StatQuest: Probability vs Likelihood

stet quest makes me feel so happy so very very very very very very very happy stat quest hello I'm Josh Dahmer and welcome to stat quest today we're gonna be talking about the difference between probability and likelihood these are two closely related concepts that are very easy to get confused even I mix them up from time to time so enough of this jibber-jabber let's get down to it for me the easiest way to understand the difference between probability and likelihood is to just see it in pictures so let's start by looking at probability with respect to a normal distribution keeping in mind that this concept applies to all continuous distributions in this case let's imagine that this is a distribution of Mouse weights it has a mean of 32 grams and a standard deviation of 2.5 on the low end we have 24 grams and on the high end we have 40 grams the probability that we will weigh a randomly selected Mouse between 32 and 34 grams is the area under the curve between 32 and 34 grams in this case the area under the curve equals zero point 2 9 meaning there's a 29% chance a randomly selected Mouse will weigh between 32 and 34 grams mathematically we say this with the following notation the probability of weighing a mouse between 32 and 34 grams given the mean of the distribution is 32 and the standard deviation is 2.5 and all this equals zero point two nine this is the part of the equation we change if we are interested in different Mouse weights for example if we wanted to know the probability of a mouse weighing more than 34 grams we would change the bit on the left side to reflect this the right side which defines the shape and location of the distribution stays the same so when we talk about probabilities we are talking about a distribution that's described by the right side of this equation and the area under the curve that is described on the left side using the same distribution we can change the left side to get a new probability BAM now that we have probability worked out let's talk about likelihood to talk about likelihood you assume that you have already weighed your mouse or mice if you have weighed more than one so here's our mouse it weighs 34 grams the likelihood of weighing a 34 gram Mouse is this point on the curve and that value is 0.12 mathematically we say this with the following notation the likelihood of a distribution with mean equals 32 and the standard deviation equals 2.5 given we weighed a 34 gram Mouse and all that equals 0.12 if we shifted the distribution over so that the mean was 34 grams the new likelihood would be zero point two one so with likelihoods the measurements on the right side are fixed and we modify the shape and location of the distribution with the left side double bam in summary probabilities are the areas under a fixed distribution and mathematically we have the probability of data given a distribution likelihoods are the y-axis values for fixed data points with distributions that can be moved mathematically this is written as the likelihood of a distribution given data if you want to see the actual equations check out the stat quest that derives the maximum likelihood estimator for the exponential distribution hooray we've made it to the end of another exciting stat quest if you like this stat quest and want to see more of them please subscribe and if you want to support stat quest well consider buying one or two of my original songs the link to my Bandcamp page is down below in the comments all right until next time quest arm

Channel: StatQuest with Josh Starmer

Views: 774,189

Rating: 4.8484111 out of 5

Keywords: StatQuest, Joshua Starmer, Probability, Likelihood, Statistics, Maximum Likelihood

Id: pYxNSUDSFH4

Length: 5min 1sec (301 seconds)

Published: Fri Mar 09 2018