What is Bayesian Thinking?

It is common knowledge that human beings commit errors in judgment all the time. In areas of uncertainty, most of us go with our gut intuition, and in most cases this intuition turns out to be wrong. Much of this is derived from the fact that humans are poor statistical thinkers, and thus poor Bayesian thinkers. What is Bayesian thinking? Let us start with an illustrative example, called the Monty Hall problem — famously depicted in the Kevin Spacey movie â€Å"21.† There are three doors, and behind each door is either a goat or a car. There will always be two doors with goats and one door with a car. The player first chooses a door without opening, and the game show host whose interests are opposed to the player, proceeds to open a different door. Since the host knows what is behind each door, he always opens a door with a goat. Now that the player is left with the initially chosen door and another closed door, the host offers an opportunity to switch to the other unopened door. Should the player switch? The answer for an intuitive Bayesian, a purely statistical thinker, should be easy. Unfortunately, human beings are not intuitive Bayesians. In fact, most people answer that it doesn't matter if the player switches or not, since the probability of winning a car is 50% between the two doors anyways. They would be wrong. Now, before we examine the correct way to think about this problem, one might ask, so what? Why does it matter if humans are not intuitive Bayesians, or even more broadly, bad statistical thinkers? Simply, Bayesian reasoning corrects some of the issues with bad statistical thinking. Bad statistical thinking leads to bad judgments and decisions, which have a wide variety of consequences in everyday life as well as in arenas such as politics and science. Thus, everyone should become better Bayesian thinkers, because under uncertainty, accurate probabilistic judgments are useful and important.To give a accurate depiction of how Bayesian reasoning works, let us return to the Monty Hall problem, and examine why not only switching doors matters, but that it is beneficial to switch. When the host first opened the door with the goat, something happened: opening the door gave the player extra information, and thus changed the probability of outcomes. By utilizing this extra information, it is no longer a 50% chance for the player to win the car after switching doors, but a ~67% (2/3) chance. Let us suppose that the player picks the door which contains the car. The host opens either the first goat door or the second (it does not matter), and the player switches to the other goat door and loses. Now, suppose the player picks the first goat door instead, which means the host is forced to open the second goat door. Since the only other door contains the car, the player switches and wins. Lastly, suppose the player picks the second goat door. The host is forced to open the first goat door, which again, means the player will win the car after a switch. These are the only three possible scenarios, and so we see that the probability of winning is two out of three if the player switches. Conversely, what if the player doesn't switch? In the first scenario, the player wins the car, but in scenarios two and three, the player obviously loses. Thus, to not switch is to have only a 33% (1/3) chance to win the car.The Monty Hall problem is a rather simple illustration of how Bayesian reasoning works, so in order to gain a more complete understanding, we must explore its principles. In 1763, a paper by Reverend Thomas Bayes was published posthumously called â€Å"An Essay towards solving a Problem in the Doctrine of Chances,† and brought about a paradigmatic shift in statistics: by using ever-increasing information and experience, one can gradually approach the unknown or understand the unknown (of course, his main motive was to prove the existence of God). Fundamentally, Bayesian reasoning believes in the correction of probabilities over time, and that all probabilities are merely estimates of the likelihood of events to occur. Through the further efforts of mathematicians like Lagrange in perfecting the Bayesian framework, we now have a modern and complete theory of probability. First, there are what we call priors, which is the strength of our beliefs, or put it another way, the likelihood that we are to change our beliefs. Then, we have our posteriors, which is the empirical aspect, or the influx of new information. The Bayesian framework then takes these two components and mathematically analyzes how posteriors affect priors. If we know nothing about an event, then all we can do is estimate a probability. However, if there is new information, then the probability must be corrected based on this new information. Over time, as experiences grow through more information, these estimates of probabilities will eventually fit â€Å"reality.