting all values in equation (i) we will get:
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12. • Imagine you are a financial analyst at an investment bank. According to your research of publicly-
traded companies, 60% of the companies that increased their share price by more than 5% in the
last three years replaced their CEOs during the period.
• At the same time, only 35% of the companies that did not increase their share price by more
than 5% in the same period replaced their CEOs. Knowing that the probability that the stock
prices grow by more than 5% is 4%, find the probability that the shares of a company that fires
its CEO will increase by more than 5%.
• Before finding the probabilities, you must first define the notation of the probabilities.
• P(A) – the probability that the stock price increases by 5%
• P(B) – the probability that the CEO is replaced
• P(A|B) – the probability of the stock price increases by 5% given that the CEO has been replaced
• P(B|A) – the probability of the CEO replacement given the stock price has increased by 5%.
• Using the Bayes’ theorem, we can find the required probability:
Example #3:
Thus, the probability that the shares of a company that replaces its CEO will grow by more
than 5% is 6.67%.
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13. • Using the cancer diagnosis example, we can show that Bayes rule allows us to obtain a much
better estimate.
• Now, we will put some made-up numbers into the example so we can assess the difference that
Bayes rule made.
• Assume that the probability of having cancer is 0.05 — meaning that 5% of people have cancer.
• Now, assume that the probability of being a smoker is 0.10 — meaning that 10% of people are
smokers, and that 20% of people with cancer are smokers, so P(smoker|cancer) = 0.20.
• Initially, our probability for cancer is simply our prior, so 0.05.
• However, using new evidence, we can instead calculate P(cancer|smoke), which is equal to
(P(smoker|cancer) * P(cancer)) / P(smoker) = (0.20 * 0.05) / (0.10) = 0.10.
• By introducing new evidence, we therefore obtained a better probability estimation.
• Initially we had a probability of 0.05, but using the smoker evidence, we were able to get to a
more accurate probability that was double our prior.
• In the given example (even with our made-up numbers), this effect should be quite logical, since
we know that smoking causes cancer.
This therefore demonstrates how Bayes rule allows us to update our beliefs using relevant
information.
Example #4:
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14. Applications of Bayes' theorem
• It is used to calculate the next step of the robot when the already
executed step is given.
• Bayes' theorem is helpful in weather forecasting.
• It can solve the Monty Hall problem.
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