Bayes' theorem describes the probability of an event based on prior knowledge of conditions related to the event. For example, a person's age can make the probability of them having cancer more accurate than without knowing their age. Bayesian inference applies Bayes' theorem to statistical analysis by updating probabilities based on new evidence. The example problem calculates probabilities of drawing a red ball from two bags with different numbers of red and black balls using Bayes' theorem. It finds the probability of a red ball being from bag A given that a red ball was drawn is 2/5 divided by the total probability of drawing a red ball from either bag.
It gives detail description about probability, types of probability, difference between mutually exclusive events and independent events, difference between conditional and unconditional probability and Bayes' theorem
It gives detail description about probability, types of probability, difference between mutually exclusive events and independent events, difference between conditional and unconditional probability and Bayes' theorem
In this presentation is given an introduction to Bayesian networks and basic probability theory. Graphical explanation of Bayes' theorem, random variable, conditional and joint probability. Spam classifier, medical diagnosis, fault prediction. The main software for Bayesian Networks are presented.
Data Science - Part XII - Ridge Regression, LASSO, and Elastic NetsDerek Kane
This lecture provides an overview of some modern regression techniques including a discussion of the bias variance tradeoff for regression errors and the topic of shrinkage estimators. This leads into an overview of ridge regression, LASSO, and elastic nets. These topics will be discussed in detail and we will go through the calibration/diagnostics and then conclude with a practical example highlighting the techniques.
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.
Many decisions are based on beliefs concerning the likelihoo.docxalfredacavx97
Many decisions are based on beliefs
concerning the likelihood of uncertain
events such as the outcome of an elec-
tion, the guilt of a defendant, or the
future value of the dollar. These beliefs
are usually expressed in statements such
as "I think that . .. ," "chances are
. . .," "it is unlikely that . .. ," and
so forth. Occasionally, beliefs concern-
ing uncertain events are expressed in
numerical form as odds or subjective
probabilities. What determines such be-
liefs? How do people assess the prob-
ability of an uncertain event or the
value of an uncertain quantity? This
article shows that people rely on a
limited number of heuristic principles
which reduce the complex tasks of as-
sessing probabilities and predicting val-
ues to simpler judgmental operations.
In general, these heuristics are quite
useful, but sometimes they lead to severe
and systematic errors.
The subjective assessment of proba-
bility resembles the subjective assess-
ment of physical quantities such as
distance or size. These judgments are
all based on data of limited validity,
which are processed according to heu-
ristic rules. For example, the apparent
distance of an object is determined in
part by its clarity. The more sharply the
object is seen, the closer it appears to
be. This rule has some validity, because
in any given scene the more distant
objects are seen less sharply than nearer
objects. However, the reliance on this
rule leads to systematic errors in the
estimation of distance. Specifically, dis-
tances are often overestimated when
visibility is poor because the contours
of objects are blurred. On the other
hand, distances are often underesti-
mated when visibility is good because
the objects are seen sharply. Thus, the
reliance on clarity as an indication of
distance leads to common biases. Such
biases are also found in the intuitive
judgment of probability. This article
describes three heuristics that are em-
ployed to assess probabilities and to
predict values. Biases to which these
heuristics lead are enumerated, and the
applied and theoretical implications of
these observations are discussed.
Representativeness
Many of the probabilistic questions
with which people are concerned belong
to one of the following types: What is
the probability that object A belongs to
class B? What is the probability that
event A originates from process B?
What is the probability that process B
will generate event A? In answering
such questions, people typically rely on
the representativeness heuristic, in
which probabilities are evaluated by the
degree to which A is representative of
B, that is, by the degree to which A
resembles B. For example, when A is
highly representative of B, the proba-
bility that A originates from B is judged
to be high. On the other hand, if A is
not similar to B, the probability that A
originates from B is judged to be low.
For an illustration of judgment b.
In this presentation is given an introduction to Bayesian networks and basic probability theory. Graphical explanation of Bayes' theorem, random variable, conditional and joint probability. Spam classifier, medical diagnosis, fault prediction. The main software for Bayesian Networks are presented.
Data Science - Part XII - Ridge Regression, LASSO, and Elastic NetsDerek Kane
This lecture provides an overview of some modern regression techniques including a discussion of the bias variance tradeoff for regression errors and the topic of shrinkage estimators. This leads into an overview of ridge regression, LASSO, and elastic nets. These topics will be discussed in detail and we will go through the calibration/diagnostics and then conclude with a practical example highlighting the techniques.
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.
Many decisions are based on beliefs concerning the likelihoo.docxalfredacavx97
Many decisions are based on beliefs
concerning the likelihood of uncertain
events such as the outcome of an elec-
tion, the guilt of a defendant, or the
future value of the dollar. These beliefs
are usually expressed in statements such
as "I think that . .. ," "chances are
. . .," "it is unlikely that . .. ," and
so forth. Occasionally, beliefs concern-
ing uncertain events are expressed in
numerical form as odds or subjective
probabilities. What determines such be-
liefs? How do people assess the prob-
ability of an uncertain event or the
value of an uncertain quantity? This
article shows that people rely on a
limited number of heuristic principles
which reduce the complex tasks of as-
sessing probabilities and predicting val-
ues to simpler judgmental operations.