† In the Monty Hall case, the moment the the host opened the goat door, that influx of new information, or change in posteriors, immediately influences the player's priors. If the host doesn't open a door, the player merely has a 33% chance to win the car between the three doors, and switching makes no difference. However, since the host removes a door, and specifically the door that contains a goat, these two new posteriors directly influence the original prior from 33% to 66%. One might think that this method of thinking is mysteriously similar to the scientific method, which is certainly true. However, To put it another way, Bayesian thinking is how to use some known information or experience to judge or predict the unknown. For example, event A is â€Å"rainy tomorrow† and event B is â€Å"cloudy tonight†. If you see cloudy tonight, what is the probability of raining tomorrow? If you use the Bayes theorem directly, you only need to know the probability of raining every day, the probability of cloudy nightly, and if one day it rains, then the probability of the cloudy night of the previous night will be substituted into the formula and done. The question is, where do these probabilities come from, and how do we infer the possibility based on the information we have . In fact, most of the valuable problems are backward problems, for example: the stock market, through those few signs can be judged to be a more or less opportunity; the hospital, through which symptoms can determine what is the disease; science Research, through several experimental data, you can construct what theory to explain the model and so on. In general, mathematicians, physicists, etc. are all about backward problems, or they can not predict or judge the outcome with few signs or phenomena, and there is no value (by the way, do not know the reverse Problem-thinking people can not fight in the financial market or the stock market. At present, the most advanced research in the speculative market is almost a process of backward stochastic process and martingale theory. It is known that the incidence of a disease is 0.001, that is, 1 in 1,000 people is sick. There is a reagent that can test whether a patient is sick or not, and its accuracy is 0.99, which means that 99% of the patients may be positive when the patient really gets sick. Its false positive rate is 5%, which means that 5% of the patients may get positive if they do not get sick. There is a positive test result of a patient, what is the probability that he does get sick?We got a staggering result of about 0.019. In other words, even if the test is positive, the probability of getting sick is only increased from 0.1% to 2%. This is the so-called â€Å"false positive†, that is, the positive result is not enough to show that the patient is sick.Why is this? Why is the accuracy of this test up to 99%, but the credibility is less than 2%? The answer is related to its false positive rate. Here we see the power of the Bayesian theorem, that it allows us to deduce the unknown probability from the known probability and the information at hand.The human brain and quantification vs heuristic thinking. The advantage of Bayesian analysis is that it does not require any objective estimation, just guess a priori casually. This is the key, because most of the events that occur in the real world have no objective probability. This is actually very similar to the scientific method: we did not know anything from the beginning, but we are willing to experiment and gradually find out the laws of nature. Bayesian reasoning operates in the same way, through continually the posterior probability in accordance with existing experimental data. Biggest problem with Bayesian reasoning is that human brains cannot quantify information easily. The most commonly raised example is Malcolm Gladwell's â€Å"Outliers†, where many people who are trained enough in certain low-chaotic environments make correct decisions and judgments without using the Bayesian framework at all. Firefighters, for example, do not undergo a Bayesian calculus before deciding whether or not it's safe to pull a child out of a burning building. They just do it because they've done it many times before, and have a rough heuristic estimate on the safety of such an action. Similarly, chess players do not use Bayesian analysis to think many turns ahead; what research has found is that through thousands of hours of practice and becoming familiar and experienced with similar setpieces in the past, gives them an ability to predict moves assuming that the opposing player is also rational. Conversely, high chaotic environments, such as the political sphere, is where Bayesian reasoning thrives due to the high amount of uncertainty.The other criticism are from the frequentists. In general, the probability of teaching in school can be called frequencyism. An event, if performed repeatedly multiple times independently, dividing the number of occurrences by the number of executions yields a frequency. For example, throwing coins, throwing 10000 times, 4976 times positive, the frequency is 0.4976. Then if the implementation of many many, the frequency will tend to a fixed value, is the probability of this time. In fact, to prove it involves the central limit theorem, but it does not start.

