This post discusses how judgments can be quantified to probabilities, and how the degree of beliefs can be structured with respect to the available evidence in decoding uncertainty leading towards Bayesian Thinking. The object of reasoning is to find out, from the consideration of what we already know, something else, which we do not know. Consequently, reasoning is good if it be such as to give a true conclusion from premises, and not otherwise.
This explores the unsung sector of probability : “Nonconglomerability” and its effects on conditional probability. This also emphasizes the idea of how important is the idea countable additivity or extending finite additivity to infinite sets. “I believe that we do not know anything for certain, but everything probably.”~ Christiaan Huygens One week into conditional probability, it’s time to get our hands dirty with the Law of Total Probability and paradoxes which have emerged out of it.
This is a post, centralized on the evolution of Bayesian Thinking and Inverse Inferences, in Probability Theory, which actually changed Statistics from a tool of Data interpretation to Causal Science. “When the facts change, I change my opinion. What do you do, sir?” - John Maynard Keynes In the climax of our last discussion, I kept my discussion about the Jelly-bean example incomplete to begin here afresh. (If you haven’t read that, you can read it before we start, here it is Judgements in a Fitful Realm.
In this post, we will be discussing mainly, Naive Bayes Theorem, and how Laplace, developed the same idea as Bayes, independently and his law of succession go. “I cannot conceal the fact here that in the specific application of these rules, I foresee many things happening which can cause one to badly mistaken if he does not proceed cautiously” - James Bernoulli. While watching a cricket match we often, try to predict what may happen in the next ball, and several time, we guess it correctly, I don’t know much about others, but my predictions very often turns out to be true, even to the extent that, if I say, " may be Next ball will be an out-side edge caught behind by the keeper" and such thing really happens withing next 2 or 3 balls if not the immediate next ball.
This article teaches how to mathematically find the length of an earphone wire by its picture. Let’s explore some truths. A Line is made up of Points. A Curve is made up of Lines. Earphones are as Messy. This article is all about connecting these three truths to a topic in Probability Theory intersection Geometry, which is not so famous among peers, yet its' usefulness has led one to make an app in Google Play Store, which has only one download (by me).