Probability theory

In definition, probability refers to the measure of the likelihood of an event happening. The probability for any event occurring falls between 1 percent and 100 percent thus meaning that the interpreted meaning of a probability equals the subject meaning held of the probability (Grinstead et al, 1997). However, it is worth noting that the application of probability or assigning of probability to the events in the effort to gratifying the axioms of probability follows some rules or basics…

This September, I started my MSc at UBC SPPH with a goal of becoming a researcher on clinical trials. During the past semester, I discovered I love it more than I could imagine. I enjoy everything that I am doing, especially my research which I can work until 3 am in the morning without feeling tired or exhausted. I count myself as a fortunate person as I have found what I love, unlike many other people who spend their entire life looking for what they like. However, as a person who wants to…

position offsets from the INS position each time it is started. Point Mass Filter (PMF) PMF is a calculation that determines the position probability density function (PDF), as said by (N. Bergman, 1999). The point mass filter estimator the priori position distributions together with the error models of the depth measurements and the map to produce a posteriori probability…

These factors could also help explain the decisions that people are making, or they could be a useful proxy for another factor such as numeracy. Age. Older individuals don’t understand risk information as well, both overestimate and underestimate probabilities (Fuller, Dudley, & Blacktop, 2001), worse risk comprehension than younger individuals (Fausset & Rogers, 2012). Much of the literature supports the idea that decision making effectiveness…

The popular Monty Hall Problem is about being on a game show where you’re either going to win a fancy sports car or a goat. It’s a no brainer on which one you would prefer: the car. You have to choose between three doors. Behind two of the doors are goats and the fancy car is the last one. Whichever door you choose, the prize behind it is yours. The sample space is one thing to consider in this problem. There is a winning door and the two remaining doors are x and y and have goats behind them…

"Struck by Lightning: the curious world of probabilities" is a book written in 2005 by Jeffrey S. Rosenthal, an award-winning Canadian statistician and author. Jeffrey S. Rosenthal graduated from Woburn Collegiate Institute in 1984, received his B.Sc. in mathematics, physics and computer science in Toronto in 1988. He later received his PhD in mathematics in Harvard University in 1992. He performs music and improv. comedy as well as being an author and supervisor of student projects. "Struck by…

This uncertainty includes the quantities resulting from lack of sufficient information. Another important concept in Bayesian methods are the need to determine the prior probability distribution (probability distribution describing our beliefs about the uncertainty in the model before data becomes available) taking into account the available information. Generally, Bayesian methods involve the sequential application of the Bayes formula…

In the book “the Signal and the noise”, author Nate Silver talks about prediction from many different angles. Silver explains how prediction is a part of our everyday life and how it affects us. From math to history, inside of a class room or on a court/field, prediction is something we deal with on a day to day basis unconsciously. Silver talks about the benefits of failure and how failure is helpful in the long run with making predictions. Throughout the years we have made progress with…

What is a Theory from Carnap and Popper Rudolf Carnap and Karl Popper both are philosophers whom tried to question what is a theory. Both of these men look at the same question from different perspectives. How can one decide if a theory is scientific or not. Carnap and Popper both came up with different ways to choose which theories are more important when compared to others. It is definitely possible to agree with both Carnap and Popper’s ways of demarcation as a theory can be both verifiable…

It seems widely acknowledged that scientific knowledge is special because it is derived from the facts of experience with application of rigorous scientific methods such as observation, experiment, measurement, statistics, and theorization, to natural phenomenon. Other academic fields like literature and jurisprudence, for example, appear to be merely based on vague and inaccurate methods such as expressing personal experience or opinion, or applying rules written in words arbitrarily…