Automobile Drivers Essay

Multi tasking has become common thing in today’s busy world. It is common to find somebody a person typing on the personal computer while taking his or her favorite drink and at the same time making a point to his friend on the other end of the line on the cellphone. This trend has been adopted by many in the current busy world. Many have argued that such an act saves time and allows somebody to accomplish so many asks within a given time. To some it has been a successful adventure but to others it has resulted to serious repercussions. Drivers have also been tempted to multitask while on the wheel, this is one of the most dangerous things to do while on the road. Use of cell phones while driving has become so common such that it attracted lawmakers’ attention as it is a disaster waiting to happen in this country. This habit has been equated to drunken driving which has claimed so many lives and left other serious injured through road accidents which have occurred in the recent past. Use of cell phone while driving is such a dangerous habit which puts the life of those driving and their passengers at risk. It is high time that a law was enacted prohibiting this particular practice before it gets out of hand. (Sturnquist, D 2006 29) Drivers who use the cellular phones either on hands free or handheld are as impaired as those who drive under the influence of alcohol. This was according to a research that was carried out by researchers from the University of Utah. The research showed that the use of hands free is just as distracting as the handheld mobile phones. To address this distraction the study recommended for the outlawing the use of cell phones while on the wheel. Use of the cell phone while driving has been known to cause physical and cognitive distraction on the driver, to start with when the phone rings the driver has to look for the phone, this means that his or her attention will be distracted as he picks the phones to answer the call. By the time the drivers mind hit back on the road an accident may have occurred or he might been forced to slow down to concentrate on the phone resulting into a traffic jam. This causes inconveniences to other road users and at the same time threatens the life of the driver as it is hard to concentrate in two involving tasks at the same time. Drivers who text while driving are even at a greater risk as this activity requires full attention than receiving or making a call. They need to look at different keys so that they can write a comprehensive text, in the course of locating these keys their eyes are off the road oftenly. It only takes a few seconds for a driver to make a mistake and through a flash of second an accident will have occurred. If strict laws were enacted prohibiting the use of short text messaging while the driver is on the road the number of accidents that have been occurring due to such a habit will be minimal. Some cities have put these laws in place and the results have been seen. The number of people driving while texting have decreased and so is the accidents. (Sturnquist, D 2006 30) Talking on the phone while driving is equally dangerous as texting, the driver will first be distracted by the ringing tone as the phone alerts him or her. This distraction can come at a time when the driver was at a point where maximum attention was required. This will drift the drivers’ attention from the road to the phone. To reach for the ringing phone or search for it the eyes will be moved from the road to the direction of the phone. The driver will have to remove one hand from the steering wheel and receive the call. As the conversation begins the drivers attention will be further drifted away to get the details. In such a situation he or she may not be in a position to apply brakes in case a pedestrian is closing the road or an approaching car comes by his side. The driver may also get news which might make him or her excited or greatly disturb. This will lead to loss of concentration as the driver tries to come in to terms with the news. He forgets that he was on the road as the mind tries to solve the current issue. At this point the driver is not in full control of the vehicle. Anything that requires an immediate action will make the driver panic and an accident will have occurred. (McDonald, K 2006 31) The use of cellular phones by automobile drivers is as dangerous as driving under the influence of the alcohol or even performing other tasks such as eating, operating a radio. The policy makers should come up with the strict laws which will restrict such a practice as it the only way through which the road carnage will decrease. Though cellular phones are convenient to use as people can communicate promptly regardless of the distance, it should be used cautiously especially for those who are driving as it might lead to serious repercussions. Whether one is sending a short message, making or receiving a call it equally dangerous as all these activities leads to the distraction of the driver. This distraction might cost one life or lead to the inconveniences of other road users. Prohibiting the use of cellular phones for the drivers might not be taken positively by the cellular service providers and the drivers themselves but it might be the only way through which the government can ensure that road accidents have been reduced. Use of phone while driving should be taken as dangerous driving as it risks the life of the drivers and other passengers as well as other road users. If drunken driving has been prohibited other dangerous habits should be outlawed so as the safety of the road users can be guaranteed. Work Cited McDonald, K Shifting Out of Pack, Lawyers and Judges Publishing (2006) Sturnquist, D Mobile Phones and Driving, Nova Publishers (2006)

