Why parsimonious model

For example, in nonparametric bootstrap one assumes a multinomial model where outcomes correspond to data instances. This multinomial distribution can then be seen as a universal complex model for the data. The particular data set is just the likeliest sample from the model. The multinomial model is not considered to be the final result, it is just a source of uncertainty alike the Bayesian prior. The uncertainty will propagate to various queries about the data such as, is mean greater than zero , and the answers will also be uncertain.

As for making use of complex models, there is an old story told in computer vision about a model that perfectly classified enemy tanks from friendly tanks. It worked perfectly on the data. Later on, they looked more closely and found that it doesn't really classify enemy from friendly tanks, but discriminates the tanks in the open photographed in broad daylight from concealed tanks photographed in the dark.

It was just an artifact of the data that all the friendly tanks were represented by good-quality pictures, and all the enemy tanks as bad-quality pictures. So complex models, yes, as sources of uncertainty to be used when answering understandable queries about the data. Complex models, yes, as proxies for data when building understandable models.

But complex models, no, when offered as a black-box explanation of a phenomenon, even if they get excellent objective performance measure scores. Rubin regarding the recent blog discussion, posted on sci. Herman is known for his "…non-separability of utility from prior" paper from From what I understand, H. Rubin sees any task of modelling a task of maximizing the expected utility. Any modelling task is seen decision-theoretically.

So a good model is what will maximize the expected utility. And as R. Neal would say that the prior is 'true', H. Rubin would say that the utility is explicit and 'true' and the prior is inseparable from utility, so it must be true too. As an example, it's quite forseeable that I would define utility as being inversely proportional to the posterior variance, for example.

Or, one could include model complexity or some other quantification of understandability as a component of utility. We're all doing this implicitly i. Of course, it's very dangerous to blindly maximize utility. One can invent a "pink shades" prior that makes everything more ideal than it really is.

In all, Rubin's view allows greater freedom, while restricting the formal methodology. My pet problem with his approach is that I often like to use the concept of value-at-risk VaR, which is popular in econometrics and finance , which isn't as sensitive to gambler's ruin as expected utility. The proponents of expected utility would respond that nothing prevents you from defining value-at-risk as your utility function, and that risk-averse utility functions are analogous to VaR.

The core question at this point is finding a healthy balance between assumptions and abstractions on one hand, and subjective human judgement on the other hand. First, I don't think that Radford would say that the prior is "true. You can use this for decision analysis if you'd like although I don't think that an explicit decision analysis is always, or even often, necessary. I don't really understand what H. Rubin is saying about the social sciences but perhaps with an example it would be clearer.

Information theory provides a natural link between Bayesian approaches and parsimony, by expressing theories and data in the same language. Minimum Message Length provides an explicitly Bayesian look at explanation vs. The more street space that is dedicated for transit, the lower the cost to users of the transit system.

However, this lower transit cost comes with a trade-off—higher cost for cars. Thus, the issue is one of balancing costs to users of both modes. The trade-off is explored by linking together two parsimonious models: one analytically constructed for transit and one empirically constructed for cars. Consider transit users first. If the transit system has a fixed number of users, N t , and operates with a fixed headway and constant commercial speed, independent of the amount of space provided for transit, then the total costs to transit users is fixed except for the user access cost which depends on the spatial coverage, i.

Now consider the N c car users. For simplicity, we define total costs to these users as the total vehicle delay experienced during our idealized rush-hour period. We assume the optimal control strategy is used to limit vehicle entry into the network. Note that the transit costs 16 increase with N t whereas car costs 17 increase with the square of the number of car users.

This happens because only cars suffer from congestion. Equations 18a and 18b yield space-allocation insights that would be hard to obtain using detailed microscopic tools. So each individual switch saves 0. This model can also be extended to determine an equilibrium distribution of car and transit trips for the city if the demand for each mode can be approximated by a function of their cost, i.

However, investments in car infrastructure are essentially wasted because they attract people who would otherwise ride transit, and as a result cannot reduce total user cost. More sophisticated transit cost functions have been developed and can be used in general cases where bus headways and commercial speeds are not fixed; see Gonzales However, the basic point remains.

Effective parsimonious models developed with aggregated data can be used to develop tentative space-allocation policies without considering which specific streets and lanes will be used by the transit vehicles. These details can be formalized once a policy has been chosen. A final detailed evaluation should confirm what the analyst already knows.

There is a history of using effective parsimonious models to describe large systems in the transportation field, especially in disciplines such as economics, planning, traffic, logistics, and urban transportation. By focusing on aggregate behavior and ignoring fine details, analysts in these disciplines have developed models that are tractable and can be used to answer big picture questions.

Properly formulated, these models can be physically realistic and quite accurate and in some cases, particularly if uncertainty is an issue, even more so than their detailed counterparts. Futhermore, since effective parsimonious models are simple and conceptually insightful, they readily yield optimal designs and policies.

Although they are not a substitute for detailed approaches, effective parsimonious models of large systems complement more detailed analysis methods. More detailed numerical techniques can then be used to refine the preliminary strategies into detailed final plans.

For the future, it should be useful to identify through analytical methods and empirical experiments additional transportation systems whose large-scale behavior is sufficiently reproducible to be captured by effective parsimonious models. Not all systems fall in this category. However, even in this case, we may look for policies that make the system predictable and for parsimonious models of the resulting behavior.

After all, policies of this type are the ones most likely to be desirable. Efforts should also be made to better understand the acuracy of these models. Applications that combine parsimonious models of different types also seem worth exploring.

Efforts should also be made on the numerical front. Detailed numerical tools typically ignore the reproducible system behavior at the aggregate level. Therefore, research into fine-tuning design algorithms that use the information obtained from parsimonious models to obtain detailed implementable solutions is worthwhile. Some fine-tuning tools of this type have been shown to perform well, as was discussed in the review portion of this paper, but these tools do not exist for every application.

In summary, for many high-level planning, design and management problems, effective parsimonious models based on aggregate values provide a fast and accurate method to search across a wide space of possible solutions. Effective parsimonious models of large systems will be one of the tools necessary to address the emerging big picture problems in the transportation field.

The solid gray line in Fig. The curved portions are only an approximation, however, because the NEF model does not describe well situations where the network accumulation changes rapidly. We shall therefore treat the departure curve as if it was linear. The resulting error is not of much consequence when the middle period is long. We imagine that N t includes all transit users for half of the day while N c includes only the car users for the rush-hour period.

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Skip to content Menu. Posted on September 23, November 4, by Zach. There are two reasons for this: 1. Adjusted R 2 : 0. How to Choose a Parsimonious Model There could be an entire course dedicated to the topic of model selection , but essentially choosing a parsimonious model comes down to choosing a model that performs best according to some metric.

Commonly used metrics that evaluate models on their performance on a training dataset and their number of parameters include: 1. LL: Log-likelihood of the model on the training dataset. D: Predictions made by the model. L h : Number of bits required to represent the model. L D h : Number of bits required to represent the predictions from the model on the training data. Published by Zach. View all posts by Zach.