In general, these heuristics are quite
useful, but sometimes they lead to severe
and systematic errors.
The subjective assessment of proba-
bility resembles the subjective assess-
ment of physical quantities such as
distance or size. These judgments are
all based on data of limited validity,
which are processed according to heu-
ristic rules. For example, the apparent
distance of an object is determined in
part by its clarity. The more sharply the
object is seen, the closer it appears to
be. This rule has some validity, because
in any given scene the more distant
objects are seen less sharply than nearer
objects. However, the reliance on this
rule leads to systematic errors in the
estimation of distance. Specifically, dis-
tances are often overestimated when
visibility is poor because the contours
of objects are blurred. On the other
hand, distances are often underesti-
mated when visibility is good because
the objects are seen sharply. Thus, the
reliance on clarity as an indication of
distance leads to common biases. Such
biases are also found in the intuitive
judgment of probability. This article
describes three heuristics that are em-
ployed to assess probabilities and to
predict values. Biases to which these
heuristics lead are enumerated, and the
applied and theoretical implications of
these observations are discussed.
Representativeness
Many of the probabilistic questions
with which people are concerned belong
to one of the following types: What is
the probability that object A belongs to
class B? What is the probability that
event A originates from process B?
What is the probability that process B
will generate event A? In answering
such questions, people typically rely on
the representativeness heuristic, in
which probabilities are evaluated by the
degree to which A is representative of
B, that is, by the degree to which A
resembles B. For example, when A is
highly representative of B, the proba-
bility that A originates from B is judged
to be high. On the other hand, if A is
not similar to B, the probability that A
originates from B is judged to be low.
For an illustration of judgment b.
On Severity, the Weight of Evidence, and the Relationship Between the Twojemille6
Margherita Harris
Visiting fellow in the Department of Philosophy, Logic and Scientific Method at the London
School of Economics and Political Science.
ABSTRACT: According to the severe tester, one is justified in declaring to have evidence in support of a
hypothesis just in case the hypothesis in question has passed a severe test, one that it would be very
unlikely to pass so well if the hypothesis were false. Deborah Mayo (2018) calls this the strong
severity principle. The Bayesian, however, can declare to have evidence for a hypothesis despite not
having done anything to test it severely. The core reason for this has to do with the
(infamous) likelihood principle, whose violation is not an option for anyone who subscribes to the
Bayesian paradigm. Although the Bayesian is largely unmoved by the incompatibility between
the strong severity principle and the likelihood principle, I will argue that the Bayesian’s never-ending
quest to account for yet an other notion, one that is often attributed to Keynes (1921) and that is
usually referred to as the weight of evidence, betrays the Bayesian’s confidence in the likelihood
principle after all. Indeed, I will argue that the weight of evidence and severity may be thought of as
two (very different) sides of the same coin: they are two unrelated notions, but what brings them
together is the fact that they both make trouble for the likelihood principle, a principle at the core of
Bayesian inference. I will relate this conclusion to current debates on how to best conceptualise
uncertainty by the IPCC in particular. I will argue that failure to fully grasp the limitations of an
epistemology that envisions the role of probability to be that of quantifying the degree of belief to
assign to a hypothesis given the available evidence can be (and has been) detrimental to an
adequate communication of uncertainty.
Conditional-probability-and-Bioinformatics.pptxRITHIKA R S
The possibility of an event or outcome occurring depending on the occurrence of a previous event or outcome is defined as conditional probability. Conditional probability is calculated by multiplying the preceding event's probability by the updated probability of the following, or conditional, event.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2. In probability theory and statistics, Bayes'
theorem (alternatively Bayes' law or Bayes'
rule) describes the probability of an event,
based on prior knowledge of conditions that
might be related to the event. For example,
if cancer is related to age, then, using
Bayes' theorem, a person's age can be used
to more accurately assess the probability
that they have cancer, compared to the
assessment of the probability of cancer
made without knowledge of the person's
age.
3. One of the many applications of Bayes'
theorem is Bayesian inference, a particular
approach to statistical inference. When
applied, the probabilities involved in Bayes'
theorem may have different probability
interpretations. With the Bayesian
probability interpretation the theorem
expresses how a subjective degree of belief
should rationally change to account for
availability of related evidence. Bayesian
inference is fundamental to Bayesian statistics.
4. We have two bags contains Red & black
Balls..
A B
RED 2
BLACK 3
A
RED 3
BLACK 4
5. Case 1: what is the probability of get’s Red Ball
from bag A??? { bag A is already selected}
Should be written as…
P(R/A) = 2/5
6. Case 2: what is the probability of Red Ball
drawn from bag A???
P(A ∩ R) = P(A)P(R/A)
Probability of
Red ball and
from bag A
7. Case 3: what is the probability of Red Ball???
P(R)=P(A ∩ R) + P(B ∩ R)
Probability of
getting red ball
from bag A
Probability of
getting red ball
from bag B
8. Case 4: Given that red ball is drawn .what is
the probability that the Ball is from bag A ???
P(A/R)=
P(A ∩ R)
P(A ∩ R) + P(B ∩ R)