Becoming an Effective Leader Essay

I have so many ideas of what an effective leader should be that I often feel overwhelmed and cannot imagine how I will become the ideal leader that I want to be. There are many effective leadership styles at my work place. I learn from them everyday. I have also read almost all the modules and sometimes I would read articles on leadership out of the magazines. In my research, I have discovered that there are many different styles of leadership and most are effective, if used in the right situation. What I have taught to myself is how to be flexible. Depends on the situations, e.g. when I started at Weber Mfg, I had to deal with employees who have lost their sense of commitment due to many circumstances. Their self-esteem was low and I strongly felt that my 100% support is very important in building their confidence. I needed to let them know when they did a bad job and very importantly when they also did a good job in order to boost their self-esteem. I do believe if an employee’s confidence and self-esteem is increased, their commitment, productivity and morale will definitely get better. Being a supervisor at WML, I feel that not only, do I have to make sure that jobs are done on time with the quality expected. I must also have a caring, respectful and responsible attitude towards to my team players. I need to have a lots of patience, must be very careful how I would approach in the conflict situations. I believe that â€Å"BALANCE† is the key of success to becoming an effective leader. I am glad; my company has given me an opportunity to take the MLCP courses. It definitely helped me to improve my skills and knowledge on Developing and coaching an effective team. I definitely appreciate the privilege.

Clinical Biochemistry Essay Questions Example | Topics and Well Written Essays - 500 words

Clinical Biochemistry Questions - Essay Example s disease is an autoimmune disorder in which certain antibodies are developed in the body against the thyroid gland which includes thyroid stimulating immunoglobulin (TSI), thyroid growth stimulating immunoglobulin (TGI) and TSH binding inhibitor immunoglobulin (TBII). The TSI antibodies bind to the receptors on the thyroid gland where under normal conditions TSH binds and stimulate the secretion of the thyroid hormone. While bound to the receptor to block the effect of TSH they actually lead to the increased secretion of the thyroid hormone. Because of the increased thyroid hormone low levels of TSH hormone are found in the blood. This results in hyperthyroidism with an enlarged thyroid gland which leads to protrusion of the eyeball, dermopathy and high basal metabolic rates. Hashimotos disease is also an autoimmune disorder which leads to destruction of the thyroid epithelial cells. CD8+ cytotoxic T cells and CD4+ T cells act against the gland leading to destruction of cells. Other antibodies against the thyroid include anti-TSH receptor antibodies, antithyroglobulin and antithyroid peroxidase. These lead to inflammation of the gland followed by wear out of cells. Hypothyroidism is the result which leads to enlargement of the gland. The basal metabolic rate drops and bradycardia, weight gain and somnolence are observed. Levels of the thyroid hormones, TSH, antibodies and basal metabolic rate (BMR) are checked in both the conditions. In graves disease thyroid hormone levels are high, TSH levels are low, BMR is high and antibodies specific for this disease are seen. In hashimotos disease the levels of thyroid hormones are low, TSH levels are high, BMR is low and the antibodies specific for this disease are found in the blood. There are four types of diabetes mellitus. Type 1 is known as insulin dependent diabetes mellitus, type 2 is referred to as non insulin dependent diabetes mellitus, the third type is

Love brief a case Essay Example | Topics and Well Written Essays - 500 words - 2

Love brief a case - Essay Example The duo purchased recording equipment and recorded conversations with officials with a view to proving harassment and spoke of filing a law suit. It was the constant encounters with the authorities that ultimately gave way to a plan to kill certain officials. After Green informed the detective of his suspicions, he agreed to wear recording equipment in conversations with the appellant. Thereafter, Green turned over a recorded conversation he had with the appellant in which the plans were discussed. The threat was deemed serious and the FBI were brought in. Thereafter the appellant and his girlfriend were under surveillance. Identified victims were informed and some relocated out of fear. Subsequent conversations between Green and the appellant were recorded and the appellant and his girlfriend began purchasing equipment and making plans in furtherance of the plan. As the appellant and his girlfriend at a store purchasing the last of the equipment they were arrested. The appellant gav e his consent to a search of his home and shop in which equipment for making a bomb was discovered. Other equipment was discovered at the appellant’s shop. Although the appellant’s Miranda rights were read to him, he waived the right to remain silent and offered various explanations for the equipment found in his possession. Legal Issues: The appellant raised several issues on appeal. The evidential grounds related to a complaint that the was not enough evidence to convict him on the RICO charge. The appellant also argued that prior bad acts were improperly admitted into evidence and that allowing victim impact evidence deprived him of his right to a fair trial. Legal Reasoning: The Supreme Court of Ohio reasoned that victim impact evidence was properly admitted by the trial judge because it demonstrated the seriousness of the offences. The court also reasoned that the appellant’s claim of insufficient evidence on the RICO count was without

Should smoking be outlawed in public areas Essay

Should smoking be outlawed in public areas - Essay Example public places should be outlawed, because it causes passive smoking, where those who are not smoking and perhaps are not smokers end up inhaling the smoke. This passive smoking has various effects; causes cancer, irritation, complications in children, fertility problems among others. Tobacco smoke includes over 4000 chemicals in the form of particles, and in these, approximately 60 substances contained in the tobacco smoke are known to causes of cancer. Lung cancer is the most common form of cancer caused by smoking. It is estimated that passive smokers have a 25% chance of developing lung cancer. Passive smoking causes irritation especially to non-smokers. The irritation may be visible irritation, but cigarette smoke is known to contain substances that cause irritation to the tissues of the respiratory system. There can also be irritation of the eye, causes cough, migraines, dizziness, nausea and other forms of irritation that the different non-smokers may exhibit. Children’s’ immune system is not fully developed, and passive smoking is extremely dangerous on them. Some of its effects on children are; asthmatic attacks, it may affect the mental growth of children. Studies also show that exposing children to passive smoking makes them more vulnerable to bronchitis and pneumonia, and will most likely be admitted in hospital for treatment in their first year of life. Passive smoking also causes fertility problems in women. Women affected by passive smoking have a 68% chance of developing fertility complications than those who have not been exposed. They may experience miscarriages and may find it very difficult to

Two creation story Essay Example | Topics and Well Written Essays - 1000 words

Two creation story - Essay Example ristian creation stories proves that the former deals with the philosophical aspect of life and the latter deals with the practical aspect of life, and the both can help human beings to view life in today’s society from a different but positive angle of view. As pointed out, the creation stories related to Hinduism deals with the philosophical side of life. To be specific, the Hindu idea is interconnected with the belief that human beings belong to pure consciousness. This pure consciousness is beyond creation and is not destroyable. On the other side, the Christian creation story is based upon a single text, named as Holy Bible. To be specific, the creation narrative (say, the Genesis) is the fundamental principle of Christian creation theory. But the Hindu creation story is based on the belief that all living things share the same pure consciousness. Jim Ollhoff stated that, â€Å"In Indian mythology, some gods come to earth in the form of people, animals, or even other gods† (4). If an individual is not ready to go beyond the limits of the material world, that individual will be forced to undergo rebirth. So, individuals must try to break this cyclic process and they can attain the pure consciousness/eternal freedom or ‘M oksa’. In the Bible, the God’s direct role is pointed out as the base of creation of the world as a whole. For instance, the God took around six days to create everything. In the end, the God decided to create human beings as an experiment. David Adams Leeming stated that, â€Å"It contains the creation myth that forms the basis of the Judeo-Christian tradition† (126). This sort of creation myth-based upon six days-is seen among different religious groups. On the other side, the Hindu creation story does not decline the fact that the Earth was created before millions or billions of years ago. Besides, Hindu creation story is based upon the God’s role in creating human beings and other living things. Similarly, Hindu mythology is of